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