A multi-compartment vehicle routing problem with time windows for urban distribution - A comparison study on particle swarm optimization algorithms

Abstract In this paper, we introduce a multi-compartment vehicle routing problem with time window (MCVRPTW) arising from urban distribution, which essentially reflects the “last mile” delivery challenge for modern logistics. The distinguishing feature of MCVRPTW is that products must be transported in independent vehicle compartments because they cannot be mixed together due to differences in their characteristics. Based on the mathematical formulation established for the optimization problem, we propose and compare two solution approaches, with one being the hybrid particle swarm optimization (HPSO) with simulated annealing, and the other being the conventional particle swarm optimization (PSO). Based on Solomon's vehicle routing problem with time windows (Solomon, 1987), experimental instances with 25 customers, 50 customers and 100 customers are developed to investigate the performance of the proposed solution approaches. The results indicate that both approaches are reasonably efficient for the MCVRPTW. Moreover, the HPSO algorithm has overall better performance, particularly in delivering the best solution, for all cases, and the HPSO algorithm becomes more efficient than the PSO algorithm as the problem size increases. On the other hand, the PSO algorithm shows a slight edge in terms of the worst solution and standard deviation.