Value-at-risk-based fuzzy stochastic optimization problems

A new class of fuzzy stochastic optimization models - two-stage fuzzy stochastic programming with value-at-risk (VaR) criteria is established in this paper. An approximation algorithm is proposed to compute the VaR by combining discretization method of fuzzy variable, random simulation technique and bisection method. The convergence theorem of the approximation algorithm is also proved. To solve the two-stage fuzzy stochastic programming problems with VaR criteria, we integrate the approximation algorithm, neural network (NN) and particle swarm optimization (PSO) algorithm, and hence produce a hybrid PSO algorithm to search for the optimal solution. A numerical example is provided to illustrate the designed hybrid PSO algorithm.