### A Cloud Theory-Based Particle Swarm Optimization for Multiple Decision Maker Vehicle Routing Problems with Fuzzy Random Time Windows

Abstract

This article puts forward a cloud theory-based particle swarm optimization (CTPSO) algorithm for solving a variant of the vehicle routing problem, namely a multiple decision maker vehicle routing problem with fuzzy random time windows (MDVRPFRTW). A new mathematical model is developed for the proposed problem in which fuzzy random theory is used to describe the time windows and bi-level programming is applied to describe the relationship between the multiple decision makers. To solve the problem, a cloud theory-based particle swarm optimization (CTPSO) is proposed. More specifically, this approach makes improvements in initialization, inertia weight and particle updates to overcome the shortcomings of the basic particle swarm optimization (PSO). Parameter tests and results analysis are presented to highlight the performance of the optimization method, and comparison of the algorithm with the basic PSO and the genetic algorithm demonstrates its efficiency.