A systematic sampling evolutionary (SSE) method for stochastic bilevel programming problems

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. Due to the involvement of randomness property and the hierarchical nature of the optimization procedure, the problem is computationally expensive and challenging. In this paper, a new meta-heuristic type algorithm is proposed that can effectively solve stochastic bilevel programs. The algorithm is based on realizing the random space, systematic sampling technique to choose a representative action from the leader's decision space and on a hybrid particle swarm optimization procedure for searching its corresponding follower's reaction for each leader's action until Stackelberg equilibrium is achieved. The algorithm is shown to be convergent and its performance is checked using test problems from literature. The simulation result of the algorithm is very much promising and can be used to solve complex stochastic bilevel programming problems.