Exploring Generative Design and Evolutionary Computation in the Environmental Optimization of Highrise Tower Typologies.
There is no doubt that this piece of work would be unachievable without certain support and contributions offered.
First, I would like to thank my supervisor Richard Coyne for discussing my work with me at length and giving me invaluable feedback. Furthermore, I would like to thank Richard for pointing me in the right direction in terms of the methodology of the paper and even on specific literature.
I would also like to thank Dr. Anton Savov and the Digital Design Unit at TU Darmstadt for providing the educational videos from which this paper’s proposed design system is developed. Consequently, Mili Kyropoulou’s kind acceptance to an interview was crucial in the last part of the paper; Mrs. Kyropoulou provided a lot of methodological and technical advice that was of great value.
I would also like to say a big thank you to my brother for his council throughout the data analysis process. Futhermore, I would like to thank my class-mate Jemima Harrison for helping with formatting and proof-reading my clumsy writing.
[2] [4] [6] [10] [14] [16] [24] [30] [44] [48] [50] [52] [56] [60]
ABSTRACT
INTRODUCTION The Three Workflows
ARCHITECTURAL GENETICS DeLanda’s Triad of Biological Frameworks.
GLOSSARY Terms Used in Evolutionary Computation
USER OPTIONEERING Combinatorial Sketching
A GENETIC DEVELOPEMENT Single Objective Optimisation
A META-HEURSITIC STRIDE Multi Objective Optimisation
CONCLUSION AND THE FUTURE OF GENERATIVE DESIGN BIBLIOGRAPHY
TABLE OF FIGURES
APPENDIX 1: LITERATURE REVIEWS
APPENDIX 2: INTERVIEW
APPENDIX 3: PYTHON CODE
Figure 1 (cover page) : A graphic illustration showing six selected results from the multi-objective optimisation workflow, but also the genomic decoding of that simulation, seen on the left of the graphic. Author’s own work.
This dissertation proposes the use of heuristic techniques, borrowing from theories in population biology to develop workflows for the environmental optimisation of urban tower typologies. Heuristics, the process of resolution by trial-and-error is used twofold: initially, in the use of evolutionary algorithms, being heuristic by nature in mimicking biological processes of elitism, cross-over and mutation. Secondly, in the iterative development of the optimisation methodology, seen in the creation of three distinct workflows, each considered for its benefits and shortcomings, leading to the creation of the next workflow. The improvement of consequent workflows will be observed in both the accuracy of the optimisation methods and their proximity to a true evolutionary process; also, in the accuracy of the architectural tower and its response to a design challenge. Aiming to optimise a tower in a way that reflects a true architectural and environmental challenge, only made possible by continuous efforts to improve the optimisation method by way of converging to a true biological process. The workflows were all developed in a computational design tool called Grasshopper, with specific workflows deploying tools like ‘Galapagos’, ‘Wallacei’ and ‘Ladybug.’ The principal finding of the dissertation is that a high level of optimisation is possible; and that the cruxes of pursuing such methods were found in both the consideration of what to optimise and how to optimise it, and also a deep understanding of biological and computational methods .
Develop generative design workflows for the environmental optimisation of urban towers, specifically in terms of their effect on solar access.
Employ evolutionary computational techniques as the optimisation driver in the generative worklows.
Assess the performance of each workflow, based on the differences improvements made between succeeding approaches and methodologies.
While the emergence of a data-driven approach to design is not new, the implementation of heuristics and evolutionary techniques in early-stage conceptual design is relatively uncharted. This dissertation does not suggest a breakthrough or an industry-changing discovery; however, the explorations made by the author here were found to be novel, at least in a local sense. In this context, Heuristics describes a process of optimising both the tower typologies, the architectural object; but also the method of optimisation itself, the architectural process, the design process. Optimising the tower typologies is heuristic in the same way that the process of evolution is heuristic, an individual tower is only found fit or unfit upon creating and analysing, there is no way to foresee the performance of a tower just by hypothesising. In doing so, the proposed workflows generate many posibilites of towers, optimised by biologically-mimicked processes, afterwhich the designer can browse and chose a desired option.
The endeavour of pursuing a generative design workflow arose from a continuous consideration of relevant literature of architectural computation. The initial inclination was to explore computation as a general tool in design; however, the writings of DeLanda, W. J. Mitchell and Christopher Alexander acted as catalysts in rethinking the computer as an active design agent itself, made possible by the use of evolutionary computation. In addition, the Digital Design Unit at TU Darmstadt produced a series of videos detailing the production of a generative design system in Grasshopper, which provided key resources for the initial stage of investigation.1 The specific system presented by the DDU (Digital Design Unit) was one that also aimed to optimize the design of a tower: more explicitly, a high-rise building aimed to reduce urban environmental disturbance by minimising overshadowing on two neighbouring sites (Fig. 2); also maximising total floor area as a metric to reflect the building’s potential as an economical product. After thoroughly understanding this system, replicating it, and using it to design several towers, it was then feasible to develop it heuristically. The focus of this dissertation will be on the iterative development of the generative system into what could be described as generations of generative design, each with its own contextual benefits and uses. The specific aims of this dissertation are largely quantitative, however, it is important to remain aware of the architectural meaning of the design challenge: optimising urban tower typologies. The metrics that go into the optimisation algorithms of this dissertation are at most four; while being able
1 Digital Design Unit TU Darmstadt, “Generative Design in Grasshopper Part 1, Parametric Model and Analysis,” video, YouTube, June 30, 2020, https://www.youtube.com/watch?v=-HLRtXSG7fQ&ab_channel=DigitalDesignUnit-TUDarmstadt.
deeply optimise the towers based on those four metrics, these workflows can never promise entirely successful architecture (which must make considerations further than performance). Political, cultural, anthropological and materialistic considerations while separate from this study, are equally as decisive in producing appropriate architecture. The uncomputable and the computable must be considered in tandem to design truly successfully in such contexts.
Iterations are not only seen in the individual towers, but also in the very workflows that are used to generate and optimise the towers. The workflows branch into three main categories, which will be reviewed independently. The first iteration is called User Optioneering (UO), an approach anchored in combinatorically generating all, or as many towers as is possible; this optimisation problem is combinatorial as it involves finding all the possible combinations of a finite set of values, that describes a tower typology.2 The towers are then analysed in terms of their overshadowing over two neighbouring sites and their total floor area. Consequently, the towers are sorted based on least total overshadowing, afterwhich the designer can choose from the assortment of variations. This approach may be the most ‘hands-on’ of the four, the designer maintains full control over every step of the process, with truly little work to be done by the computer (apart from sorting the towers based on least overshadowing). Despite this, it is the hardest to implement as it requires a significantly greater amount of front-loading, amounting in a high input, low output process.
The optioneering approach will be advanced with the use of the Genetic Algorithm (GA): bringing a stratum of biological evolution as the vehicle for architectural high-rise optimisation. The GA is a computational technique that pproximates biological variance and evolution; it is heavily dependent on surrounding GA terms, such as genome, phenotype, mutation and cross-over, the biological processes that are applied in a computational setting as variables associated with a design challenge. The combinatorically generated towers of the optioneering approach become a population of parent towers and children towers, with high-performing ones surviving, the notion of elitism; high performance is described by
Figure 2 : User Optioneering, the first workflow presented. Neighbour and Park are the two sites where overshadowing will be minimised. Author’s own work
2 Sean Luke, Essentials of Metaheuristics A Set of Undergraduate Lecture Notes, Second (San Francisco: Editor No Identificat, 2016), https://cs.gmu.edu/~sean/book/metaheuristics/Essentials.pdf 147.
Figure 3 : Single Objective Optimisation (SOO), allthough identical to UO in its’ approach to site, optimisation improvements were apparent. Author’s own work.
the fitness function, a functions that measures performance, or “fitness” relative to the fitness objectives (FOs), the design variables
. This approach requires the plugin ‘Galapagos’: a single-objective-optimization (SOO) tool for Grasshopper. SOO is the crux of this approach as the design challenge of optimizing several metrics as related to the tower is aggregated into one fitness objective. The benefit of this approach is reflected in simplifying a design challenge to quickly produce many results, but this is not without its antithesis: it risks dissolving the architectural challenge into a fitness coefficient, with little ability for nuanced, FO-specific performance.
A heuristic advance is made in the final workflow, both in terms of approach to site, but also method of environmental analysis. The site, an urban block in Manhattan, New York City (see Fig. 4), being an appropriate choice as solar access is greatly restricted due to building density, thus desired in the winter months. The design object also changes from one tower to three towers concurrently optimised, in an attempt to boast the freedom a designer can have in such an approach. Environmental analysis is reconsidered from a set of quasi-random sun vectors to the incident radiation on neighbouring buildings, but also on the towers themselves. Incident radiation being a more accurate metric, due to reflecting both solar access and its associated energy. This workflow follows from interesting discussions with Mili Kyropoulou in an aim to push the project further to fully appreciate the initial workflow capabilities in a more nuanced context. The tools ‘wallacei’3 and ‘ladybug’4 areused as the evolutionary solver and environmental anlysis tools respectively. Furthermore, patterns are unfolded in the morphological makeup of the towers, different patterns that repond best for specific FOs. This is seen as a method of decoding the topological makeup of the towers, or what is later described as the genome.
the last approach could never describe a complete architectural scenario, as human agents affecting both design and inhabitation patterns are not omitted. This produces a design process heavily based on a specific type of performance, a computable one. The non-computable considerations, such as human agents, of a tower are reflected upon, in an attempt to paint a more coherent picture of the architectural landscape.
All three workflow investigations are fundamental in informing ideas. Initial explorations of the UO and SOO offer understanding of certain outcomes and constraints, which then allow for deeper analysis in MOO. In tandem, the workflows can be considered holistically, offering opportunity to scrutinize the potential of pursuing the generative approach. The design metrics outlined in
3 Wallacei, “An Evolutionary Multi-Objective Optimization and Analytic Engine for Grasshopper 3D”, https://www.wallacei.com/ 4 Ladybug Tools, Making Environmental Design Knowledge and Tools Freely Accessible to Every Person, Project and Design Process, https://www.ladybug.tools/index.html#header-slide-show
Figure 4: Multi-Objective Optimisation (MOO) using Wallacei. This method made consideable improvements both in its approach to the site and the towers, but also in the environmental analysis method. Author’s own work.
Figure 5 (opposite): Illustration of the genomes, composed of 24 genes, split into the three sections of the tower, bottom, middle and top. DeLanda’s abtract building. Author’s own work.
Computational techniques often use, or even overuse the terms and methodologies discovered by population biology and genetics. It is imperative to establish a framework of biological thinking before exploring the three workflows, allowing initial understanding of the workflows as part of a simulated biological procedure. What is the architectural significance of evolutionary techniques? Manuel DeLanda is a writer and philosoper who has written a great deal on genetics and their application in architecture. He points out that if genetic techniques are to be used in architecture, three premises should be considered: populational, intensive and topological thinking.5 The ideas are reconsidered from Deleuze, the French philosopher; DeLanda outlines topological thinking with the contrast of biological evolution and the one produced by computational algorithms. Computational techniques seem to exhaust the design space of new possibilities, every new individual is too close to older individuals. Conversely, biological processes show wha DeLanda observes as: “combinatorial productivity,”6 seen in the vast breadth of variation in the natural kingdom. Therefore, it is the goal of this dissertation to apply this idea to the design, or topological definition of the towers ; seen in the increase of the number of possible towers that can be generated in the three succeeding workflows. It is the key aspect needed to communicate with the computer what a tower is. The computer needs a general classification of a tower in order to permutate it into all its combinations. This is a way of describing the general topological and geometric qualities of the tower as a flexible data structure that can be permutated to generate any permuttable instance of the tower. DeLanda uses the metaphor of the body plan, or the abstract vertebrate: a general classification of vertebrates that can be used to extract any exact vertebrate, like a human. Onwards, this will be described as the ‘genome definition’; although the exact definition will vary from the first to the third workflow, the overarching methodology will be shown to be one of binary variation. The topological qualities of the tower will be described as a series of 1s and 0s, 1 being used to denote the existence of mass and 0 being used to denote the absence of mass. Figure 5 illustrates the genome visually; the tower is split in three vertical sections of 9 boxes each. Additionally, the central squares are maintained as 1s to provide a service core. The consequent 3 sets of 8 boxes can be permutated as 1s and 0s represented a string of 24 binary digits. This string is in fact the genome, this is DeLanda’s topological thinking applied to the tower, illustrated in Figure.
