A neighborhood comprehensive learning particle swarm optimization for the vehicle routing problem with time windows

Vehicle routing problem with time windows (VRPTW), which is a typical NP-hard combinatorial optimization problem, plays an important role in modern logistics and transportation systems. Recent years, heuristic and meta-heuristic algorithms have attracted many researchers' attentions to solve the VRPTW problems. As an outstanding meta-heuristic algorithm, particle swarm optimization (PSO) algorithm exhibits very promising performance on continuous problems. However, how to adapt PSO to efficiently deal with VRPTW is still challenging work. In this paper, we propose a neighborhood comprehensive learning particle swarm optimization (N-CLPSO) to solve VRPTW. To improve the exploitation capability of N-CLPSO, we introduce a new remove-reinsert neighborhood search mechanism, which consists of the removed operator and the reinsert operator. When performing the removed operator, the probability of adjacency between two customers is calculated by an information matrix (IM), which is constructed based on the customers' time-space information and elite individuals' local information. When executing the reinsert operator, the IM and a cost matrix (CM), which is introduced to record the cost of customer insertion, are used to find an optimal insert position. Moreover, to enhance the exploration of N-CLPSO, a semi-random disturbance strategy is proposed, in which elites' longest common sequences (LCS) are saved, aiming to prevent population degradation. The N-CLPSO algorithm is tested on 56 Solomon benchmark instances, and it attains the optimal solutions on 29 instances. The simulation results and comparison results illustrate that the proposed algorithm outperforms or can compete with the majority of other 3 PSO variants as well as other 12 state-of-the-art algorithms.