An improved hybrid particle swarm optimization algorithm for fuzzy p-hub center problem

The p-hub center problem is useful for the delivery of perishable and time-sensitive system such as express mail service and emergency service. In this paper, we propose a new fuzzy p-hub center problem, in which the travel times are uncertain and characterized by normal fuzzy vectors. The objective of our model is to maximize the credibility of fuzzy travel times not exceeding a predetermined acceptable efficient time point along all paths on a network. Since the proposed hub location problem is too complex to apply conventional optimization algorithms, we adapt an approximation approach (AA) to discretize fuzzy travel times and reformulate the original problem as a mixed-integer programming problem subject to logic constraints. After that, we take advantage of the structural characteristics to develop a parametric decomposition method to divide the approximate p-hub center problem into two mixed-integer programming subproblems. Finally, we design an improved hybrid particle swarm optimization (PSO) algorithm by combining PSO with genetic operators and local search (LS) to update and improve particles for the subproblems. We also evaluate the improved hybrid PSO algorithm against other two solution methods, genetic algorithm (GA) and PSO without LS components. Using a simulated data set of 10 nodes, the computational results show that the improved hybrid PSO algorithm achieves the better performance than GA and PSO without LS in terms of runtime and solution quality.