An Evolutionary Scatter Search Particle Swarm Optimization Algorithm for the Vehicle Routing Problem With Time Windows

Vehicle routing problem with time windows (VRPTW) contains two crucial objectives: minimizing the number of vehicles and minimizing the total travel distance. However, most algorithms focus on the number of vehicles, while the travel distance should be considered as the primary objective in some practical situations, especially in the modern logistics. Research has shown that designing a systematic framework to combine multiple algorithms with different characteristics will significantly improve the overall performance of the hybrid algorithm. This paper proposes an evolutionary scatter search particle swarm optimization algorithm (ESS-PSO) to solve the VRPTW with the objective of minimizing the total travel distance. In ESS, a genetic algorithm and a new “route+/−” evolutionary operator are introduced in scatter search template. In addition, we proposed a discrete PSO that sets the route-segment as the velocity of particles and in which the velocity and position updating rules are designed based on the concept of “ruin and recreate.” These two algorithms work in a cascade learning architecture, in which PSO learns from the exemplary solutions in the reference set maintained by ESS. The search direction of the algorithm is adjusted by analyzing the relationship between the number of vehicles and the total travel distance in real time. We designed a new solution representation called “auxiliary code” based on customer allocation to maintain the diversity of the reference set. Experiments with the Solomon benchmark show that ESS-PSO is effective and efficient, and it achieves very competitive results, especially in the datasets of the category “2.”