DeLanda explains Deleuze’s reconsideration of intensive thinking,
or rather intensive quantities; they cannot be subdivided spatially. This is seen in this dissertation as the density of tower segmenets, or blocks observed in a phenotype of a tower, and produced by the genomic configuration. This density responds to a specific type of design scenario, seen as solar optimisation. The tower’s density, the binary density that produces a unique solution is the intensive quantity; it cannot be spatially subdivided to alter its width or height, instead it is the distribution of density of tower blocks that responds to the environemental analysis, and thus is optimised. Therefore, this directly applies to the evolutionary process of op timising the towers, configuring their genomic makeup produces the intensive quantity of the density in their genes, thus the density in their morphology.
Populational thinking is what DeLanda coins as thinking of the design objects as a population in a species.8 A set of generat ed towers can be seen as a generation, the improvement of the towers in terms of performance between generations results in a population of towers. This population of towers is manifested by the set of all generations of towers, the improvements made between generations represent not only an improvement between towers but also an improvement that propagates throughout the population; this results in the convergence of the population to a set of optimal results.
The outlining of topological, intensive and populational thinking works in tandem with the terminology required to grasp said frameworks. Considering all three types of thinking, topological techniques give rise to the genome, the string of numbers or data structure that represents all the possible towers. Under environmental analysis, a specific genome of a tower, its geometry and the numbers associated with its overshadowing are grouped together to represent a phenotype. The quality, or degree of performance of each genome is summarised in the fitness function, and is measured against overshadowing areas and floor area, each being a Fitness Objective (FO). FO1 could be total overshadowing, FO2 neighbouring overshadowing. Under a populational framework, a select ‘elite’ number of high performing towers are allowed to breed by extracting genes from both the ‘father’ and ‘mother’ genomes, acting as the method of genetic inheritance which will define the genomic data of the two children produced. To reflect a realistic biological procedure, mutation is introduced as randomly selected genes of children are flipped before adding the children to a generation.
1 - 1 - 0 - 1 - 1 - 0 - 0 - 1
5 Manuel DeLanda, “Deleuze and the Use of the Genetic Algorithm in Architecture,” in Designing for a Digital World, ed. Neil Leach (United Kingdom: Wiley-Academy, 2002), 119.
6 Manuel DeLanda, “Deleuze and the Use of the Genetic Algorithm,” 119.
7 Manuel DeLanda, “Deleuze and the Use of the Genetic Algorithm,” 119.
8 Manuel DeLanda, “Deleuze and the Use of the Genetic Algorithm,” 119.
1 - 1 - 0 - 1 - 1 - 0 - 0 - 1 - 0 - 1 - 1 - 1 - 1 - 0 - 1 - 0 - 1 - 1 - 0 - 1 - 1 - 0 - 0 - 1
This foundational explanation identifies key terms and concepts which will be discussed, in an attempt to offer confidence in the topics before further dissecting certain methodologies. The following glossary aims to act as a useful reference throughout the text.
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Figure 6: Tree of life, a data structure representing many body plans at once. Ernst Haeckel, 1866. Pyhlogenetic tree - I. Tree of Life.
1 - 1 - 0 - 1 - 1 - 0 - 0 - 1 - 0 - 1 - 1 - 1 - 1 - 0 - 1 - 0 - 1 - 1 - 0 - 1 - 1 - 0 - 0 - 1
“of or relating to exploratory problem-solving techniques that utilize self-educating techniques (such as the evaluation of feedback) to improve performance,” 1 a problem solving technique explored in its application through the principle of survival of the fittest, or elitism. Seen in this dissertation in the optimisation of the tower typologies. The search and optimisation of the optimal solution is as a result of processes aproximating biological phenomena like natural selection and evolution.
A single slot within a chromosome, or genome, 2 denoting the presence, or lack thereof of a tower block, represented in a 1 or a 0 respectively. Genes can be thought of as the smallest building block of the towers, they are a reference to a unique position within the tower.
The unique sequence of genes, represented as a string of binary values, 1 denoting the presence of a tower block, 0 denoting the abscence of tower block from that position.
The performance and geometrical makeup of the tower that its genome refers to. Put simply, an individual tower geometry and its performance in relation to the fitness objectives, the observable traits of the genome: the tower and its performance 3
A process tha takes two parents, swaps a certain number of genes of each parent with the other parent and usuall produces two children. 4 This is known as ‘sexual’ breeding, it is the principal manner in which towers are generated, but it is also the way in which genetic inheritance of high performing towers is seen in succeeding generations.
Tweaking of the children genomes in specific positions along the genome to approximate biological mutation. Known as ‘asexual’ breeding, this process helps produce variance in the population and usually the chance of mutation on a given genome’s gene is given by 1/l , with being the length of the genome. 5
1 Merriam-Webster Dictionary, “heuristic,” https://www.merriam-webster.com/dictionary/heuristic.
2 Sean Luke, Essentials of Metaheuristics, 31
3 Sean Luke, Essentials of Metaheuristics, 31
4 Sean Luke, Essentials of Metaheuristics, 31
5 Sean Luke, Essentials of Metaheuristics, 31
6 Sean Luke, Essentials of Metaheuristics, 31
7 Antony Radford and Garry Stevens, CADD Made Easy (McGraw-Hill Companies, 1987), 233.
8 Sean Luke, Essentials of Metaheuristics, 133
A design metric that is associated with the design challenge in question. In this dissertation, fitness objectives include: Maximising Tower Winter Incident Radiation, or Maximising Tower Floor Area. Abbreviated by ‘FO’, such as: ‘FO1,’ ‘FO2,’ etc...
A function whose input is the fitness objectives, or design metrics. With outut being a value denoting the overall performance, considering all fitness objectives. It represents the overall performance landscape of the population.
Figure 7 : left:The genomic structure, the overarching tool that allows the generation and analysis of the towers. Author’s own work. right: the processes of cross-over and mutation.Author’s own work.
A generation is one cycle of fitness assesement, population re-assembly, cross-over and mutation. The ensemble of all generations is said to be the population. The genomes that get analysed, crossed-over and mutated each generation as said to be the individuals.6
Ideas borrowed from computer science; Low-level is a completely non-abstract process that is normally difficult for humans to do. High-level processes are abstracted and easily understood by humans. An example of a low-level process would be inputting machine code into a computer to write a paper, or perform any task, a completely meaningless process for a human, however, the computer, by definition, eventually compiles all tasks by means of machine code (a series of 0s and 1s). On the other hand, humans use abstracted means of communicating with computers such as a mouse and keyboard. In this dissertation, a low-level process would be hard-coding the individual tower genomes, wheras a high-level process would be making intuitive design decisions; the goal is to perform as much high-level work as a designer while letting the computer to perform the low-level tasks.7
The set of solutions in a generation that are non-dominated. Put simply, there is no means to increase the performance of one Fitness Objective without equivelant or larger detriment to another FO. “Let’s say you have two candidate buildings, M and N. M is said to Pareto dominate N if M is at least as good as N in all objectives, and superior to N in at least one objective.” 8
Figure 8: Graph showing the performance of towers based on two FOs: maximising volume and maximising winter incident radiation. The pareto front is labelled as the solid line, showing the non-dominanted solution of the last generation. Author’s own work.
Figure 9 : Illustration of fitness function of MOO, a grid of heights, or fitness, of all the individuals in the generations, higher height of the surface denoting a higher fitness, or performance of a solution. Author’s own work.
Figure 10 : The design space of the User Optioneering approach, presenting the designer with a plethora of options, afterwhich the designer can manipulate the PCP, the graph seen on the left to set maximum and minimum values for the different design metrics, i.e., restric the design space to towers with a maximum overshadowing value of 6000 m, or a floor area bigger than 500,000. The user interface is replicated from the DDU’s method. Author’s own work.
In advance of using complex evolutionary algorithms and analysis methods, it is important to highlight the first generative design workflow explored. This workflow’s emergence is twofold: an effort to learn generative design by making rather than observing, but also a way to become familiar with the intricacies of the genome as the body plan. It seems a tricky task, how does one go about generating all tower genomes? Is it efficient to generate them all? These questions are not intuitive and are resolved upon further consideration. The approach outlined below is described as: User Optioneering (UO), this is because it is void of computer optimisation and the user must optioneer (explore the design space and chose solutions based on their performance or other external architetural factors).9 This approach in the first instance aims to devise a way to generate as many tower genomes as possible. Second, measure the tower’s volume but also overshadowing as three metrics: total, neighbour and park overshadowing. Finally, Construct a UI interface where the designer can optioneer. Only after meeting this criteria can the UO workflow be assessed.
Figure 11 : Recreation of the DDU’s tower definition, producing a uniform, monolithic form of sub-towers, or blocks, each having varying heights, seen in https://www.youtube.com/watch?v=-
HLRtXSG7fQ&ab_channel=DigitalDesignUnit-TUDarmstadt . Author’s own work.
middle
bottom
three sections
top middle core tower
Figure 12 : The tower definition of the UO, but also consequent SOO workflows. Seen as a developement of the DDU’s method, it introduces gaps in the section that allow light to penetrate the mass. Author’s own work.
The prior introduction to the genome offered a definition which can now be considered in the context of a specific tower. To begin this task, a square footprint for the tower is used, and a simple grid has been adopted, to disset it into nine blocks. These can then act as the genes that respond to optimisation, with exception of the centre block (which will act as the core, remaining consistent throughout optimisation). The tower definition outlined above is a direct developement from the DDU’s and Savov’s methodology; seen in Fig. 11, their tower is also composed of 9 blocks, each always connected to ground, only their height is varied. This strategy has been developed further by cutting the tower into three vertical sections (bottom, middle, top), which expands the scope of potential optimisation, as there are more genes per tower to consider (see Fig. 12). These sections are introduced as an attempt to allow light to pass through, or inbetween the uniform, vertical blocks of the DDU’s approach. These three sections of 8 possible positions can either be 0 or 1, True or False. This produces a string of 24 bits, the genome. When considering all the possible combinations that can arise from this genome, the answer comes to 224 In order to generate the towers, the four values of Volume (alternative for Floor Area, easier to compute), Total Overshadowing, Neighbour Overshadowing and Park Overshadowing must be calculated for each tower. This would in turn give us 2^24 9 “Optioneering.” Generative Design Primer, https://www.generativedesign.org/02-deeper-dive/02-02_ optioneering
geometries and 4*(224) data points; needless to say, this amount of information cannot be concurrently held and displayed by any modern computer. This is because each geometry has a set of faces, edges and vertices, each requiring information based on its cartesian co-ordinates, plane, direction etc. Furthermore, the complex matrix calculations needed to compute the odd shadow shapes is another obstacle. Within Grasshopper, the maximum number of the towers found to be feasible to generate is approx imately 3,000. This is somewhat disappointing as 3,000 towers is not nearly 1/1000th of a percent of our true genome definition encompassing 224 towers. It is arguable that all genomes could be generated, to then select the initial 3000, or a random set of 3,000 genomes. This would be vastly inaccurate as such a small subset of the genomes is insignificant in terms of its correlation with the total number of genomes. Alternatively, three generations of towers can be produced. Generation one being all the towers containing three 1s per section, or three boxes per section. Generation two, four boxes per section and generation three, five boxes per section. This route eliminates the need for the human to optioneer for floor area as the floor areas would be constant within a generation, leaving the human to only optioneer for shadow area. For example, if a tower within generation 1 (3 boxes per section) is found to have similar overshadowing values to that of a tower in generation 2 (4 boxes per section), the designer can decide to objectively select the 2nd gen tower, as it overshadows marginally more, but vastly increases floor area, or the designer can decide based on specific design priorities, external to the UO workflow. This is helpful in achieving some optimization by excluding the floor area from the sorting of towers made in one generation, instead floor area is optioneered between generations.
