Capacitated Colored Traveling Salesman Problem With Time Windows

Abstract

This work proposes a variant of Colored Traveling Salesman Problem (CTSP) called Capacitated Colored-traveling-salesman Problem with Time-windows (CCPT), which comes from time-sensitive logistics applications. CCPT is first formulated via mathematical programming formulations, and an Elite-guided Memetic Algorithm (EMA) is developed to tackle it. EMA is able to preserve an active archive of elites during an evolution process. It comprises three schemes, i.e., neighborhood-list-2-opt, relocation move, and cross-arc exchange. They are organized in a variable neighborhood descent framework to optimize a specific high-quality individual. Ablation studies fully show their importance for EMA’s performance. 28 CCPT cases are designed based on representative traveling salesman problem instances to conduct benchmark tests. The statistical comparison shows that EMA is significantly better than Variable Neighborhood Search (VNS), Delaunay-triangulation-based VNS, local search, and memetic algorithm in over 85% of the cases. It achieves faster convergence to the solutions than its competitors.Note to Practitioners—This work is motivated by practical needs for distribution logistics with time-sensitive requirements. A capacitated colored-traveling-salesman problem with time-windows is modeled and can be applied to time-sensitive transportation tasks with multiple goods. An elite-guided memetic algorithm is developed to tackle this problem. It executes the local optimization on a specific high-quality solution during the search process. Extensive comparisons demonstrate that the proposed algorithm can provide decision-makers with significantly better routes than other state-of-the-art algorithms.