Abstract
When optimizing for multiple environments, one usually needs to sacrifice performance in one environment in order to gain better performance in another. Ultimately, there may not be a single solution that meets the performance requirements for all environments. In this paper, we propose to find multiple solutions that each serve a certain group of environments. We call this formulation Robust Optimization with Multiple Solutions (ROMS). Two evolutionary approaches to ROMS are proposed, namely direct evolution and two-phase evolution. A benchmark problem generator is also suggested to produce uniform-random ROMS problems. The two approaches are then experimentally studied on a variety of synthetic problems.
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References
Beyer, H.-G., Sendhoff, B.: Robust optimization - a comprehensive survey. Computer Methods in Applied Mechanics and Engineering 196(33), 3190–3218 (2007)
Ben-Tal, A., Ghaoui, L., Nemirovski, A.: Robust Optimization. Princeton University Press (2009)
Roy, B.: Robustness in operational research and decision-aiding: A multi-faceted issue. European Journal of Operational Research 200(3), 629–638 (2010)
Pita, J., Jain, M., Tambe, M., Ordóñez, F., Kraus, S.: Robust solutions to Stackelberg games: addressing bounded rationality and limited observations in human cognition. Artificial Intelligence 174(15), 1142–1171 (2010)
Jin, Y., Branke, J.: Evolutionary optimization in uncertain environments - a survey. IEEE Transactions on Evolutionary Computation 9(3), 303–317 (2005)
Deb, K.: Recent developments in evolutionary multi-objective optimization. Trends in Multiple Criteria Decision Analysis, 339–368 (2010)
Bertsimas, D., Sim The, M.: price of robustness. Operations Research 52(1), 35–53 (2004)
Goldberg, D.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Professional (1989)
Storn, R., Price, K.: Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997)
Suganthan, P., Hansen, N., Liang, J., Deb, K., Chen, Y.-P., Auger, A., Tiwari, S.: Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization, technical report, Nanyang Technological University (2005)
Strang, G.: Introduction to Linear Algebra, 4th edn. Wellesley Cambridge Press (2009)
Diaconis, P., Shahshahani, M.: The subgroup algorithm for generating uniform random variables. Probability in the Engineering and Informational Sciences 1(1), 15–32 (1987)
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Yang, P., Tang, K., Li, L., Qin, A.K. (2015). Evolutionary Robust Optimization with Multiple Solutions. In: Handa, H., Ishibuchi, H., Ong, YS., Tan, K. (eds) Proceedings of the 18th Asia Pacific Symposium on Intelligent and Evolutionary Systems, Volume 1. Proceedings in Adaptation, Learning and Optimization, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-13359-1_47
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DOI: https://doi.org/10.1007/978-3-319-13359-1_47
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-13358-4
Online ISBN: 978-3-319-13359-1
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