Robust optimization approach in a competitive vehicle routing problem in an uncertain condition by using improved differential evolution

A vehicle routing problem (VRP) is an important issue that has attracted great attention of researchers in recent years. This paper presents a competitive VRP to get short routes with the maximum sale by providing suitable services to customers before delivering the goods to other competitive distributors. To distribute the goods with a short lifetime, in which customers need a special device for keeping them, the arriving time to customers effects on a number of sales, in which classical VRPs are unable to calculate these kinds of assumptions. According to the real world, the arriving time of the competitors is uncertain because of customer demands, traffic, weather conditions, etc. A scenario-based approach is used to handle the uncertainty of the arriving time of rivals. The purpose of this paper is to solve this problem by optimizing the sale of products to customers before delivering the products to other competitor distributors in an uncertain condition by robust optimization. To evaluate the performance of the presented model, the improved differential evolution (IDE) algorithm is used. The related results in small and medium-sized problems are compared with the result obtained by an exact solution method. Additionally, in order to evaluate the performance of the proposed IDE algorithm, a few sample tests in large sizes are solved and their results are compared with other two differential evolution algorithms. The results show that the proposed IDE algorithm has a suitable accuracy and performance for solving the presented model.