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Short Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2011

Evolutionary Decision Making Algorithm for Patriot Missile Yothesh Kumar Narendran1, Kothai Thirumalai2 1

PSG College of Technology, Coimbatore, India Email: 2 PSG College of Technology, Coimbatore, India Email: Abstract—In this paper, we propose an evolutionary algorithm for the working of patriot missiles more efficiently and accurately. The backronym is “Phased Array Tracking Intercept Of Target”.The operating protocol failure was primarily because of the inefficiency of the tracking system (Range Gate Algorithm) which was not able to perform efficiently in long run. So we concentrate on replacing the Range Gate Algorithm with Bio inspired Forager Bee algorithm, the Tactical Algorithm with Ant Colony Optimization Routing Algorithm with Tabu Search, which collectively forms a strategy in Military Swarming, inorder to increase the probability of kill and to improve the operating time.

II. EDMAP A. Military Swarming A population of interacting individuals that optimizes a goal by collectively adapting to the local or global environment is called Swarm intelligence [2]. Whenever military operations are non-linear, dispersed, and decentralized, swarming is an effective tactic. In our case we encounter nonlinear tactical missiles for High Angle of attack missiles. Massive, instinctively coordinated crisis response:Bees exhibit it when defending the hive, and it is useful to remember that a bee dies after it stings, so it is more analogous to a missile than a combat unit. Information is necessary both to avoid fratricide and target the enemy.

Index Terms—Range Gate Algorithm, Bio Inspired Computation, Forager Bee algorithm, Ant Colony Optimization, Routing Algorithm, Tabu Search, Military swarming

B. Military swarming using Forager Bee A model of Artificial Bee colony System is adapted for Patriot missile detection [1]. A new optimization algorithm for coordinate selection that uses the bee behavior in food foraging as the functions to be used by the Weapon Control System processing engine. The following notations are used in the ABC algorithm: X: number of scouts. Sx: the xth scout bee. The scout bees are the electrical pulses from the radar surveillance in each scan.Y: number of foragers. The FRy means the yth forager bee. The forager bees are the anticipated intruder signal which is sent to the patriot station. N: number of bees in the colony population. The bees are the agents which determine α variant and the coordinate of impact. Where,

I. INTRODUCTION PATRIOT, the most advanced Missile Defense System, which is used to track and destroy incoming targets, suffers from a disadvantage because of the Range Gate Algorithm. A. PATRIOT General Architecture The Patriot operates as part of a battalion usually composed of six batteries. Each battery is made up of one ground-based radar unit for surveillance and target detection, tracking, and engagement managed by Engagement Control Station, Information Coordination Cente, Weapons control computer [6]. The Patriot’s weapons control computer, heart of Patriot system, obtains target information from the system’s radar. Patriot operators use the software to instruct the system to identify, track, and intercept these missiles, important information of certain types of objects such as planes, cruise missiles, or tactical ballistic missiles. The range gate, an electronic detection device within the radar system which calculates an area in the air space where the system should next look for it. The range gate filters out information about airborne objects outside its calculated area and only processes the information needed for tracking, targeting, and intercepting Scuds. Finding an object within the calculated range gate area confirms that it is a Scud missile. The software faults of the early patriot missiles are: (1) Patriot computer only had 24-bit precision, so it chopped one by tenthousand off timing values. (2) The system fell behind by 0.0034 sec at 7mph. (3) Accuracy threshold is 20 hours. (4) Systm had been runnig for 100 hours, losing 0.3433 seconds, or 687 meters. (4) Range gate affected cumulatively by timing error. © 2011 AMAE DOI: 02.ARMED.2011.01.23

N  X Y Moreover, X is 5 to 10 percent of N. I: number of orbits. Where i stands for the ith orbit. The orbit is determined by constructing the 2D convex hull from the desired coordinateswhich are reported by agents in each iteration. CM: colony moral, it is a parameter defined algorithm goals. The goal is to minimize the response time. FSij: This means the jth food source at the ith orbit. It means the optimized points of the imapact coordinates with reference to α variant and limited by boundry of convex hull. M: Number of maximum iterations. FSQij: the net gain of energy from the food source, FSij. It is calculated based on distance, Dij, and the food source quality, FSQij. Where:

