Capacitated profitable tour problem with cross-docking

This paper addresses a real-world transportation problem arising from Industrial Internet platforms, where logistics companies selectively respond to requests for shipping products from manufacturers to customers. We formulate the problem as the capacitated profitable tour problem with cross-docking (CPTPC), which involves not only the selection of requests based on profit, but also the planning of vehicle routes with respect to capacitated constraints. The CPTPC, a generalization of the profitable tour problem and the vehicle routing problem with cross-docking, presents significant computational complexity. In this paper, we propose an effective hybrid genetic algorithm (HGA) tailored to address the problem. The algorithm integrates a dedicated two-level edge assembly crossover operator to generate promising offspring solutions. Additionally, it incorporates a streamlined technique-driven local search approach to improve each solution. Empirical evaluations showcase the robust performance of the algorithm on benchmark instances, and experimental analyses provide insights into the key search components inherent in the proposed algorithm. In addition, we conduct a case study to assess the practical utility of our HGA in improving the operational efficiency and profitability of logistics companies.