A Genetic Algorithm for Multiobjective Bilevel Convex Optimization Problems

Multiobjective bilevel programming problem (MBPP) has a wide field of applications and has been proven to be an NP-hard problem. In this paper, a special multiobjective bilevel convex programming problem (MBCPP) is studied, and it is first transformed into an equivalent single objective bilevel convex programming problem by weighted sum of objectives. Then, for the equivalent problem, we design a scheme for generating weight vectors. Thereafter, a crossover operator and mutation operator are designed. Based on all these, a genetic algorithm called Ga-BCPP is proposed for MBCPP. At last, the simulation is made and the performance of the proposed algorithm is compared with one peer genetic algorithm. The results show that the proposed algorithm is effective.

[1]  U. Kirsch,et al.  Two-level optimization of prestressed structures , 1997 .

[2]  Mitsuo Gen,et al.  Genetic algorithms and engineering design , 1997 .

[3]  Nataliya I. Kalashnykova,et al.  Optimality conditions for bilevel programming problems , 2006 .

[4]  Teng Chun.  A Class of Genetic Algorithms on Bilevel Multi-objective Decision Making Problem , 2000 .

[5]  Mahyar A. Amouzegar,et al.  Determining optimal pollution control policies: An application of bilevel programming , 1999, Eur. J. Oper. Res..

[6]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[7]  Z. Michalewicz,et al.  A modified genetic algorithm for optimal control problems , 1992 .

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

[9]  G. Eichfelder.  Solving Nonlinear Multiobjective Bilevel Optimization Problems with Coupled Upper Level Constraints , 2007 .

[10]  Hai Yang,et al.  Traffic assignment and signal control in saturated road networks , 1995 .

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

[12]  M. Sakawa,et al.  Stackelberg Solutions to Multiobjective Two-Level Linear Programming Problems , 1999 .

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

[14]  J. Clegg,et al.  Bilevel programming applied to optimising urban transportation , 2001 .

[15]  Patrice Marcotte,et al.  Bilevel programming: A survey , 2005, 4OR.

[16]  S. Dempe,et al.  Optimality conditions for bilevel programming problems , 2006 .

[17]  Yuping Wang,et al.  U-measure: a quality measure for multiobjective programming , 2003, IEEE Trans. Syst. Man Cybern. Part A.

[18]  J. Morgan,et al.  Semivectorial Bilevel Optimization Problem: Penalty Approach , 2006 .