A Dynamic Colored Traveling Salesman Problem With Varying Edge Weights

A colored traveling salesman problem (CTSP) is a generalization of the well-known multiple traveling salesman problem. In it, each city has one to multiple colors and allows a salesman in the same color to visit exactly once. This work presents for the first time a CTSP whose edge weights among the cities change over time. It can be applied to dynamic routing problems arising in logistic distribution systems with various goods accessibilities to different types of vehicles. A non-linear integer mathematical program is constructed. A Variable Neighborhood Search (VNS) algorithm with a direct-route encoding and random initialization is then presented to solve it. To increase the convergence rate and population diversity of VNS, it is further combined with two-stage greedy initialization and an appropriate population immigrant scheme to perform the population search in a dynamic environment. Then, off-line performance evaluation and Wilcoxon test of the proposed algorithms are performed. The results show that their solution quality is improved by 30% ~ 60% over the basic VNS's. They can track the environmental changes of CTSP-VEW more rapidly and effectively. In the end, a case study with a practical scenario is conducted.