To inject optimized fuel for the journey of patriot missile. FSQTij: food source total quality is calculated based on food source net gain, FSGij, and the scout’s rank SRx which find 30

Short Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2011 this food source in the case the scout with a better food source will be rewarded. Where

(e) Update the CM. } } At each process the convex hull is generated by GRAHAMS algorithm to generate the orbital positions. ALGORITHM: GRAHAM SCAN Find interior point x, label it p0. Sort all other points angularly about x, label p0,....,pn-1. Stack S = (p1,p1) = (pt,pt-1) and t indexes the top. i=3 while i<n do if pi is left of (pt-1,pt) then PUSH (pi,S) and set i=i+1 else POP(S)

SRx: the rank of the xth scout and this value will be updated every time forager chooses the source found by this scout. FSVij: the number of visits by the foragers for FSij. There are two tables that will be used by the proposed algorithm. These are FTT: Food Taboo Table, this table contains all food sources that had been visited by the scouts. This table contains all the impact coordinates. It is used to prevent more scouts from visiting the same food source. This table contains the parameters: FSij, Sx and Srx. JST: Job Sheet Table, any food source visited by scouts will be added to this table. Each forager picks up one of the food sources, FSij, to collect food from. This table contains the following. The following algorithm is reffered from the notations in each step for better visualisation. 1) Initialization: a) X: number of scouts. b) Y: number of foragers. c) N: number of bees in the colony population. d) I: number of orbits. e) CM: colony moral. f) FSij: the jth food source at the ith orbit. g) M: number of maximum iterations. h) FSQij: the quality of the food source, FSij. i) Dij: the direct distance between colony and FSij. 2) Assumptions: a) The food sources have been previously defined. b) Every scout bee, Sx , visit only one food source, FSij, per each trip. 3) REPEAT X times (i.e. all scouts, X, finish one trip): { a) Scout should choose one food source, Fsij, find its distance, Dij, quality FSQij, and net gain of energy FSGij:

C. ACO Tabu search method for tactial missile A Meta-Heuristic Combinatorial algorithm has been proposed to overcome the “Missing Range” problem of the Range Gate algorithm [4]. In general Traveling Salesman Problem is having multiple destinations. But the problem with the Range Gate algorithm is it has unique destination and no solution for Blind Alley Problem. Blind Alley problem is nothing but a state where there are no further nodes available to traverse, that is, similar to missing range [5]. To overcome this problem TSP alone is not sufficient, so a combinatorial algorithm of ACO with Tabu search in combination with TSP is proposed. Thus, when one ant finds a good (i.e., short) path from the colony to a food source, other ants are more likely to follow that path, and positive feedback eventually leads all the ants following a single path. The idea of the ant colony algorithm is to mimic this behavior with “simulated ants” walking around the graph representing the problem to solve. At any instant of time there will be a static parameter and dynamic parameter associated with the nodes. The static parameter is known at any instant of time as it is fixed and the dynamic parameter represents the continuously evaporating pheromone quantity. Each node has a product of static value and dynamic value. There are two judging parameters used in ACO, they are ‘q’ and ‘q0’. The former is a random number between 0 and 1 whereas the latter is the fixed value or generated value. Certain mathematical constraints are followed: If(q<q0) Next adjacent node to be selected based on the product value Less value of the product is preferred If(q>q0) If an agent wants to move from ith node to jth node Probability of selecting jth node is

FSGij  FSQij / Dij b) Update JST table. c) Update FTT table. } REPEAT UNTIL the CM goal is achieved or reached the maximum number of iterations, M: { REPEAT Y times (all foragers, Y, complete one trip): { (a) Generate a random number, RN. (b) Calculate food source total quality

FSQTij  FSGij  SR x (c) Foragers, FRy , choose which food source, FSij, to forage by comparing the random number, RN, with FSQTij on the JS table. If FSQTij > RN Then Choose FSij and go to (h) Else Repeat (g) End If (d) Update JST. © 2011 AMAE DOI: 02.ARMED.2011.01. 23

