A hybrid modified PSO approach to VaR-based facility location problems with variable capacity in fuzzy random uncertainty

This paper studies a facility location model with fuzzy random parameters and its swarm intelligence approach. A Value-at-Risk (VaR) based fuzzy random facility location model (VaR-FRFLM) is built in which both the costs and demands are assumed to be fuzzy random variables, and the capacity of each facility is unfixed but a decision variable assuming continuous values. Under this setting, the VaR-FRFLM is inherently a two-stage mixed 0–1 integer fuzzy random programming problem, to which analytical nonlinear programming methods are not applicable. A hybrid modified particle swarm optimization (MPSO) approach is proposed to solve the VaR-FRFLM. In this hybrid mechanism, an approximation algorithm is utilized to compute the fuzzy random VaR objective, a continuous Nbest–Gbest-based PSO and a genotype–phenotype-based binary PSO vehicles are designed to deal with the continuous capacity decisions and the binary location decisions, respectively, and two mutation operators are incorporated into the PSO to further decrease the possibility of becoming trapped in the local optima. A numerical experiment illustrates the application of the proposed hybrid MPSO algorithm and lays out its robustness to the system parameter settings. The comparison shows that the hybrid MPSO exhibits better performance than that when hybrid regular continuous-binary PSO and genetic algorithm (GA) are used to solve the VaR-FRFLM.