Applying Social Choice Theory to Solve Engineering Multi-objective Optimization Problems
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Multi-objective optimization problems usually do not have a single unique optimal solution, for either discrete or continuous domains. Furthermore, there are usually many possible available algorithms for solving these problems, and one typically does not know in advance which of these will be the most effective for solving a particular problem instance. Hyper-heuristics (HHs) are often used as a means to make this choice. In particular, the underlying idea of HHs is to run several algorithms or heuristics and dynamically decide, based on different criteria, which problem or part of the problem should be solved by which algorithm or heuristic. On the other hand, the domain of social choice theory studies how to design collective decision processes by aggregating individual inputs into collective ones. In this paper, we explore the use of social choice theory in creating HHs. By using HHs based on different voting methods, like Borda, Copeland and Kemeny–Young, we show how we can solve both continuous and discrete engineering multi-objective optimization problems and discuss the results obtained by each of these methods. Our obtained results show that our strategy has found solutions that are at least equals to the ones generated by the best algorithm among the studied ones, and sometimes even overcomes these results.
KeywordsHyper-heuristics Multi-objective evolutionary algorithms Voting methods Crashworthiness Car side impact Machining Water resource planning Multi-objective travel salesperson problem
Vinicius Renan de Carvalho was supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior-Brasil (CAPES)-Grant Code 001, and by CNPq, Brazil, Grant Agreement No. 140974/2016-4.
- Adra, S. F. (2007). Improving convergence, diversity and pertinency in multiobjective optimisation. Ph.D. thesis, Department of Automatic Control and Systems Engineering, The University of Sheffield.Google Scholar
- Burke, E., Hyde, M., Kendall, G., Ochoa, G., Ozcan, E., & Woodward, J. (2010). A classification of hyper-heuristic approaches. In Handbook of metaheuristics (Vol. 146, pp. 449–468). Springer.Google Scholar
- de Carvalho, V. R., & Sichman, J. S. (2017). Applying copeland voting to design an agent-based. In Proceedings of the 16th conference on autonomous agents and multiagent systems (pp. 972–980).Google Scholar
- de Carvalho, V. R., & Sichman, J. S. (2018a). Multi-agent election-based hyper-heuristics. In it Proceedings of the 27th international joint conference on artificial intelligence.Google Scholar
- de Carvalho, V. R., & Sichman, J. S. (2018b). Solving real-world multi-objective engineering optimization problems with an election-based hyper-heuristic. In OptMAS 2018: International workshop on optimisation in multi-agent systems.Google Scholar
- Elarbi, M., Bechikh, S., Ben Said, L., Datta, R. (2017). Multi-objective optimization: Classical and evolutionary approaches. In Recent advances in evolutionary multi-objective optimization (pp. 1–30). Springer.Google Scholar
- Kumar, S., & Gans, N. (2016). Extremum seeking control for multi-objective optimization problems. In 2016 IEEE 55th conference on decision and control (CDC) (pp. 1112–1118). https://doi.org/10.1109/CDC.2016.7798416.
- Mao, A., Procaccia, A. D., & Chen, Y. (2013). Better human computation through principled voting. In Proceedings of the twenty-seventh AAAI conference on artificial intelligence, 14–18 July 2013, Bellevue, Washington, USA.Google Scholar
- National Crash Analysis Center. (2012). Toyota Camry, detailed model. Ph.D. thesis, The George Washington University.Google Scholar
- Nebro, A. J., Durillo, J. J., & Vergne, M. (2015). Redesigning the jmetal multi-objective optimization framework. In Proceedings of the companion publication of the 2015 annual conference on genetic and evolutionary computation, ACM, New York, NY, USA, GECCO Companion ’15 (pp. 1093–1100).Google Scholar
- Van Veldhuizen, D. A. (1999). Multiobjective evolutionary algorithms: Classifications, analyses, and new innovations. Ph.D. thesis, Air Force Institute of Technology, Wright Patterson AFB, OH, USA, aAI9928483.Google Scholar
- Zitzler, E., & Künzli, S. (2004). Indicator-based selection in multiobjective search. In PPSN. Lecture Notes in Computer Science (Vol. 3242, pp. 832–842). Springer.Google Scholar
- Zitzler, E., Laumanns, M., & Thiele, L. (2001). SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization. In Evolutionary methods for design optimization and control with applications to industrial problems, CIMNE (pp. 95–100).Google Scholar