Ant colony optimization with clustering for solving the dynamic location routing problem

Ant colony algorithm can resolve dynamic optimization problems due to its robustness and adaptation. The aim of such algorithms in dynamic environments is no longer to find an optimal solution but to trail it over time. In this paper, a clustering ant colony algorithm (KACO) with three immigrant schemes is proposed to address the dynamic location routing problem (DLRP). The DLRP is divided into two parts constituted by a location allocation problem (LAP) and a vehicles routing problem (VRP) in dynamic environments. To deal with the LAP, a K-means clustering algorithm is used to tackle the location of depots and surrounding cities in each class. Then the ant colony algorithm is utilized to handle the VRP in dynamic environments consisting of random and cyclic traffic factors. Experimental results based on different scales of DLRP instances demonstrate that the clustering algorithm can significantly improve the performance of KACO in terms of the qualities and robustness of solutions. The ultimate analyses of time complexity of all the heuristic algorithms illustrate the efficiency of KACO with immigrants, suggesting that the proposed algorithm may lead to a new technique for tracking the environmental changes by utilizing its clustering and evolutionary characteristics.