Computer Engineering and Applications ›› 2021, Vol. 57 ›› Issue (2): 237-250.

### Pigeon-Inspired Optimization and Intelligent Water Drops Algorithm for Multiple-objective Vehicle Routing Problem with Multiple Time Windows

MA Long, WANG Chunxi, ZHANG Zhengyi, DONG Rui

1. College of Economical and Management, Xi’an Aeronautical University, Xi’an 710077, China
• Online:2021-01-15 Published:2021-01-14

### 多目标多时间窗车辆路径问题的鸽群-水滴算法

1. 西安航空学院 经济管理学院，西安 710077

Abstract:

According to the problems of the slow convergence and poor calculation accuracy for the vehicle path with time window based on intelligent water drop algorithm, firstly, depending on applying requirement of the vehicle path planning, using integer linear programming methods, a multiple-objectivesand multiple time windows vehicle path model is constructed, taking the minimum transportation cost, the shortest transportation distance and the minimum vehicle number as targets, the vehicle starting point, service point and loading capacity as well as other constraints are comprehensively considered. Secondly, in order to quickly solve this model, a complementary and improved optimization algorithm is proposed which is related to the pigeon inspired optimization and intelligent water drop algorithm, water droplets is discrete binary transformation. The map compass operator and landmark operator are used, flow speed and direction of water droplet are improved, and adaptive variable neighborhood perturbation strategy is employed to interfer the soil amount, improve the development and exploration capabilities of the water droplet algorithm. Finally, the multiple-objectives function and constraint conditions are processed using the ideal point method and the penalty function with multiple-objectives hybrid method, and taking two classic vehicle path with time windows as example, the calculation results of genetic algorithm, intelligent water drop algorithm, and pigeon-water drop algorithm are compared. The results show that the pigeon inspired optimization, water drop algorithm, and the basic water drop algorithm are compared, the transportation path is shorten by about 20 km, and the transportation cost is saved by about 403 yuan under the same algorithm parameters and economic indicators. At same time the solution time and iteration times of the algorithm are also significantly better than the other two artificial intelligence algorithms