4 boxes / section 5 boxes / section 3 boxes / section
Figure 13: Three examples of each generation, each having a different number of boxes per section, a way to control floor area while sorting for total shadow area; effectively reducing the amount of variables the user has to consider while optioneering. However, increasing the amount of optioneering that has to occur, as three generations need to be considered. Author’s own work.
The three generations of towers have these respective floor areas:
Generation 1 : 142,830 m^2
Generation 2: 190,440 m^2
Generation 3: 238,050 m^2
generate the genomes to the end user optioneering with the PCP and design space. Author’s own work.
Figure 15: Top view seen on the top, showing the three types of angle used from west to east componnts. The elevation view seen on the bottom shows the two types of altitudes of angles used. This produces 6 angles to reflect an overshadowing scenario that encompasses many different times of year. Author’s own work.
These values provide clarity to generate the genomes. One set of genomes will be produced for each generation, mainting the set size below 3-4,000, to meet the computational limits of Grasshopper and the laptop that was used. The sets of genomes were generated with a custom script in Python by considering the three sections of the tower (bottom, middle, top). Consider gen 1:
+ each section can only have 3 blocks in 8 possible positions. +therefore, the aim is to permutate the number of 1s in a set of 8 positions.
Consequently, this yields 56 possible sub-genomes, or chromosomes; which, if we permutate gives us (56*56*56 = 175616) possible genomes for the towers in gen 1. These genomes are then sifted so that every 56th genome is chosen, giving 175616/56, or 3136 genomes. This process repeats for gen 2 and gen 3. Python offers a clear edge in performance and ease of use for a purely mathematical operation, such as the above, as compared to Grasshopper. The logic for this algorithm is available to refer to in the Appendix.
ple angles consider varying solar conditions, to create an honest range from which to optimize. Solar analysis considers direct light from both high and low angles, with three directions, from east to west - refer to fig. The six angles, in the format of name: azimuth, altitude are:
1. High West: 112,83
2. High Middle: 126-79
3. High East: 137-77
4. Low West: 122-54
5. Low Middle: 140-42
6. Low East: 137-45
The generation of the tower genomes gives way for the overshadowing analysis to begin. The a-contextual approach (with abstract surroundings of ‘neighbour’ and ‘park’) offers limited scope to effectively optimize for overshadowing, as this does not depict more realistic scenarios in which there would likely be nearby facades in shadow to consider. however, to consider overshadowing, multi-
Assuming that the designer is not able to cross-over and breed thousands of towers by hand, iteratively sorting each generation and hand-picking elite individual tower phenotypes; the design space is described by W. J Mitchell as a data structure where designs are mapped onto, to consequently choose from.10 This data structure is a grid of towers. The UI part of the workflow is directly replicated from the DDU’s videos as it produced a very impressive interface for optioneering and was applicable to this genome definitions and analysis.11 The important parts of the interface are first, the design space: a grid of towers that shows the best n towers (n defined by the designer) sorted by total overshadowing. Second, the PCP or parallel-co-ordinate plot, a graph that maps the overshadowing values on four axes, creating many lines, each line corresponding to a unique tower phenotype.
Figure 16: The User Interface of the UO approach, showing the design space and the PCP. Author’s own work.
10
11
30, 2020, https://www.youtube.com/watch?v=-HLRtXSG7fQ&ab_channel=DigitalDesignUnit-TUDarmstadt.
neighbour overshadowing park overhadowing total overshadowing
Figure 17 : Two graphs showing the only optimization present is in terms of total overshadowing, there is little to extract concerning neighbour and park overshadowing. Author’s own work.
Considering the downfalls of not generating all possible genomes, but also deploying the use of quasi-random sun vectors, the results are respectively more qualitative than quantitative. The benefits being the PCP and the design space, allowing real-time interaction with the system and visualization of desired tower phenotypes. As for the towers themselves, all three generations have been sorted.
For each of the 6 angles, the top performing tower in terms of total overshadowing was chosen. This produced 18 towers. The first graph of Overshadowing/Building (see Fig) deduces that the method of sorting by total overshadowing successfully produced two clusters of values, that correspond to the low and high sun angles, illustrated by the two squares on the graph. However, it is seen in the following graph that an informed decision based on total overshadowing is not apparent, the increase of total overshadowing from the high angles to the low angles is uniform, and so is the increase between generations (3, 4, 5 blocks per section).
As for the neighbour and park overshadowing component, no sorting was performed, thus no variance is seen on those two FOs in the two graphs.
What are the drawbacks, and how could they be resolved? By reflecting upon what was beneficial in this workflow, the parallel co-ordinate plot and vast design space can be considered reliable aids both visually and interactively; specifically, for the designer’s own exploration of the produced tower phenotypes. The genome generation and the optimization of the towers however, were found to be lacking; this way of producing genomes is too rudimentary, simply producing a small fraction of all possible genomes and sorting them. A more competent way to approach this would be to employ a more nuanced version of DeLanda’s population thinking, primarily treating the towers as generations, allowing reproduction and multiplication, resulting in the fittest survivors. Mitchell describes the problem of choosing a design in such an approach, it is not definitive what design to choose, if one is chosen , it is not easy to confirm if the design is appropriate.12
high west
12 William John Mitchell, Computer-Aided Architectural Design (Van Nostrand Reinhold Company Inc., 1977), 46.
high middle
high east
low west
low middle low east
Figure 19 : The 6 results from the second methodology of Single-Objective-Optimisation (SOO), producing higher performing towers than the UO approach, but removing the ability of the user to optioneer effectively. Author’s on work.
Parent 1
Single-Objective-Optimisation (SOO)
Traversing the boundary of interdisciplinary methods, generative systems demand that a stratum of natural morphogenesis is provided to the workflow, specifically achieved by applying populational thinking, employing the Genetic Algorithm (GA)13 to both generate and optomise tower genomes. This is as a result of a cumbersome genome generation and unfavourable level of analysis. Again, the focus is principally on the approach and method itself than the results, it is a way of exploring and learning about generative design tools. With a simillar thinking Achim Menges points out:
“the main objective here lies not solely in the prediction of precise data, but mainly in the recognition of behavioural tendencies and patterns, the instrumental contributions of such tools are significant.”14
The exercise of developing the generative systems becomes as important a task as reflecting on their results, with the anchor of evolutionary computation as the driving optimization agent.
approach. Considering fitness objectives, they are: Total Overshadowing, Neighbour Overshadowing, Park Overshadowing and Volume. Following from that, the Fitness is defined as the multiple of Volume, Park Fitness and Neighbour Fitness. Neighbour and Park fitness are both a ratio of Unshaded Area divided by Shaded Area of their respective site. This produces an aggregate number, representing three of the four fitness objectives; not ideal as we are excluding total shadow area, however, it can be noted that sorting purely by Total Shadow Area, like in User Optioneering, is redundant reveals little about the overshadowing over the two principal sites. It is important to state that the above fitness function is replicated as a methodological approach from the DDU’s videos. 18
Parent 2
+ = Child 1 Child 2 Child 1 mutation
Figure 20: The processes of cross-over and mutation, showcasing the way in which towers’ genetic information is carried over to consequent generations. Author’s own wok.
There is an abundance plugins and algorithmic techniques to employ evolutionary computation within 3D modelling software like Rhino. Due to being somewhat previously sheltered from interacting with evolutionary algorithms; Galapagos (being one of the most user-friendly tools) was consequently used not least for its quick runtimes, a single-objective-optimization (SOO) tool for Grasshopper in Rhino. 15 Galapagos is developed by David Rutten and is one of, if not the first embedded optimisation tool, specifically targetted for Rhino 3D modelling softwre. 16The significance of these plugins lies in their ability to respond to multiple objectives, or their inability to do so, in the case of Galapagos. The issue in this case is that only one objective is optimised, which is somehwat unfavourable, as compared to the succeeding workflow of MOO. It should however be noted that the most technical workflow should not be adopted by default, rather an informed decision should be made to choose the appropriate workflow for the given context.
The problem then becomes how to condense the four fitness objectives (FOs) into one variable that represents them all.
David W. Newton describes this as the ‘aggregate’ method, 17 a method to achieve MOO-like performance but with an SOO
13 Sean Luke, Essentials of Metaheuristics A Set of Undergraduate Lecture Notes, Second (San Francisco: Editor No Identificat, 2016) 36.
14 Achim Menges, “Integral Formation and Materialisation,” in Computational Design Thinking, ed. Achim Menges and Sean Ahlquist (New Jersey: Wiley, 2011), 206.
15 Galapagos, Grasshopper Docs, version 1.0.0007, Dec. 15th, 2019, https://grasshopperdocs. com/addons/galapagos.html.
16 Imdat As and Prithwish Basu, The Routledge Companion to Artificial Intelligence in Architecture (Abington, Oxon New York Routledge, 2021) 96.
17 Imdat As and Prithwish Basu, The Routledge Companion to Artificial Intelligence in Architecture (Abington, Oxon New York Routledge, 2021).281.
When the algorithm is run, the same angles are analysed from the previous UO approach (three high - three low), producing a total of six optimized designs; each requiring 10-15 minutes to be converged by the simulation, the following link leads to the video of the simulation [ click: https://www.youtube.com/ watch?v=nZm3avenq6c&ab_channel=AntonisMavrotas ] . The algorithm starts by generating a randomly permutated set of 50 towers, allowing the most elite towers (in terms of fitness) to reproduce by cross-over. In addition, the user can introduce mutation, should the simulation appear stuck at local maximum performance (see Fig). Mutation is classified as asexual breeding, 19 it does not involve the cross over of two parent genomes; rather, it introduces variance into the population, if like mentioned above, the algorithm seems to get stuck around a local optimum. It is diffuclt to define if this truly is a local optimum, or rather a true global optimum reached, nonetheless it is still unlikely that the algorithm will converge quickly, and so mutation can be efficient. Local and Global optimums are used to denote a locally high performing tower and the highest performing tower possible, respectively.
According to the previous indication of angles, there were 6 responding result towers from the Galapagos simulation. This is a better convergence of the UO approach, choosing is easier as there are 6 distinct choices, see Fig. The particular design scenario
18 Digital Design Unit TU Darmstadt, “Generative Design in Grasshopper Part 1, Parametric Model and Analysis,” video, YouTube, June 30, 2020, https://www.youtube.com/watch?v=-HLRtXSG7fQ&ab_channel=DigitalDesignUnit-TUDarmstadt.
19 Sean Luke, Essentials of Metaheuristics A Set of Undergraduate Lecture Notes, Second (San Francisco: Editor No Identificat, 2016) 31.
Figure 21: The six results produced from Galapagos in the SOO approach. Three for the high angles, three for the low angles. Author’s own work.
