Abstract
This article presents CoBRA, a new parallel coevolutionary algorithm for bi-level optimization. CoBRA is based on a coevolutionary scheme to solve bilevel optimization problems. It handles population-based meta-heuristics on each level, each one cooperating with the other to provide solutions for the overall problem. Moreover, in order to evaluate the relevance of CoBRA against more classical approaches, a new performance assessment methodology, based on rationality, is introduced. An experimental analysis is conducted on a bi-level distribution planning problem, where multiple manufacturing plants deliver items to depots, and where a distribution company controls several depots and distributes items from depots to retailers. The experimental results reveal significant enhancements with respect to a more classical approach, based on a hierarchical scheme.
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References
Anandalingam, G., White, D.: A solution method for the linear static stackelberg problem using penalty functions. IEEE Transactions on Automatic Control 35(10), 1170–1173 (1990)
Ben-Ayed, O., Blair, C.: Computational difficulties of bilevel linear programming. Operations Research 38(3), 556–560 (1990)
Calvete, H., Galé, C.: A Multiobjective Bilevel Program for Production-Distribution Planning in a Supply Chain. In: Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems, pp. 155–165 (2010)
Cordeau, J., Gendreau, M., Laporte, G.: A tabu search heuristic for periodic and multi-depot vehicle routing problems. Networks 30(2), 105–119 (1997)
Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms. John Wiley & Sons, Inc., New York (2001)
Deb, K., Agrawal, R.: Simulated binary crossover for continuous search space. Complex systems 9(2), 115–148 (1995)
Deb, K., Goyal, M.: A combined genetic adaptive search (geneas) for engineering design. Computer Science and Informatics 26, 30–45 (1996)
Didi-Biha, M., Marcotte, P., Savard, G.: Path-based formulations of a bilevel toll setting problem. In: Optimization with Multivalued Mappings, pp. 29–50 (2006)
Eichfelder, G.: Multiobjective bilevel optimization. Mathematical Programming 123(2), 419–449 (2010)
Erkut, E., Gzara, F.: Solving the hazmat transport network design problem. Computers & Operations Research 35(7), 2234–2247 (2008)
Fliege, J., Vicente, L.: Multicriteria approach to bilevel optimization. Journal of optimization theory and applications 131(2), 209–225 (2006)
Koh, A.: Solving transportation bi-level programs with differential evolution. In: IEEE Congress on Evolutionary Computation, CEC 2007, pp. 2243–2250. IEEE (2008)
Li, X., Tian, P., Min, X.: A hierarchical particle swarm optimization for solving bilevel programming problems. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 1169–1178. Springer, Heidelberg (2006)
Loridan, P., Morgan, J.: Weak via strong stackelberg problem: New results. Journal of Global Optimization 8, 263–287 (1996), doi:10.1007/BF00121269
Lv, Y., Hu, T., Wang, G., Wan, Z.: A penalty function method based on Kuhn-Tucker condition for solving linear bilevel programming. Applied Mathematics and Computation 188(1), 808–813 (2007)
Oduguwa, V., Roy, R.: Bi-level optimisation using genetic algorithm. In: 2002 IEEE International Conference on Artificial Intelligence Systems (ICAIS 2002), pp. 322–327 (2002)
Or, I.: Traveling salesman-type combinatorial problems and their relation to the logistics of regional blood banking. Northwestern University, Evanston (1976)
Potter, M.A., Jong, K.A.D.: Cooperative coevolution: An architecture for evolving coadapted subcomponents. Evolutionary Computation 8, 1–29 (2000)
Potvin, J., Bengio, S.: The vehicle routing problem with time windows part II: genetic search. INFORMS Journal on Computing 8(2), 165 (1996)
Talbi, E.-G.: Metaheuristics: from design to implementation. Wiley (2009)
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., Grunert da Fonseca, V.: Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)
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Legillon, F., Liefooghe, A., Talbi, EG. (2013). CoBRA: A Coevolutionary Metaheuristic for Bi-level Optimization. In: Talbi, EG. (eds) Metaheuristics for Bi-level Optimization. Studies in Computational Intelligence, vol 482. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37838-6_4
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DOI: https://doi.org/10.1007/978-3-642-37838-6_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37837-9
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