Abstract
This paper considers two additional factors of the widely researched vehicle routing problem with time windows (VRPTW). The two factors, which are very common characteristics in realworld, are uncertain number of vehicles and simultaneous delivery and pick‐up service. Using minimization of the total transport costs as the objective of the extension VRPTW, a mathematic model is constructed. To solve the problem, an efficient multiswarm cooperative particle swarm optimization (MCPSO) algorithm is applied. And a new encoding method is proposed for the extension VRPTW. Finally, comparing with genetic algorithm (GA) and particle swarm optimization (PSO) algorithm, the MCPSO algorithm performs best for solving this problem.
Highlights
Vehicle routing problem with time windows VRPTW is an important issue in logistics system which has been researched widely in recent years
We study a case of the VRPTW both with uncertain number of vehicles and simultaneous delivery and pickup service
Vehicle routing problem with time windows VRPTW can be defined as choosing routes for limited number of vehicles to serve a group of customers in the time windows
Summary
Vehicle routing problem with time windows VRPTW is an important issue in logistics system which has been researched widely in recent years. The problem can be described as choosing routes for limited number of vehicles to serve a group of customers in the time windows. Kolen et al 5 described a branchand-bound method Those classical approaches less efficient in solving complex problems. The multiswarm cooperative particle swarm optimization MCPSO was proposed as an improved PSO in 6. We study a case of the VRPTW both with uncertain number of vehicles and simultaneous delivery and pickup service.
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