Figure 22: A 3D representation of the fitness landscape, each point on it is an individual tower, with the height of the point, thus the colour, denoting performance. A local optimum would at first appear as elite in terms of performane, but once the simulation is finished, doesnt reflect the global optimal. Author’s own work.
chosen as the design challenge could inform the optioneering process. For instance, if either the park or neighbour is to have heavy use in the summer months, later in the day, the tower optimised for High West sun can be used. On the other hand, if the park and neighbour are to be used throughout the day in winter, the low-middle option can be adopted. This is not without disadvantages; what Galapagos boasts in speed and usability, it lacks in data visualization, the PCP and design space as a grid were helpful visual aids for optioneering. It perhaps isnt’t the optimal result that is the most exciting but the ability to chose from a set of results, not restricted to six generated options. However, the premise of Galapagos producing more optimal results hasnt yet been made concrete, how can the 6 results claim to be more efficient? As the UO approach sorted by total shadow, a direct shadow comparison for each sun angle would not be suitable. The only comparison that can be made is one that computes the fitness for the 18 UO towers, afterwhich, said fitness values can be compared with the fitness values of the 6 towers produced via the Galapagos simulation.
fitness, as defined by the forementioned formula.The fact that the HO towers were not sorted to reflect this fitness function, as this function was only defined after the UO approach, means a direct comparison of performance between towers is not entirely appropriate. However, what the graph does reveal, is that the methodology has improved. It has resulted in a smaller number of towers, meaning a more decisive level of optimization, while at the same time producing higher performing towers. One detail that has to be noted is that the tower corresponding to the low-east angle of generation 2 is higher performing than that of the same sun angle of generation 3. This means that a higher performance was achieved with a lower volume of tower, showing insreasing ability to minimise overshadowing. Nevertheless, this is not generally the case; the overarching trend between the generation sets seems to be that with increased volume there is increasing performance; i.e., an increase in volume does not affect the overshadowing components to as big of a degree as it improves the overall fitness.
Figure 23: Fitness (y), Sun Angle (x) graph; the improvement in fitness, thus methodology is apparent in the htched area, showing the different of fitness between the SOO towers, and the highest performing towers of the UO workflow. Author’s own work.
The graph below (see Fig) plots exactly that. The three blue lines highlight the three different generations sets, composed of 3,4 or 5 boxes per section of tower. The red line emphasizes the results produced from Galapagos. The metric plotted on the y-axis is the
Put concisely, this short experiment with Galapagos is a step in the right direction. The architectural conceptualisation of biological thinking has made significant improvements in performance from the brute-force approach of UO. The towers cannot be compared at a specific instance as the UO approach did not consider the Fitness’s mathematical definition; however, it can still be confirmed that reconsidering the generative workflow and improvements in terms of ‘populational’ thinking have benefited the results across the board, reflecting a methodological advance. Despite this, there are drawbacks; as mentioned before, the lack of visualization apart from the animation, which only serves as a purely visual aid have reduced the generative workflow to purely data-centred approach. There is little room for actual optioneering, no design space to be explored is offered by Galapagos, no data visualization tools are available to see trend while the algorithm is running. Was it easy for it to converge? Did it really converge or did it just stop after a set number of generations, unable to trully converge? Not least of all, for either UO or SOO, environmental analysis approach has to be reconsidered, the quasi-randomness of the sun vectors and the analysis of randomly conceived neighbouring sites is methodologically lacking. The goal must then be to bring back data visualization aids like the ones seen in the UO approch, with the help of evolutionary computation, as well as an attempt to reflect on the environmental analysis further, aiming to follow this with a system capable of providing both desired benefits - data visualization and well rounded evolutionary optimisation.
+14.3 % +12.9 % +16.7 % +12.1 % +19.4 % +18.6 %
Figure 24: A comparison of the 6 highest performing UO towers, and the SOO towers (the hatched region in the graph). Author’s own work.
Figure 25 : A result from the last approach, deploying multi-objective-pptimisation. Advances in both optimisation but also visualisation were made in MOO, showing a clear reconfiguration of the system both in its evolutionary optimisation but also in the environmental analysis. Author’s own work.
Figure 26 : The site chosen for MOO, a block in Manhattan, where three current buildings are to be redesigned as the three genomic towers. The ensemble of the towers can be thought as the genomes, each tower’s individual genome becomes a chromosome in this case. Author’s own work.
Evolutionary computation can take many forms, all dependent on two key data structures: the genes and the fitness functions. Genes are what produce the geometric variance within each phenotype (observable, unique trait of tower). On the other hand, the fitness function is a process of ranking the collections of genes: the genomes, based on how they respond to said function. In either of the three approaches, the goal remains to achieve a high enough variance in our population of towers, allowing optioneering but also effective cross-over and breeding without redundancies. Furthermore, the fitness function and the algorithmic nuances chosen should be adequate to allow convergence to a single solution, or a set of solutions. If we examine the UO and SOO methodologies, there are benefits; UO provides a level of data visualization with the PCP and the design space that SOO doesn’t, while SOO involves a true version of DeLanda’s populational thinking, letting towers evolve from generation to generation with changes to a single tower phenotype propagating and affecting the whole population. Not least, both workflows lack in their environmental analysis accuracy. Convergence is considered as the development and arrival towards the last workflow; converging to a best solution should be the goal, employing an advanced version of populational thinking by using advanced evolutionary algorithms. In doing so, this goal also aims to abandon rudimentary environmental analysis methods for ones that respond to the sun’s role as an energy source.By taking the design challenge out of solution from the diluted SOO aggregate method of combining many fitness aims into one; all while reformulating the environmental analysis methodology. The above will be considered via the following: 1) Site strategy, 2) Genome definition, 3) Environmental analysis, 4) the use of an MOOA (Multi-Objective-Optimisation Algorithm).
as it considers the incident angle of the sun at a particular time, therefore produces an energetically accurate description of the design challenge. In context, this approach aims to increase the average solar energy received in winter by both the optimised tower and its milieu, while simultaneously ensuring the opposite for summer. This is a much more accurate description of the solar effect on buildings: for one, it considers the energy input of the sun, the metric responsible for varying thermal comfort; secondly, it considers the summer months as well, a more nuanced manner of considering the sun’s effect within a whole calendar year. The neighbours have been chosen strategically as the buildings that would be affected the most by a change in the tower geometry. The above was made possible with the help of the plugin ‘Ladybug’, an environmental analysis tool. A decision was made to consider design ranges rather than days or times, taking a broad chronological spectrum as the analysis range reflects a more broad overshadowing scenario. The specific ranges are as follows: Winter Range (1st Dec. -> 28th Feb. 12-15pm), Summer Range (1st Jun. -> 31 Aug. 1215pm). It should now be clear that the environmental analysis has made great leaps of improvement; encouraged by an informative discussion seeking such next steps with Mili Kyropoulou (see Appendix 1), architect and researcher at the University of Houston who wrote a very interesting paper on designing for maximum overshadowing in Houston. 20 The next step is to look at the Wallacei tool and how it compares a an MOO wokflow to the previous UO and SOO.
design high
average monghtly dry-bulb temperature design low
Figure 27 : Dry-Bulb temperature graph for New York city, with the two ranges chosen hatched, note that the winter range includes december. Author’s own work, data acquired from Climate Consultant analysis softwre.
he first step must be adjusting the existing site strategy; this is done before considering the idiosyncrasies of Wallacei as a tool, because it is first the design challenge that informs the method of analysis and not vice versa. The site strategy chosen is an urban block in Manhattan, where three buildings are to be redesigned in terms of four fitness objectives: 1) Maximising Volume, 2) Maximising Neighbour Winter IR, 3) Maximising Towers Winter IR, 4) Minimising Tower Summer IR. IR refers to Incident Radiation, a metric more accurate than shadow areas
A multi-objective-optimization (MOO) approach improves the optioneering process by allowing a plethora of options, arising from the algorithmic nuances of perfecting multiple objectives at once.21 Furthermore, the designer’s understanding of genomic variance is heightened as the interrelations of the fitness objectives and the genome structure are defined. The MOO tool employed here is ‘Wallacei,’22 an evolutionary solver based on the NSGA-II algorithm (Deb. Et al. 2002),23 its inner workings are not important, it works on the concept of elitism and preserving diversity among generation.
20 Mili Kyropoulou, ‘Shading Design For Outdoor Learning in Warm And Hot Climates Using Evolutionary Computation: A Case Study In Houston Tx.’, 2022 Annual Modeling and Simulation Conference (ANNSIM), San Diego, CA, USA, IEEE, pp. 682–693, DOI: 10.23919/ANNSIM55834.2022.9859518.
21 Imdat As and Prithwish Basu, The Routledge Companion to Artificial Intelligence in Architecture (Abington, Oxon New York Routledge, 2021, 95.
22 Wallacei, “An Evolutionary Multi-Objective Optimization and Analytic Engine for Grasshopper 3D”, https://www.wallacei.com/ 23 K. Deb et al., “A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II,” IEEE Transactions on Evolutionary Computation 6, no. 2 (April 2002): 182–97, https://doi. org/10.1109/4235.996017.
Figure 28 : The Wallacei interface, one can optioneer by choosing different individual tower phenotypes, seeing how they perform among the rest of the population. Author’s own work.
Figure 29 : The three towers seen in blue, with the white boxes being the excluded genes from the definition, chosen as always being in a value of 1, or full, they make no difference to overshadowing criteria as they are directly adjacent to buildings to their south.Author’s own work.
Wallacei’s, and by inference the NSGA-II benefits are the ability to optimize the towers for multiple objectives; in other words, optimising both for each objective separately but also for all objectives at the same time. Furthermore, Wallacei provides interactive data visualisation methods that other MOO tools don’t. Wallacei’s key features that were found helpful was the analysis tab, allowing optioneering of all types: from picking based on only one objective to K-means clustering, a machine learning algorithm to cluster solutions with similar fitness values. Additionally, the diamond chart is an illustrative tool, communicating the performance of an individual in terms of all chosen objectives. Wallacei needs two key data streams to work: 1) genomes, 2) fitness objectives. The latter has been explained in detail in the previous section, where the four fitness objectives are outlines.
stagnant sections (see Fig 29) were excluded from the genome
Figure 30: Mean Trend Value graphs for the four FOs, showing a trend of convergence across all FOs, with however, not a complete convergence as a plateau is not reached. Author’s own work.
Genomes are then the crux of the workflow. Reconfiguring the genome definition will be explained with the above illustration (see Fig 29), showing areas of the tower excluded from permutation, as they offer little to no effect on solar access; this is highlighting the flexibility of the genome definition as a universal scheme of codifying buildings, while also considering the contextual particularities of the Manhattan site as drivers in the genome detailing. The conceptualisation of the building as a number seen in UO is crucial, DeLanda’s abstract building is reconsiderd; in doing so, reflecting on the binary permutation as a viable precedence. The genomes defined in MOO are still binary string, however, instead of having three vertical sections, this increses to 7, increasing the number of genes, therefore variance, while maintaining the footprint of 9 squares per section (as not to increase the number of genes too much, slowing runtime). Considering the combinatorical framework created here, this produces 3 towers, with each having 63 genes; leading to a design space of 2(63*3) possible design options. This is a broad design space, something favourable for the MOO approach, the goal is not to be conservative like UO and SOO; rather, it is to move away from the modest 24-box genomes to a higher level of genomic refinement. The increased number of genes per buildings, coupled with the increased number of buildings ensures diversity in the simulation, and leads to more interesting results, something suggested by Mrs Kyropoulou (see Appendix 1). Further refinements were made, as mentioned above these refinements concern removing tower blocks from the genomes, the one that do not affect solar access (see Fig). These
definition to reduce the number of total genes permuttable, in an effort to further reduce runtime. Following from the above, the genome is composed of three chromsome, one for each tower. The chromosomes are themselves made of genes, 47 for tower 0, 51 for tower 1 and 45 for tower 2 (all reduced from 63). The genome is a string of binary digits, composed of three parts, or chromosomes, each chromosome being the individual set of binary digits of each tower; each tower is a chromosome within the triad of towers, the genome. When extrapolated to an urban scale, the role of the chromosome is clarified, as the number of genes and genomes moves to a larger number, the architectural scenario reflects a more realistic biological simulation. A city of 46 towers would have 46 chromosomes, just as many as a human has, with the human’s DNA being a reflection of the genome of 46 chromosomes of towers. This is purely metaphorical in terms of biological thinking; we can never assume that any design system is as detailed or nuanced as true biological evolution.
