基于粒子群算法的单仓储多车物流配送优化

Optimizing multi-car logistics and distribution in single-storage center via particle swarm optimization

为解决单仓储多车物流配送中的带时间窗车辆路径问题(VRP),提出了一种基于粒子群优化(PSO)算法框架的优化算法。针对多数PSO求解算法中普遍存在的编码取整和排序问题,构造了一种基于后继的排位编码方法,并结合编码特点设计了基于"学习"和"变异"的粒子更新方法。首先,种群中的部分粒子发生变异,在解空间进行勘探;然后每个粒子向个体最优和全局最优学习,完成对解空间的开采;最后在反复勘探和开采后种群收敛至最优解。仿真实验中,在适应度值越小越好的前提下,针对相同算例该算法求得最优解的适应度值为979. 98,明显优于参考文献中PSO算法的最优解1 025. 77。同时通过实验分析了参数对算法收敛精度的影响。实验结果表明,所提算法能够有效求解单仓储多车物流配送情境下的带时间窗车辆路径问题,且算法对参数不敏感,可在相对宽泛的区间内自由选取。

An optimization algorithm based on Particle Swarm Optimization(PSO)algorithm framework was proposed to solve the Vehicle Routing Problem(VRP)with time windows in single-storage multi-car logistics and distribution.Concerning the issues of encoding representation-rounding and-sorting widely existing in various PSO-based approaches,a successor-based ranking representation scheme was designed to express the particle entities.Meanwhile,a method for updating the particles based on“learning”and“mutation”was designed in accordance with the characteristics of representation.Firstly,some of the particles went through mutation and explored in the solution space.Secondly each particle learned from personal and global optimal solutions to complete the exploitation of the solution space.Finally,the population converged to the optimal solution after repeated exploration and exploitation.In the simulation experiment,the fitness value obtained by the proposed algorithm was 979.98,which was obviously superior to 1 025.77 of the PSO algorithm in the reference,for the same example and under the premise of the smaller the fitness value the better.In addition,the influence of parameters on the convergence accuracy of the algorithm was analyzed through experiments.The experimental results show that the proposed algorithm can effectively solve the vehicle routing problem with time windows in single-storage multi-car logistics and distribution.Besides,the proposed algorithm is not sensitive to parameters,which can be freely determined from relatively wide intervals.