A dynamic colored traveling salesman problem and its solution

The colored traveling salesman problem (CTSP) is a generalization of the well-known multiple traveling salesman problem (MTSP). In CTSP, each city has one to multiple colors, allowing a salesman in the same color to visit exactly once. This work presents a dynamic CTSP (DCTSP) in which the weights of edges among the cities change over time. To solve the DCTSP, we propose a variable neighborhood search (VNS) algorithm with a direct-route encoding and random initialization. The VNS is initialized by greedy operations at two stages and an appropriate population immigrant scheme is used in it to perform the population search in the dynamic environment. Extensive experiments are conducted to test the effectiveness of the greedy initialization and the immigrant scheme with the best population. The results show that the enhanced VNS can track the environment changes of DCTSP more rapidly and effectively.