Following from the above, the next step is to configure the simulation before running it; a step that was not crucial before, now becomes important as the number of variables, genes and objectives reaches a number calling for further refinement. The principal reason for this refinement is to reduce runtime. For example, the default settings of 100 generations with 50 individuals per generation would yield a runtime of 130 hours. Therefore, the number of generations was switched to 50, with 20 individuals per generation. This reduced the estimated runtime down to 13 hours, a more manageable timescale, the following link leads to a video of the simulation [ click: https://www.youtube.com/watch?v=xV-UvNyHBnk&ab_channel=AntonisMavrotas]. Conversely, the number of generations and individuals could not be reduced to 1 gen, 1 ind., there would be no heuristic optimisation present, only seen as an effect through generations. Likewise, the reconfiguration reduced the population size from 5,000 individuals down to 1,000 individuals; running the risk of not converging properly. This will be tested from the graphs that Wallacei provides (Fig. 30 and 31). Namely, the Mean Value trendlines (MVT) and Standard Deviation (SD) graph are helpful in showing presenting variance and convergence: if the MVTs show a plateau in the later generations, it means that fitness across generations remain constant, thus the simulation has converged. The MVTs in this case show partial convergence,
Figure 31: The Standard Deviation graphs of all the generations. Convergence is seen in the red curve, variance is seen in the bluer curves. Author’s own work.
Figure 32: Gen 46, Ind. 0: solution best at maximsing Towers Volume. Author’s own work.
Figure 33: Gen 45, Ind. 3. Solution best as maximising Tower IR in the winter months. Author’s own work.
seen in the gradient of the graphs, however not a complete plateau (see Fig 30). Moreover, the SD graphs (Fig 31) show whether early generations are varied enough, with a wide and short bell curve, converging to a taller and thinner bell curve. The simulation was run, taking 13 hours. The SD graphs show increasing convergence in later generations, seen in the tall, thin red curves, also earlier generations had enough variance, seen in the flat, wide bell curves. The MVTs do confirm that the simulation reached a level of convergence, with the mean values of Volume, Tower Winter IR and Neighbour Winter IR increasing across the board. Furthermore, the Tower Summer IR has decreased accordingly, a favourable outcome. However, the trendline never plateaued, hinting at the simulation not fully converging. It could be that the simulation could converge in the 51st generation, if it was allowed, but this cannot be confirmed. The SD graphs illustrate that there was indeed sufficient convergence in earlier generations, seen by the flat blue curves; with later generations seen in red becoming taller and thinner, exemplifying reducing variance and increase performance. Decisively, the simulation can be deemed successful; a certain level of performance is in effect, with sufficient variance in early generations. Full convergence might not have been achieved but there was the need for a trade-off of runtime and convergence, with 13 hours being the threshold.
Collecting results can be seen as a method of optioneering, facilitated by Wallacei’s comprehensive user interface. There are several methods available in order to optioneer, three of which will be illustrated. These three are: 1) the best individuals for each FO, 2) The best individuals overall, 3) the Pareto Front solutions, crusted by K-means machine learning algorithm. The first method entails merely choosing the best performing individual for each FO. These individuals are:
diamond chart seen is a visual aid for illustrating the individual’s performance in terms of the four FOs. These four results are the easiest to intuitively understand as a designer. The solution representing the highest volume is visibly the one that is bulkier, the best for Tower Winter IR has largely south facing facades across the towers, maximising surface available for solar gain. Conversely, the one best for minimising summer IR has the least amount of surface are exposed on the roof, seen as it is the one with the least amount of red on the roof (red denoting IR values of over 200 kWh/m2). These are useful in demonstrating simulation worked as intended; furthermore, it is possible to optioneer to a greater extent, the possibilities of the MOO open the design space to degree that SOO didn’t.
The second approach to optioneering is seen in the best overall solutions, these two solutions are:
1) Lowest Relative Difference, the individual with the most uniformity across FOs;
2) Average of Fitness Ranks, the solutions with the average fitness rank of the entire population.
There is no inherent benefit in choosing one over the other, instead the decision is contextual. While the Lowest Relative Difference solution is generally more consistent, the average of fitness ranks outperforms the former in Volume, but also Neighbour Winter IR. Both solutions represent adequate trade-offs between all the FOs and either can be chosen. The absolute differences between the highest ranked individual in one FO and those two solutions is marginal, however, the lack of complete convergence can be attributed as the deciding factor.
Figure 36: Gen 10, Ind. 15. Solution with the lowest relative difference between FOs. Author’s own work.
Figure 34: Gen 41, Ind. 3. Solution best for maximising Neighbour’s IR durin the winter months. Author’s own work.
1)FO1 (Maximise Volume): Gen: 46, Individual (Ind): 0 (FIg. 32),
2)FO2 (Maximise Tower Winter IR): Gen:45, Ind: 3, 3)FO3 (Maximise Neighbour Winter IR): Gen: 41, Ind: 3,
4)FO4 (Minimise Tower Summer IR): Gen: 41, Ind: 5.
Figures 32-35 show the solutions mentioned above, the towers on the left are simply the same towers, but with the summer IR analysis period displayed as the thermal map. The three pie charts are to indicate the volume of the three towers as a fraction of the total volume possible (if the genome was a string of just 1s). The
The third conclusive approach to optioneering is the Pareto Front, along with K-means clustering. A pareto-dominant solution is labelled as such if it is not dominated by any other solution, when there can be no improvement to one of the FOs, without another FO’s deterioration. Again, considering the partial convergence of this workflow, the pareto front in this case is only locally optimal, if more generations were allowed to be produced, the set of pareto-dominant solutions would change accordingly. K-means clustering is a method of supervised machine learning that clusters solutions relative to their closeness to a cluster. This is an effort to classify the genome, effectively grouping similar solutions out of an already dominant set of solutions, allowing for the discovery of differently performative individuals. The use of machine
Figure 37: Gen 24, Ind. 11. Solution with the average of Fitness Ranks. Author’s own work.
Figure 35: Gen 41, Ind. 5.Solution best for minimising Tower’s IR uring the summer. Author’s own work.
1
learning is not to be confused with the generative workflow, its use here is simply limited to clustering the pareto front; it is not involved in any part of the simulation itself. K-means clustering is a tool directly available from the Wallacei interface and requires no further implementation. The 20 solution have been gathered into 3 clusters, this is a decision made by trial and error, if too many clusters are chosen then the clusters are not so easy to distinguish from one another; conversely, if too few clusters are chosen, the clusters are too broad and sub-clusters can be easily seen within them. The three clusters are seen in Fig 38, showing the objective space. The objective space is a three-dimensional graph that maps each solution as a coordinate of its performance on the three FOs.
for the summer.
Figure 38: The three clusters of the pareto-dominant solutions. Author’s own work.
Cluster 1
This excludes the fourth FO: minimising tower summer IR, which is shown as a gradient of red to green. The three clusters are:
cluster 1) Pareto-Front (PF) solutions with high performance in Tower Winter IR (see Fig 39) cluster 2) PF solutions with high performance in Maximising Neighbour Winter IR, cluster 3) PF solution withhigh performance in Maximising Tower Volume.
Figure 39: The towers of the first cluster, demonstrating higher performance in Tower Winter IR. Author’s own work.
Cluster 2
The smaller boxes seen in Fig 38 illustrate the whole objective space, all the solutions of the simulation ranked in the three-dimensional plot. Having four FOs and only three axes, FO4 (minimise Tower Summer IR) is illustrated as most fit (green) and least fit (red). In doing so, the emergence of the reddest (least fit for summer IR) solutions near the highest performing Tower Winter IR solutions illustrate the difficulty of the algorithm to optimise both at the same time. This is a phenomenon that comes without surprise; the two objectives are conflicting, not meaning that optimization for summer is not concurrently possible with optimization for winter; rather, that the optimisation for both seasons produces conflicting results: the best perfoming towers for the winter are not as suitable
The optioneering method of choosing from either of the options mentioned above has been shown to be a useful aid of design. However, this workflow can be pushed further by looking at patterns within clusters, FO-specific patterns. Just like an evolving population of biological organisms, the simulation shows convergence of the towers to specific high-performing versions that are not dominated by any other individuals; these are shown to be the pareto front. Considering the difference in genomes from the first generations to the last (where the pareto front is), then it is expected to detect patterns in genomic sequences. This is because certain genes that are high performing have a higher chance of being passed down multiple generations. This is illustrated in Figure 42, where each column is a genome, traversing horizontally in time, or in increasing generations; the forementioned patterns are easily seen here. What looks like noise at generation 0, evolves towards visualised patterns in generation 49. Decoding this pattern means identifying the gene positions that converge. While this is useful in decoding the genome, it is not informative in how those genes perform relative to specific FOs; instead, it is the aim uncover which genes converge to either a 1 or a 0, but also why they converge: what specific FO does a convergent gene correspond to? Performing this kind of analysis for the whole simulation is laborious, but also redundant as earlier generations are not of interest, patterns are not as apparent, and there is risk of concluding with data that is messy. Instead, the pareto front solution must be considered in isolation, it provides the set of solutions that are the highest performing in the whole population, if patterns are considered as meaningful, it is in the pareto front. In doing, so the K-means clustering uncovers the phenomenon of FO-specific patterns. Seen in Figure 43, the three clusters can be easily ob-
tower 2
Figure 40: The towers of cluster 2, demonstrating higher performance in maximising Volume. Author’s own work.
Cluster 3
Generations
Genomes
6th
Figure 41: The towers of cluster 3, showing higher performance in Neighbour Winter IR. Author’s own work.
6th
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5th 6th
4th 5th
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3rd 4th
2nd 3rd
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ground 1st
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Figure 43: The genomic makeup of the three clusters, patterns within the chromosomes can be detected. Author’s own work.
Figure 42: The genomes of all the generations, three colours showing the chromosomes, the different towers. Within them the two contrasting colours are 0s and 1s. Author’s own work.
Figure 44: Dominant genes of cluster 1. White shows the genes that converge to a 1, red shows the ones that converge to a 0, the absence of blocks denotes that the genes at this position did not converge. Author’s own work.
Figure 45: Dominant genes of cluster 2. White shows the genes that converge to a 1, red shows the ones that converge to a 0, the absence of blocks denotes that the genes at this position did not converge. Author’s own work.
Figure 46: Dominant genes of cluster 3. White shows the genes that converge to a 1, red shows the ones that converge to a 0, the absence of blocks denotes that the genes at this position did not converge. Author’s own work.
Figure 47: Gen. 45, Ind. 3 - Towers best at maximising Tower Winter IR. Author’s own work.
Figure 48: Gen 46 - Ind. 0 - Towers best at maximising volume. Author’s own work.
Figure 49: Gen 41 - Ind. 3 - Towers best at maximising Neighbour Winter IR. Author’s own work.
