A particle swarm optimization with adaptive multi-swarm strategy for capacitated vehicle routing problem

Capacitated vehicle routing problem with pickups and deliveries (CVRPPD) is one of the most challenging combinatorial optimization problems which include goods delivery/pickup optimization, vehicle number optimization, routing path optimization and transportation cost minimization. The conventional particle swarm optimization (PSO) is difficult to find an optimal solution of the CVRPPD due to its simple search strategy. A PSO with adaptive multi-swarm strategy (AMSPSO) is proposed to solve the CVRPPD in this paper. The proposed AMSPSO employs multiple PSO algorithms and an adaptive algorithm with punishment mechanism to search the optimal solution, which can deal with large-scale optimization problems. The simulation results prove that the proposed AMSPSO can solve the CVRPPD with the least number of vehicles and less transportation cost, simultaneously.