A Self Adaptive Penalty Function Based Genetic Algorithm for value-Bilevel Programming Problem

This paper propose a self adaptive penalty function for solving constrained value-bilevel programming problem using genetic algorithm. This self adaptive penalty function based genetic algorithm both used in the higher level and the lower level problem's solving process. In the constraint handing method, a new fitness value called distance value, in the normalized fitness-constraint violation space, and two penalty values are applied to infeasible individuals so that the genetic algorithm would be able to identify the best infeasible individuals in the current population. The method aims to encourage infeasible individuals with low objective function value and low constraint violation. The number of feasible individuals in the population is used to guide the search process either toward finding more feasible solutions or toward finding the optimum solution. The proposed method is simple to implement and does not need parameter tuning. In this paper using self adaptive penalty function based Genetic Algorithm to solve the leader and the follower optimization module in the value-bilevel optimization problem. The performance of the algorithm is tested on an value-bilevel optimization problem. The results show that the approach is able to find very good solution. Keywords-value-bilevel programming problem; genetic algorithm; constraint handing

[1]  Michel Gendreau,et al.  A hybrid Tabu-ascent algorithm for the linear Bilevel Programming Problem , 1996, J. Glob. Optim..

[2]  Yuren Zhou,et al.  An Adaptive Tradeoff Model for Constrained Evolutionary Optimization , 2008, IEEE Transactions on Evolutionary Computation.

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

[4]  Gary G. Yen,et al.  A generic framework for constrained optimization using genetic algorithms , 2005, IEEE Transactions on Evolutionary Computation.

[5]  G. Anandalingam,et al.  Genetic algorithm based approach to bi-level linear programming , 1994 .

[6]  Abdollah Homaifar,et al.  Constrained Optimization Via Genetic Algorithms , 1994, Simul..

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

[8]  Joaquim Júdice,et al.  A sequential LCP method for bilevel linear programming , 1992, Ann. Oper. Res..

[9]  Yafeng Yin,et al.  Genetic-Algorithms-Based Approach for Bilevel Programming Models , 2000 .

[10]  Andres Angantyr,et al.  Constrained optimization based on a multiobjective evolutionary algorithm , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[11]  Xin Yao,et al.  Search biases in constrained evolutionary optimization , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[12]  K. Deb.  An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

[13]  Jonathan F. Bard,et al.  A Branch and Bound Algorithm for the Bilevel Programming Problem , 1990, SIAM J. Sci. Comput..

[14]  Thomas Bäck,et al.  A Survey of Evolution Strategies , 1991, ICGA.

[15]  Jonathan F. Bard,et al.  Practical Bilevel Optimization: Algorithms and Applications (Nonconvex Optimization and Its Applications) , 2006 .

[16]  Christopher R. Houck,et al.  On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA's , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[17]  Pierre Hansen,et al.  New Branch-and-Bound Rules for Linear Bilevel Programming , 1989, SIAM J. Sci. Comput..

[18]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[19]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[20]  Jonathan A. Wright,et al.  Self-adaptive fitness formulation for constrained optimization , 2003, IEEE Trans. Evol. Comput..