Conclusively, the last approach has revealed great patterns in the genomic makeup of the towers, but also advances in both optimisation and environmental analysis. The results gathered here are exceedingly more useful than the ones in UO or SOO, they represent a truer definition of the solar scenario of overshadowing. A greater breadth and depth of optimisation was provided by Wallacei, providing many techniques for choosing towers, individual FOs, best trade-offs and the pareto front with the schema of dominant genes. Furthermore, an advance in the environmental consideration of the design challenge proved to improve the workflow in its accuracy to a real-world scenario. The genomic configuration, and subsequently the towers produced are in stark contrast with those of the UO and SOO approaches; the refined genomes show a strategic subtraction of tower blocks from the genome to reflect redundant areas of the tower, redundant in terms of their effect on overshadowing. Furthermore, the consideration of the simulation as a set of converging genomes unfolds emerging patterns in dominant genes. Certain genes are seen to converge in either a 1 or a 0, or not converge at all, providing a true definition of DeLanda’s abstract building. The topological relations of the different genes are not only refined spatially (more blocks per tower, compared to UO and SOO); but also show topological relations of blocks corresponding to dominant genes, for instance the halo-like shape of the towers in cluster 1. Convincingly, the MOO approach is qualitatively superior to the two former workflows, quantitative comparisons are obsolete as the data is vastly different in its type but also the method that gave rise to it. Computationally speaking, UO is much more difficult to implement if one is not familiar with Python; allthough, MOO requires a more careful consideration of the architectural challenge. The design process comes closer to a tangible outcome, three towers in New York City, as opposed to a randomly generated site.
The closing statement of this dissertation will start with the contrast of the three workflows; what has been achieved. The three workflows have clear links and were directly succeeded from each owns predecessor, to develop and advance. User Optioneering is an approach that allows for the most amount of low-level refinement; low-level work is seen in the explicit definition and coding of every single genome instance as a list of values input into Grasshopper. Coding the three sets of genomes is a low-level task, architecturally speaking; it removes the designer from making meaningful design decisions, forcing them to spend time developing algorithms which are not needed in the first place, and can be more efficiently and accurately executed by Galapagos or Wallacei. However, the UO approach proved useful in the visualisation aids of the PCP and the design space, allowing a fruitful optioneering workflow. On the other hand, the Single-Objective-Optimisation (SOO) workflow dictates more low-level tasks to the computer, an advantage. Genomes are no longer brute-forced by the designer, they are automatically generated and made to follow biological processes of evolution, such that they produce a population of evolving towers. The designer can then make informed architectural decisions, a high-level task, while the computer performs the combinatorically laborious task of evolutionary computation. Multi-objective optimisation (MOO) is the final advance, a refined level of evolutionary computation is seen in the use of Wallacei, low-level tasks are not only prescribed to the computer, but they are made more combinatorically robust, further approximating a true biological simulation. The advance in evolutionary optimisation is in tandem with the improvement of contextual consideration, the abstract, methodologically lacking approach of UO and SOO. The two random sites of neighbour and park become the real urban fabric in Manhattan. Furthermore, the tower is refined, genomically speaking, to introduce more genes per genomes but also more chromosomes per genome, i.e., three towers. The three towers’ ensemble is a genome, each tower is a chromosome; more variance is seen. The environmental methodology is also improved by opting for the use of Incident Radiation as a solar objective, a more energetically accurate variable than overshadowing areas. Furthermore, the analysis period is lengthened to summer and winter periods, reflecting a wholistic solar scenario. This is a true reflection into DeLanda’s triad, populational thinking is improved by means of increasing genomic variance, more blocks per towers and more towers; coupled with the increased optimisation performance of a MOO tool like Wallacei, the variance, thus convergence, thus optimisation seen goes one step closer to a biological process. Furthermore, topological considerations are made, excluding areas
of the tower from the genome, in an attempt to reduce runtime by not accounting for areas of the tower that do not affect solar access on neighbouring buildings. Put simply, the three workflows show significant improvement in increasingly approximating biological productivity, by means of evolutionary computation. This, coupled with the environmental methodology advances produced high performing towers in the MOO workflow. However, it is not to be seen as de facto superior to the other workflows. Decisively, advances in the workflow were reflected in the increasing accuracy and performance of the respective results.
The aim is to develop Generative design further, the place to start is perhaps where MOO concluded, the genomic decoding. The idea behind decoding the genomic makeup of the population of towers is to extract patterns from data, patterns that speak to the overarching topological and intensive qualities of the design challenge. These are patterns that can unfold morphological structures that are FO-specific and respond best to certain conditions. Considering that patterns of the computable (genomes, performance, etc..) are discoverable, the question becomes: how does one detect patterns more effectively, perhaps of the uncomputable? What is the uncomputable? Uncomputable qualities can be seen as highest-level quantities, very difficult to communicate to a computer. These quantities are aspects of design that aim to bring communities together rather than divide them, they aim to culturally and socially improve on the city in which they are built in, they aim to be an active social tool in the improvement of the city, the polis. The means with which to do this could be revealed by recent advancements in artificial intelligence, a cath-phare in today’s technology age and foreshadowed by the tech-orientated approach of this dissertation. However, it is not entirely clear that AI is not capable of conceiving abstract, human, emotional or anthropological concepts. Given enough relevant data and a good training model, modern AI can do a lot more than captions on YouTube videos. The overarching conundrum is whether a computer can think of the uncomputable, at least in an architectural sense. ChatGPT is a new tool developed by OpenAI, an online resource built for the mass-use of AI tools. It is a language model, optimised for dialogue, and when asked by the author: “write a poem on the environmental and social, political and anthropological optimisation of urban architecture.” The response is more intriguing:...
“
The cityscape stretches far and wide, With towering buildings reaching for the sky.
It’s a bustling hub of human activity, A melting pot of diversity.
But as we look upon this urban scene, We must ask ourselves, what does it mean?
For the environment and for society, Are we optimizing our urban architecture wisely?
We must consider the impact on the earth, And the ways in which our buildings give birth To emissions and waste, to pollution and strain, On the natural world that we must sustain.
Figure 50: Image generated by Midjourney, an AI image generation system. This was produced given the prompt from the poem above: “We must think about the social implications, Of the spaces we create and the communities we form. Are we fostering connection and inclusivity, Or perpetuating inequality and division?”
We must think about the social implications, Of the spaces we create and the communities we form. Are we fostering connection and inclusivity, Or perpetuating inequality and division?
experienced developer cannot understand how the model works. it is a tradeoff of transparency in favor of end-user convenience.”
Just like ChatGPT, AI models are black-box, the poem, just like an ‘intelligent’ design approach offer little to no trnsparency, the user is not able to explicitly control the results, they are generated by the statistical and stochastic methods used to unravel and unfold millions of data points into a poem, or the design of a chair; or indeed a tower. If powerful models are found, ones that are able to encapsulate human nature and cultural drivers in design, the crux is to make those model intuitive, to allow the high-level understanding, facilitated by human perception while also deploying advanced intelligent models. It is a dichotomy of human and machine that will no doubt, play a decisive role in future design efforts. Gone could be the days where AI is asked to write a poem, and instead asked to design a tower.
Figure 51: image generated by Midjourney, an AI image generation system. This was produced given the prompt: “Urban Tower Optimisation”
And what of the political implications, Of the choices we make and the policies we implement? Are we promoting justice and democracy, Or enabling corruption and oppression?
As we plan and build our cities anew, Let us strive for environmental and social, Political and anthropological optimization, For a better future and a brighter urbanization.”24
It is the realisation that this poem, even the very fact that a computer can generate a poem is a phenomenon hinting at the machine’s ability to replicate, or partially understand human emotion. Thus, the computer might be able to detect the patterns in genomes that correspond to societal change, transforming the architectural object to a social one. A romantic idea to say the least; AI has been explored in architectural optimisation, but for much more specific workflows than that simply stated in the poem prompt. Bidgoli and Veloso developed Deepcloud, a Machine Learning generative design tool for the design of different kinds of products, who speak on the contrast of parametric and intelligent design models: “Compared with the parametric modeling workflow [like the ones in this dissertation] this one does not require highly-trained users in all parts of its lifecycle. However, it is black box, so even a keen and
24“ChatGPT: Optimizing Language Models for Dialogue,” OpenAI, November 30, 2022, https:// openai.com/blog/chatgpt/.
Alexander, Christopher. Notes on the Synthesis of Form. Cambridge, Mass.: Harvard Univ. Press, 2002.
Anderson, Stanford “Problem-Solving and Problem-Worrying,” (A.A, London, 1966). http://web.mit.edu/soa/www/downloads/1963-69/TH_AALond-Lect_66.pdf
Bidgoli, Ardavan, and Pedro Veloso. ‘DeepCloud. The Application of a Data-Driven, Generative Model in Design.’ CoRR abs/1904.01083 (2019), 10, http://arxiv.org/abs/1904.0108
Bidgoli, Ardavan, and Pedro Veloso. ‘DeepCloud. The Application of a Data-Driven, Generative Model in Design’. CoRR abs/1904.01083 (2019). http://arxiv.org/abs/1904.01083.
Ceccato, Christiano. “The Architect as Toolmaker: Computer-Based Generative Design Tools and Methods.” CAADRIA proceedings, 1999.
DeLanda, Manuel. “Deleuze and the Use of the Genetic Algorithm in Architecture.” in Designing for a Digital World, ed. Neil Leach (United Kingdom: Wiley-Academy, 2002), 117-122.
Galapagos, Grasshopper Docs, version 1.0.0007, Dec. 15th, 2019, https://grasshopperdocs.com/addons/galapagos.html.
Herr, Christiane, and Thomas Fischer. “Teaching Generative Design.” Paper presented at International Conference on Generative Art, January, 2001, https://www.researchgate.net/publication/30869860_Teaching_Generative_Design.
Imdat As, and Prithwish Basu. The Routledge Companion to Artificial Intelligence in Architecture. Abington, Oxon New York Routledge, 2021.
Kyropoulou, Mili. ‘Shading Design For Outdoor Learning in Warm And Hot Climates Using Evolutionary Computation: A Case Study
In Houston Tx.’. 2022 Annual Modeling and Simulation Conference (ANNSIM), San Diego, CA, USA, IEEE, pp. 682–693 [Online]. DOI: 10.23919/ANNSIM55834.2022.9859518.
Ladybug Tools, Making Environmental Design Knowledge and Tools Freely Accessible to Every Person, Project and Design Process, https://www.ladybug.tools/index.html#header-slide-show
Leach, Neil, and Riba Future Studies. Designing for a Digital World. Chichester: Wiley-Academic, 2002.
Luke, Sean. Essentials of Metaheuristics : A Set of Undergraduate Lecture Notes. Second. San Francisco: Editor No Identificat, 2016.
Menges, Achim. Computational Design Thinking. Chichester: Wiley, 2011.
Merriam-Webster Dictionary, “heuristic,” https://www.merriam-webster.com/dictionary/heuristic.
Mitchell, John WIlliam. Computer-Aided Architectural Design. Van Nostrand Reinhold Company Inc., 1977.
OpenAI. “ChatGPT: Optimizing Language Models for Dialogue,” November 30, 2022. https://openai.com/blog/chatgpt/.
Radford, Antony, and Garry Stevens. CADD Made Easy. McGraw-Hill Companies, 1987.
Turing, M., Allen. “Computing Machinery and Intelligence, ” Mind volume 59, 236 (1950): 433.
Wallacei, “An Evolutionary Multi-Objective Optimization and Analytic Engine for Grasshopper 3D”, https://www.wallacei.com/ “ChatGPT: Optimizing Language Models for Dialogue”, OpenAI, November 30, 2022, https://openai.com/blog/chatgpt/.
“Optioneering.” Generative Design Primer, https://www.generativedesign.org/02-deeper-dive/02-02_optioneering
Figure 1 : A graphic illustration showing six selected results from the multi-objective optimisation workflow, but also the genomic decoding of that simulation, seen on the left of the graphic. Author’s own work.
Figure 2 : User Optioneering, the first workflow presented. Neighbour and Park are the two sites where overshadowing will be minimised. Author’s own work
Figure 3 : Single Objective Optimisation (SOO), allthough identical to UO in its’ approach to site, optimisation improvements were apparent. Author’s own work.
