Constructing evolutionary algorithms for bilevel multiobjective optimization

We propose a procedure to construct evolutionary bilevel optimization algorithms based on recent theoretical advances that have established connections between bilevel optimization and multiobjective optimization. In the proposed procedure, a new algorithm is defined by integrating an evolutionary multiobjective optimization algorithm with a partial order that is compatible with bilevel optimization. The advantages of the procedure include the ability to harness the methodology of evolutionary multiobjective optimization for bilevel optimization and to systematically develop new algorithms for single-objective and multiobjective bilevel optimization. No regularity assumptions are used, which ensures maximal applicability of the optimization algorithms constructed by the procedure. The necessary theoretical foundation is developed and the steps of the procedure are illustrated with an example.

[1]  Peter J. Fleming,et al.  On the Evolutionary Optimization of Many Conflicting Objectives , 2007, IEEE Transactions on Evolutionary Computation.

[2]  Johannes Jahn,et al.  Vector optimization - theory, applications, and extensions , 2004 .

[3]  János FÜLÖP.  On the equivalency between a linear bilevel programming problem and linear optimization over the efficient set 0 , 2007 .

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

[5]  Yuping Wang,et al.  A Genetic Algorithm for Multiobjective Bilevel Convex Optimization Problems , 2009, 2009 International Conference on Computational Intelligence and Security.

[6]  Lothar Thiele,et al.  A Preference-Based Evolutionary Algorithm for Multi-Objective Optimization , 2009, Evolutionary Computation.

[7]  Paul H. Calamai,et al.  Bilevel and multilevel programming: A bibliography review , 1994, J. Glob. Optim..

[8]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

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

[10]  S. Dempe.  Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints , 2003 .

[11]  Yoshitsugu Yamamoto,et al.  Optimization over the efficient set: overview , 2002, J. Glob. Optim..

[12]  Patrice Marcotte,et al.  An overview of bilevel optimization , 2007, Ann. Oper. Res..

[13]  Marco Laumanns,et al.  Combining Convergence and Diversity in Evolutionary Multiobjective Optimization , 2002, Evolutionary Computation.

[14]  Kalyanmoy Deb,et al.  An Interactive Evolutionary Multiobjective Optimization Method Based on Progressively Approximated Value Functions , 2010, IEEE Transactions on Evolutionary Computation.

[15]  Günter Rudolph,et al.  Convergence properties of some multi-objective evolutionary algorithms , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[16]  Kalyanmoy Deb,et al.  Solving Bilevel Multi-Objective Optimization Problems Using Evolutionary Algorithms , 2009, EMO.

[17]  Kaisa Miettinen,et al.  Connections Between Single-Level and Bilevel Multiobjective Optimization , 2012, J. Optim. Theory Appl..

[18]  Stephan Dempe,et al.  Foundations of Bilevel Programming , 2002 .

[19]  Yafeng Yin,et al.  Multiobjective bilevel optimization for transportation planning and management problems , 2002 .

[20]  Jonathan F. Bard,et al.  Practical Bilevel Optimization , 1998 .

[21]  Jonathan F. Bard,et al.  Practical Bilevel Optimization: Algorithms and Applications , 1998 .