Where T is the Decay value and B is the scaling factor. Thus the probability of selecting next co ordinate is proportional to product of pheromone amount distance between i and j. Pheromone update can be done in one of the two ways. Local update is the decay parameter.Global update is best pheromone value. At each stage, the ant chooses to move from one node to another according to some rules: 31

Short Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2011 But the proposed Meta-Heuristic combinatorial algorithm retraverses the graph in reverse manner using the tabu search and if it finds some unvisited node it calculates the shortest path using the TSP and again traverses towards the correct range via the optimized path, thereby bringing the missed missile back into range and thus solving the blind alley problem.

1. It must visit each node exactly once. 2. A distant node has less chance of being chosen (the visibility). 3. The more intense the pheromone trail laid out on an edge between two nodes; the greater the probability that that edge will be chosen. 4. Having completed its journey, the ant deposits more pheromones on all edges it traversed, if the journey is short. 5. After each iteration, trails of pheromones evaporate. The resultant graph is formulated with the help of Tabu search. Simulated annealing is a related global optimization technique which traverses the search space by generating neighboring solutions of the current solution. A superior neighbor is always accepted. An inferior neighbor is accepted probabilistically based on the difference in quality and a temperature parameter. The temperature parameter is modified as the algorithm progresses to alter the nature of the search. Tabu search is similar to simulated annealing in that both traverse the solution space by testing mutations of an individual solution. While simulated annealing generates only one mutated solution, tabu search generates many mutated solutions and moves to the solution with the lowest fitness of those generated. To prevent cycling and encourage greater movement through the solution space, a tabu list is maintained of partial or complete solutions. It is forbidden to move to a solution that contains elements of the tabu list, which is updated as the solution traverses the solution space. In simpler terms tabu search maintains a tabular column of visited, unvisited and candidate nodes. Initially all the nodes remain unvisited and the agent is initially marked as candidate node and visited nodes are nil [7]. As the iteration progresses the tabular column contents are updated. When there are no further unvisited nodes, the problem of Blind alley comes into picture. In such scenario the normal Range Gate algorithm fails.

Š 2011 AMAE DOI: 02.ARMED.2011.01.23

CONCLUSIONS In this paper, we reviewed how military swarming could increase the reliability of the patriot missiles. The reaction process is replaced by the A Bee Colony Optimization technique and the blind alley problem could be solved efficiently by the Ant Colony Optimization Routing Algorithm with Tabu Search. Future enhancements would include better retrieval time of the missiles and to reduce the working time of the algorithms. REFERENCES [1] AlRashidi, M. R., & El-Hawary, M. E. A survey of particle swarm optimization applications in electric power systems. IEEE Transactions on Evolutionary Computation, 2009, 13(4), pp. 913918. [2] A.B Edwards, Sean J.A. Swarming on the Battlefield: Past, Present, and Future. Rand Monograph MR-1100, Rand Corporation. ISBN 0-8330-2779 [3] Banks, A., Vincent, J., & Anyakoha, C. A review of particle swarm optimization. Part I: background and development. Natural Computing, 2007, 6 (4), pp. 476-484. [4] Banks, A., Vincent, J., & Anyakoha, C. A review of particle swarm optimization. Part II: hybridization, combinatorial, multicriteria and constrained optimization, and indicative applications. Natural Computing, 2008, 7 (1), 109-124. [5] Eberhart, R. C., & Kennedy, J. A new optimizer using particle swarm theory,1995. In Proceedings of the 6th Symposium on Micro Machine and Human Science, Nagoya, Japan, pp. 39-43. Piscataway,NJ: IEEE Service Center. [6] MIM-104 Patriot. Janeâ&#x20AC;&#x2122;s Information Group. 2008-08-12. Retrieved 2008-08-26 [7] Hendtlass, T., & Randall, M. A survey of ant colony and particle swarm meta-heuristics and their application to discrete optimisation problems. In Proceedings of the Inaugural Workshop on Artificial Life, Adelaide, Australia, April 2001,pp. 15-25.