Can We Solve the Traveling Salesman Problem with a Light Sensitive Chemical Reaction? Jake Bordenca, Hugh H. Cheung, Sabrina G. Sobel (Mentor)
Department of Chemistry, Hofstra University, Hempstead, NY 11549-1510
Abstract
Materials and Methods
The traveling salesman problem (TSP) is a problem that asks how a hypothetical person, i.e. a traveling salesman, would visit several points of interest once each and return to the starting point in the shortest possible distance. This has applications in many industries such as the transport and delivery of food or mail. The solving of the TSP has been attempted using AI, neural networks and slime mold. The purpose of this experiment is to use an inorganic reaction (the Belousov−Zhabotinsky Reaction or BZ Reaction) as opposed to a biological or computorial method to solve the TSP. Currently, there has been research done on this reaction using a light sensitive ruthenium-catalyzed reaction and extensive light hardware and software, but we came up with another possible solution using a dual-catalyzed recipe of Ruthenium and Ferroin with a simpler light set-up to simulate a grid and potentially make the TSP solvable.
Reagent
Initial Initial Volume Concentration (M) (mL)
Final Concentration (M)
We used the equal parts Ru(bpy) and Ferroin recipe for the first trials to develop our experimental setup to test the light sensitivity of our recipe. All of our trials reacted in 90mm diameter petri dishes and used a total volume of 12.1 mL reactants in order to best simulate thin wave BZ Ru(bpy)3SO4 0.0098 0.785 0.000636 oscillatory dynamics. Our first setup involved the use of an LED light plate and a 500 Lumen Flashlight that shone [Fe(o-phen)3]SO4 0.0125 0.015 0.000015 directly on the petri dish with a mounted iphone camera to record the wave action. After first testing the recipes ability to be inhibited by light, we placed cardboard cutouts over KBrO3 0.25 7.50 0.155 the dish to block some of the light to see if we can have Malonic Acid 0.20 2.50 0.0413 oxidation waves appear only in the shade which they did; however, the cardboard cutouts directly on top of the petri Sulfuric Acid 6.0 0.600 0.298 dish made it difficult to film the reaction. Finally, we moved Water N/A 1.200 N/A onto a setup using a projector mounted onto ring stands and a light plate at the bottom. With a projector, not only KBr 0.20 1.000 0.0165 was it far easier to film the reaction, but we had a greater Table 1 - Dual Catalyst BZ Recipe freedom on what shapes we wanted to produce in the BZ medium. However, due to the projector being much dimmer than the flashlight, we had to experiment with different recipes with higher concentrations of Ruthenium to try to get the same inhibitory effect as we got with the 500 Lumen flashlight.
Introduction One common formula for the BZ reaction uses ferroin, [Fe(phen)3]2+, which is oxidized to ferriin, [Fe(phen)3]3+. Ferroin is red, while ferriin is blue, allowing the waves to be tracked. This dual catalyst recipe uses both ferroin and the structurally analogous trisbipyridyl ruthenium (II), [Ru(bpy)3]2+, which is an orange-yellow color. [Ru(bpy)3]2+ and its oxidized form, [Ru(bpy)3]3+ , however, are light-sensitive. The addition of this Ru-based catalyst allows the reaction to be inhibited by light. From this starting point, different concentrations and ratios between ferroin and [Ru(bpy)3]2+ can be mixed and tested to elucidate which recipe works the best with a given intensity of light.
The Ru(bpy)3SO4 was synthesized from Ru(bpy)3Cl2, so as to not add another anion to the reaction medium.
Dual Catalyzed Oscillations Structure of [Ru(bpy)3]2+
Structure of Ferroin
Acknowledgements The authors of this paper would like to acknowledge Hofstra University for supporting this research financially and the Chemistry Department for providing the reagents for this investigation.
References
Figure 1 - Recipe under no external conditions
Figure 2 - Recipe after a flashlight is shined on reaction
Figure 3 - Recipe with obstructions to flashlight
Figure 4 - Recipe influenced by projector light
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Conclusion ● ● ● ●
[Ru(bpy)3]2+ can be used instead of, or alongside ferroin in the BZ Reaction to make it light sensitive. Ruthenium//Ferroin dual catalyst BZ reactions can form more complex patterns than single catalyst reactions. These light-sensitive waves can be made to avoid a section of the reaction medium if enough light is applied. Future work includes finding the ideal recipe for the current projector set-up and designating points to attempt to solve the TSP