Figure 4 : Multi-Objective Optimisation (MOO) using Wallacei. This method made consideable improvements both in its approach to the site and the towers, but also in the environmental analysis method. Author’s own work.
Figure 5 : Illustration of the genomes, composed of 24 genes, split into the three sections of the tower, bottom, middle and top. DeLanda’s abtract building. Author’s own work.
Figure 6 : Tree of life, a data structure representing many body plans at once. Ernst Haeckel, 1866. Pyhlogenetic tree - I. Tree of Life. Place: Subcollection: Rare Books,
Repository: Division of Rare and Manuscript Collections, Cornell University Library, Archival Location: QH351.H13. httpleft:The genomic structure, the overarching tool that allows the generation and analysis of the towers. Author’s own work. right: the processes of cross-over and mutation.Author’s own work.s://library.artstor.org/asset/ SS35197_35197_19437225.
Figure 7 : left:The genomic structure, the overarching tool that allows the generation and analysis of the towers. Author’s own work. right: the processes of cross-over and mutation.Author’s own work.
Figure 8 : Graph showing the performance of towers based on two FOs: maximising volume and maximising winter incident radiation. The pareto front is labelled as the solid line, showing the non-dominanted solution of the last generation. Author’s own work.
Figure 9 : Illustration of fitness function of MOO, a grid of heights, or fitness, of all the individuals in the generations, higher height of the surface denoting a higher fitness, or performance of a solution.
Figure 10 The design space of the User Optioneering approach, presenting the designer with a plethora of options, afterwhich the designer can manipulate the PCP, the graph seen on the left to set maximum and minimum values for the different design metrics, i.e., restric the design space to towers with a maximum overshadowing value of 6000 m, or a floor area bigger than 500,000. The user interface is replicated from the DDU’s method. Author’s own work.
Figure 11 Recreation of the DDU’s tower definition, producing a uniform, monolithic form of sub-towers, or blocks, each having varying heights, seen in https://www.youtube. com/watch?v=-HLRtXSG7fQ&ab_channel=DigitalDesignUnit-TUDarmstadt . Author’s own work.
Figure 12 The tower definition of the UO, but also consequent SOO workflows. Seen as a developement of the DDU’s method, it introduces gaps in the section that allow light to penetrate the mass. Author’s own work.
Figure 13 : Three examples of each generation, each having a different number of boxes per section, a way to control floor area while sorting for total shadow area; effectively reducing the amount of variables the user has to consider while optioneering. However, increasing the amount of optioneering that has to occur, as three generations need to be considered. Author’s own work.
Figure 14 Production workflow from Python to algorithmically generate the genomes to the end user optioneering with the PCP and design space. Author’s own work.
Figure 15 Top view seen on the top, showing the three types of angle used from west to east componnts. The elevation view seen on the bottom shows the two types of altitudes of angles used. This produces 6 angles to reflect an overshadowing scenario that encompasses many different times of year. Author’s own work.
Figure 16 The User Interface of the UO approach, showing the design space and the PCP. Author’s own work.
Figure 17 : Two graphs showing the only optimization present is in terms of total overshadowing, there is little to extract concerning neighbour and park overshadowing. Author’s own work.
Figure 18 The 18 results from the UO methodology, providing a large breadth for optioneering, however, not allowing for a sufficient enough level of optimisation. Author’s own work.
Figure 19 : The 6 results from the second methodology of Single-Objective-Optimisation (SOO), producing higher performing towers than the UO approach, but removing the ability of the user to optioneer effectively. Author’s own work.
Figure 20 The processes of cross-over and mutation, showcasing the way in which towers’ genetic information is carried over to consequent generations. Author’s own work.
Figure 21 The six results produced from Galapagos in the SOO approach. Three for the high angles, three for the low angles. Author’s own work.
Figure 22 A 3D representation of the fitness landscape, each point on it is an individual tower, with the height of the point, thus the colour, denoting performance. A local optimum would at first appear as elite in terms of performane, but once the simulation is finished, doesnt reflect the global optimal. Author’s own work.
Figure 23 Fitness (y), Sun Angle (x) graph; the improvement in fitness, thus methodology is apparent in the htched area, showing the different of fitness between the SOO towers, and the highest performing towers of the UO workflow. Author’s own work.
Figure 24 A comparison of the 6 highest performing UO towers, and the SOO towers (the hatched region in the graph). Author’s own work.
Figure 25 A result from the last approach, deploying multi-objective-pptimisation. Advances in both optimisation but also visualisation were made in MOO, showing a clear reconfiguration of the system both in its evolutionary optimisation but also in the environmental analysis. Author’s own work.
Figure 26 The site chosen for MOO, a block in Manhattan, where three current buildings are to be redesigned as the three genomic towers. The ensemble of the towers can be thought as the genomes, each tower’s individual genome becomes a chromosome in this case. Author’s own work.
Figure 27 Dry-Bulb temperature graph for New York city, with the two ranges chosen hatched, note that the winter range includes december. Author’s own work, data acquired from Climate Consultant analysis softwre.
Figure 28 : The Wallacei interface, one can optioneer by choosing different individual tower phenotypes, seeing how they perform among the rest of the population. Author’s own work.
Figure 29 The three towers seen in blue, with the white boxes being the excluded genes from the definition, chosen as always being in a value of 1, or full, they make no difference to overshadowing criteria as they are directly adjacent to buildings to their south.Author’s own work.
Figure 30 : Mean Trend Value graphs for the four FOs, showing a trend of convergence across all FOs, with however, not a complete convergence as a plateau is not reached. Author’s own work.
Figure 31 The Standard Deviation graphs of all the generations. Convergence is seen in the red curve, variance is seen in the bluer curves. Author’s own work.
Figure 32 Gen 46, Ind. 0: solution best at maximsing Towers Volume. Author’s own work.
Figure 33 Gen 45, Ind. 3. Solution best as maximising Tower IR in the winter months. Author’s own work.
Figure 34 Gen 41, Ind. 3. Solution best for maximising Neighbour’s IR durin the winter months. Author’s own work.
Figure 35 Gen 41, Ind. 5.Solution best for minimising Tower’s IR uring the summer. Author’s own work.
Figure 36 Gen 10, Ind. 15. Solution with the lowest relative difference between FOs. Author’s own work.
Figure 37 Gen 24, Ind. 11. Solution with the average of Fitness Ranks. Author’s own work.
Figure 38 The three clusters of the pareto-dominant solutions. Author’s own work.
Figure 39 The towers of the first cluster, demonstrating higher performance in Tower Winter IR. Author’s own work.
Figure 40 The towers of cluster 2, demonstrating higher performance in maximising Volume. Author’s own work.
Figure 41 The towers of cluster 3, showing higher performance in Neighbour Winter IR. Author’s own work.
Figure 42 The genomes of all the generations, three colours showing the chromosomes, the different towers. Within them the two contrasting colours are 0s and 1s. Author’s own work.
Figure 43 The genomic makeup of the three clusters, patterns within the chromosomes can be detected. Author’s own work.
Figure 44 Dominant genes of cluster 1. White shows the genes that converge to a 1, red shows the ones that converge to a 0, the absence of blocks denotes that the genes at this position did not converge. Author’s own work.
Figure 45 Dominant genes of cluster 2. White shows the genes that converge to a 1, red shows the ones that converge to a 0, the absence of blocks denotes that the genes at this position did not converge. Author’s own work.
Figure 46 Dominant genes of cluster 3. White shows the genes that converge to a 1, red shows the ones that converge to a 0, the absence of blocks denotes that the genes at this position did not converge. Author’s own work.
Figure 47 Gen. 45, Ind. 3 - Towers best at maximising Tower Winter IR. Author’s own work.
Figure 48 Gen 46 - Ind. 0 - Towers best at maximising volume. Author’s own work.
Figure 49 Gen 41 - Ind. 3 - Towers best at maximising Neighbour Winter IR. Author’s own work.
Figure 50 “Image generated by Midjourney, an AI image generation system. This was produced given the prompt from the poem above:
“We must think about the social implications, Of the spaces we create and the communities we form. Are we fostering connection and inclusivity, Or perpetuating inequality and division?””
Figure 51 “image generated by Midjourney, an AI image generation system. This was produced given the prompt:
Reading done early on in research that was not directly correlated with the research in question. However, relevant to the overarching theme of computational and generative design
“Under the influence of concepts, he not only does things from a biased point of view but sees them biasedly as well. The concept controls his perception of fit and misfit – until in the end he sees nothing but deviations from his conceptual dogmas and loses not only the urge but even the mental opportunity to frame his problems more appropriately”.1 Here Alexander points out to the problem of dogmatizing architecture with its time’s societal aesthetics or societal goals; that is to say that architecture is a product of its time but sometimes too much so. He brings the example of the proclivity for engineering and functionalism in Roman architecture only after Vitruvius formalised his thesis on functionalism.2 Seen in the need for architects to create something “modern”, when consideration is given to building performance demands. Alexander puts forth a crucial point as the architect should not be worried about questions of abstracting the concept of a design in the detriment of performance or efficiency, he should be looking to define the problem that the building will solve primarily. This is especially important in our times as architects have a responsibility over the world’s resources and using them under the guidance of abstract aesthetic rules should be a secondary consideration coming only after satisfying an appropriate problem statement. “[the diagram] is an abstract pattern of physical relationships which resolves a small system of interacting and conflicting forces, and is independent of all other forces, and of all other possible diagrams”.3 Here Alexander defined the pattern what he deems to be the most important idea developed in this book. Essentially creating an abstraction of a design problem by breaking it down to its individual components; this abstraction can be done symbolically or mathematically. This idea was of significant help both in finding a way to describe a building as a series of numbers, i.e an abstraction of a building typology into ones and zeros but also to create a abstract pattern to describe the diagrams that were generated using the genetic algorithm, something which the designer has little control over. The use of the pattern made it easier to track changes during the working of the GA.
“Typically, a generative system does not directly produce the actual object which is sought. Instead, it produces representation, model, or design for the object, which can then be translated into reality”4
Here Mitchell points out that the generative system is merely a tool for design, a representation of a design solution relative to a problem and not the physical solution itself. This might seem self-evident, after all its only pixels on a screen; on the contrary it is easy for one to think that the solutions presented are the absolute architectural truth and convey a perfectly optimiSed system. This is an important distinction as it is easy to give all your trust to the computer, the designs which it offers need to be scrutinized only as representations of a final form and not as the final form itself.
“If evolved architectures are to enjoy the same degree of combinatorial productivity as biological ones they must also begin with an adequate diagram, an ‘abstract building’ corresponding to the ‘abstract vertebrate’.”5 Here Manuel De Landa talks about the ability of designers to use generative systems by altering what he calls the abstract building, that is the blueprint of all buildings that are to be generated, giving their ethos to the project, which each generative project being unique to a designer. The abstract building is reformulated as the genome in this paper, it can not only describe every proposed solution generated by the machine, but it also describes the overarching structure of generating solutions in the first place. This idea proved as a turning point onto how to develop my own personal version of a generative design system and how to describe a building first symbolically in an abstract diagram and then as a number to plug into the machine. This idea resonates with Alexander’s use of patterns or diagrams.
