CoBRA: A Coevolutionary Metaheuristic for Bi-level Optimization

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.

[1]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[2]  D. White,et al.  A solution method for the linear static Stackelberg problem using penalty functions , 1990 .

[3]  Andrew Koh Solving transportation bi-level programs with Differential Evolution , 2007, 2007 IEEE Congress on Evolutionary Computation.

[4]  Samy Bengio,et al.  The Vehicle Routing Problem with Time Windows Part II: Genetic Search , 1996, INFORMS J. Comput..

[5]  Patrice Marcotte,et al.  Path-based formulations of a bilevel toll setting problem , 2006 .

[6]  Rajkumar Roy,et al.  Bi-level optimisation using genetic algorithm , 2002, Proceedings 2002 IEEE International Conference on Artificial Intelligence Systems (ICAIS 2002).

[7]  Gabriele Eichfelder,et al.  Multiobjective bilevel optimization , 2010, Math. Program..

[8]  L. N. Vicente,et al.  Multicriteria Approach to Bilevel Optimization , 2006 .

[9]  Herminia I. Calvete,et al.  A Multiobjective Bilevel Program for Production-Distribution Planning in a Supply Chain , 2008, MCDM.

[10]  Ryszard Tadeusiewicz,et al.  Artificial Intelligence and Soft Computing - ICAISC 2006, 8th International Conference, Zakopane, Poland, June 25-29, 2006, Proceedings , 2006, International Conference on Artificial Intelligence and Soft Computing.

[11]  Jacqueline Morgan,et al.  Weak via strong Stackelberg problem: New results , 1996, J. Glob. Optim..

[12]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[13]  Kalyanmoy Deb,et al.  A combined genetic adaptive search (GeneAS) for engineering design , 1996 .

[14]  Tiesong Hu,et al.  A penalty function method based on Kuhn-Tucker condition for solving linear bilevel programming , 2007, Appl. Math. Comput..

[15]  Erhan Erkut,et al.  Solving the hazmat transport network design problem , 2008, Comput. Oper. Res..

[16]  Kenneth A. De Jong,et al.  Cooperative Coevolution: An Architecture for Evolving Coadapted Subcomponents , 2000, Evolutionary Computation.

[17]  Charles E. Blair,et al.  Computational Difficulties of Bilevel Linear Programming , 1990, Oper. Res..

[18]  El-Ghazali Talbi,et al.  Metaheuristics - From Design to Implementation , 2009 .

[19]  Xiangyong Li,et al.  A Hierarchical Particle Swarm Optimization for Solving Bilevel Programming Problems , 2006, ICAISC.

[20]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[21]  G. Laporte,et al.  A tabu search heuristic for periodic and multi-depot vehicle routing problems , 1997, Networks.