Two stage stochastic bilevel programming using Stochastic Systematic Evolutionary(SSE) method

Abstract

Stochastic bilevel programming is a bilevel program having some form of randomness in the problem definition. The main objective is to optimize the leader’s (upper level) stochastic programming problem, where the follower’s problem is assumed to be satisfied as part of the constraints. Evaluation of the solution requires its corresponding lower level optimal reaction for each leader’s action. In addition, due to the existence of randomness property, the problem is computationally so expensive and challenging. In this paper, we considered a two stage stochastic bilevel program and we proposed a new algorithm for solving such kind of problems and the algorithm is checked using constructed test problem. This algorithm is a meta-heuristic type algorithm based on systematical partitioning of upper level decision space for searching the optimal reaction for leader’s action from its own decision space and applying particle swarm optimization for searching a better follower’s reaction. The result of the numerical simulations of the algorithm is very much promising. The algorithm can be used to solve complex stochastic bilevel programming problem.