1 Christopher Alexander, Notes on the Synthesis of Form (Cambridge, Mass.: Harvard Univ. Press, 2002), 70.
2 Alexander, Notes on the Synthesis of Form, 70.
3 Alexander, Notes on the Synthesis of Form, Preface, 1.
- THE APPLICATION OF A DATA-DRIVEN, GENERATIVE MODEL IN DESIGN, by Ardavan
“Compared with the parametric modelling workflow, this one does not require highly trained users in all parts of its life cycle. However,
4 William John Mitchell, Computer-Aided Architectural Design (Van Nostrand Reinhold Company Inc., 1977), 38.
5 Manuel DeLanda, “Deleuze and the Use of the Genetic Algorithm in Architecture,” in Designing for a Digital World, ed. Neil Leach (United Kingdom: Wiley-Academy, 2002), 120.
it is black box, so even a keen and experienced developer cannot understand how the model works. It is a trade-off of transparency in favour of end-user convenience.”6 This is a quote from Bidgoli and Veloso’s generative design system based on Machine Learning (ML). Here they describe the difference between a model like the one that will be described in this paper and a ML model. This was motivation to study a parametric model as it is much easier to implement and as mentioned by Veloso and Bidgoli potentially offers greater transparency over designs but with an inferior end-user experience.
[short introduction of the project is given to Mrs. Kyropoulou]
site to be overshadowed?
Mili Kyropoulou- Guest (MK) : the two sites are what exactly?
Antonios Mavrotas - Author (AM): they are placeholders for some given site conditions
MK: you’re working on the massing level, not looking at whether this will be translated into a building later?
AM: yes good question... I am not sure. It was both as a test to learn Wallacei but yes there isnt a reason. Normally it should all be maximised.
AM: yes in the site level, but any suggestions you have to make this better could be implemented because I realise that what I am doing is not perfectly correct. Nevertheless am doing this mainly for testing and learning Wallacei. But the results are somewhat redundant as the form is obviously cutting the bottom part of the building and keeping the top part. am trying to see if this could be done better to get more insightful results.
MK: Yes. Right now us in Houston all we need is more shadowing, so its easy to find something for overshadowing. That what you could do, to possibly change your climate: say I go to Greece, to Athens and... or Crete where its even hotter. And you will say I want to maximize overshadowing only in summer, the summer months. I want overshadowing those months, to have shadow, to have comfort, to make coffee shops, for any reason you want overshadowing in that specific site.
AM: Yes I understand... To be more strategic in what I do with overshadowing.
Appendix 2 Interview with architect and researcher Mili Kyropoulou, format: online date: 16th November, 2022.
note: interview taken after early attempts at using Wallacei, the work of which was used for discussion and subsequent developement into the New York site, seen in the MOO approach, however not shown in this dissertation.
MK: I am just turning off my camera to hear you better, I think the connection broke a little bit there but think I got the main idea of what you were saying. You want to minimize overshadowing over those two sites right?
AM: yes MK: how have you identified those sites, are they playing a specific role in your design?
MK: You could also bring in other buildings in, neighbouring buildings. In Norway that would be interesting. Have you heard of the solar envelope?
AM: No
AM: Those two... I had followed a tutorial on youtube, there was a professor from TU darmsdat, who was making a simillar system but only with Galapagos, and also he was making genes himself, and then sorting the solutions. Attempting to develop this... his sites were rectilinear and not freeform, two boxes. They are nevetheless completely random in their placing.
MK: Yes but why are those two benefiting from...., so for instance, are those two are where the green spaces are and you want to have vegetation?
MK: Or Solar Rise. These are keywords you can search up. In NYC there is more work done on this. Essentially this is about the setback that happens on higher floors in appartment buildings, in Athens too this happens. This happens to bring natural light to lower floors of the neighbouring building. So you can do that, evaluate the solar radiation, or something. You are measuring the solar radiation?
AM: emm... yes yes
MK: Or sunlight hours?
AM: yes that’s correct, its the average of sunlight hours.
AM: correct, correct... this is a park and this other is just named as a neighbour. But they are not given a specific use as of yet. I realise this is not advantageous to the project as they don’t have a specific...yes...specific use. What do you think, should I find something?
MK: Given tha this is in Norway, why do you want the rest of the
MK: Yes, I don’t know which one is more applicable to you but either way, you can focus on the lower third of the building, or even the whole building, the neighbouring building. Those buildings need to be solar oriented. So if you are in the northern hemisphere, it’s the southern elevation that you are analysing and your building is south of the neighbouring building. And the.. You are using ladybug?
AM: yes ladybug
MK: Do you have Ladybug Legacy or the new Ladybug?
AM: emm.. I have.... I have... the normal Ladybug.
MK: he normal ladybug, ah yes...em.. They havent brought over all of the components...click on ‘Analyse Geometry’, the red one called Solar Fan or Solar Envelope.
AM: Human to Sky relation?
MK: The ‘solar envelope’ component
intensive simulations and couldn’t add too many genes, but you don’t have that intensive simulations therefore you can put more genes. did a workshop with Wallacei’s creators and they showed an example with an urban application. THey put so many paremers and sliders and at that piint you were losing control. There was no way to relate the optimized the result to the design challenge. In my paper I wanted to do it such that I could understand why the optimized result was in fact optimal.
AM: yes.
sun angle to optimize for.
AM: You want this fan to be as high... yes as high as you can correct?
MK: uhm, yes you want to have it higher if you want to build more units. Your central part should not be always present, it should go away if the neighbouring 8 are also away.
AM: Do you have any mre advice on what else could impliment as a aparemet, not only the overshadowing parameter. Whether I could optimize something to do with the building itself not the site.
AM: yes had two ladybug componets one for the neighbouring sites and one for the whole site.
MK: yes you might need to make your total site the negative space between the site and the neighbours.
AM: yes that is correct, I think it is all of it, yes, this would make more sense.
AM: SOlar Envelope... ah yes... okay, okay.
MK: look at this component, its somewhat like formfinding where you give the geometry and the obstacles and it outputs a geometry of sun angles where below or above, depending on your problem you are allowed to build or not. Say, you cannot build.....ah basically I can think of a project that used this, let me think of where this could be, might have access to this.
AM: so what you are suggesting is to relate this to a neighbouring building and not just a footpring?
MK: I think it will give you more interesting shapes.
AM: okay
MK: yes, wait I will try and find it quickly. (Mili spends some time trying to find a paper related to the topic) I cant find it this quickly, give me one more minute if I can find it. But if you look up the ladybug component and you google solar envelope or solar fan. THis create.. You say that the neighbouring buildings, all of its floors, you want them to have solar acess, especially in Norway with really low solar angles you don’t want to give solar exposure the whole winter but even two hours a day, even from 12-2 pm direct solar access, across the whoel winter. This will give you a literal fan, like the one seen in the component, and this shape says that from there and below you can build. Also if you make your blocks smaller that would help. The more parameters you put...Also don’t be afraid to put more …. I did this study with only 3 parameters, with only 3 or 4 things I was controlling, the genes were limited. had very
MK: If you feel comfortable putting in more parameters even if it means you don’t distinguish the result and why it works, you should do it, even if the result seems complicated. The more complicated the scenario is the beter the algorithm works. I am saying all this very roughly don’t know if it directly applies to your project.
MK: sorry the connection isnt very good, you are asking to find parameters that affect the bulding itself?
AM: yes or anything else you have advice on to impliment.
MK: yes maybe it would give different results, this way there would be no overlap therefore there would be two different results. And then you compute the average hours?
AM: yes the average hours.
MK: how much time does this take to run, it should be fast.
AM: yes that makes sense, to make the blocks smaller too. When I read your paper, your simulations took 9hrs?
MK: yes but it was annual, thermal and daylight simulations, you are doing only solar where you don’t use irradiance or EnergyPlus from ladybug, you are working only with ladybug not with honeybee, which means its less intensive. By the way, found the paper I was looking for. Yes this is it, this is a lecture where they talk abut the setbacks. This person: Ralph Knowles is the first to speak of the solar envelope. It is the logic of the setbck like the appartment buildings in Athens. The problem is to find the exact angle, with which your work, from which sun angle and below do you want to work with. For example this is a street in NYC before this became a law. You see the sky very minimally. This project wasn’t even a competition, it was an internal competition for an office I used to work for. So this is an existing building and there is a carpark on which we are to build. So the sun comes from the southern side of the building and this creates this solar fan. It essentially ‘sculpts’ the buildings. So whatever is below this point becomes sculpted. This is how it works.
MK: Your building is quite monolithic, you could make it more like a tree where you can add or remove boxes, with a given site you maximise south orientation. You are in a massing stage rightnow, there are no window?
AM: this takes roughly 2-3 hours.
AM: I see, this makes sense, hadnt understood exatly what this fan was. And this doesn’t need wallacei it just a standalone component.
AM: yes that’s correct no windows.
MK: Yes only in a massing stage, Have you done a climatic analysis based on building strategies. Even from there you might be able to extract information, with the climate of norway. There are several software you can do this with. Climate Consultant is one, it makes useful links to the 2030 challenge, with several buildings that have done it, you can see buildings that have used this strategies for climates like the one of norway.
AM: yes that’s a very good idea, this makes more sense. I also wanted to show you the graphs that it showed, this one... can you see the screen. I think after generation 20 it converges too quickly and it seems redundant to continue the simulationa fter that.
MK: Wallacei has a good interface, especially if you cant do scripting on your own. It is a strong plugin which is free with a good community. You will not find too many application that relate it to performance, most are formative. On their site thhey have a list of published papers. Especially on how to visualize these results. With other plugins, they tend to give you only the last result; whereas
in Wallacei you can go back to any result or any generation and rebuild essentially all the results that isnt necessrily completely optimal or it is only optimal on one parameter. You essentially have more power in postprocessing.
AM: yes that’s the hard part sometimes, to viausalise them. I had used octopus but it was quite hard to use and visualize.
(Mili asked the author if there were more questions, after brief closing statements, the Author thanked Mili Kyropoulou and the interview was concluded).
MK: yes how did you make you simulations. How did u set up your grids, two in your bubbles and one as your site?
AM: what is this for?
MK: yes, how can you use wallacei... if you put neighbouring buildings and you see which ones you want to allow solar acces for, because of the low sun angles and also both becaue of daylight and also energy. You could set the variable as the sun angle, which
MK: For the genes, you said you have minimised overshadowing, maximised overshadoing in the rest and minised form factor.
importing packages necessary for combinatorial algorithms (itertools), but also transfering the genomes to excel (pandas)
import pandas as pd import itertools
a = [1,1,1,1,0,0,0,0] cache = []
Appendix 3 The Python script that was developed the genomes of the UO approach. The first part of the algorithm permutates the 8 blocks of a section of a tower, for either 3,4 or 5 possible 1s, the three generations.
The second part of the algorithm is concerned with finding all the possible combinations of three sections, the chromsomes, each having 56 possible combinations. The genomes are the sifted to pick a subset of 3136 genomes.
setting up the algorithm for generation set 2 (4 bblocks per section), seen in variable ‘a’ where four 1s are configured in a set of 8 values
def tree(mutation, locs): if mutation in cache: return else: cache.append(mutation) for ind in locs: if ind + 1 < len(mutation) and mutation[ind + 1] != 1: new_list = list(mutation) new_list[ind], new_list[ind + 1] = 0, 1 new_locs = list(locs) new_locs[new_locs.index(ind)] =ind + 1
tree(new_list, new_locs)
algorithm to find the 56 possible chromsomes: the genomic makeup of one of three tower sections
taking every 100th element in the genome list, to reduce the number of genomes to below 4,000. This is done to ensure computational feasibility by Grasshopper.
tree(a, [0,1,2,3])
bottom = cache middle = cache.copy() top = cache.copy() res = []
for combination in itertools.product(bottom, middle, top): comb = [] for i in combination: for j in i: comb.append(j) res.append(comb) y = [] for i in range(0, len(res), 100): y.append(res[i])
print(y) print(len(y)) a = pd.DataFrame(y) a.to_csv(‘genomes4.csv’)
transferring the sifted genomes into an excel file, named “genomes4.csv’’
setting up variables for the three sections (bottom, middle, top), in order to permutate the 56 resulting chromsomes from the “tree” function into full genomes
using itertools to find all the possible genomes, all the permutations of genomes in generation set 2