A Novel Approach to Solve Multi-objective Fuzzy Stochastic Bilevel Programming Using Genetic Algorithm

A bilevel programming is a two-level optimization problem, namely, the upper level (leaders) and the lower level (followers). The two level’s decision variables are entwined with each other which increases the complexity to obtain the global solution for both the optimization problems. Each level aims to optimize their own objective function under the given constraints at both the levels. To reduce the complexity partial cooperation between the two levels has been exploited in obtaining the Pareto solution. A novel solution procedure is proposed for a multi-objective fuzzy stochastic bilevel programming (MOFSBLP) problem is studied and solved using genetic algorithm. In this paper, previous information of the lower level is used as a fuzzy stochastic constraints in the upper level along with its constraints. Then with the solution of the combine constraints, the lower level solution is evaluated. The proposed solution procedure is illustrated by a numerical example taken from Zheng et al., and results are compared. A simpler version is solved using GAMs software to analyze the result of the numerical example. The proposed method highlights the importance of partial cooperation in solving bilevel programming problem. The advantage of the proposed solution method is that it creates common constraint space which helps in convergence of the algorithm.