The knowledge-driven adaptive late acceptance iterative hill-climbing heuristics for the bus and ADR collaborative delivery problem

Urban-rural bus transit services encounter a dilemma between the necessity for enhanced services and the challenge of low profitability due to scant travel demand. Combining freight transportation with passenger services can enhance the efficiency and profitability of buses in both urban and rural areas, while also reducing environmental impacts. A case in point is the integration of freight deliveries into rural bus networks in China. Concurrently, with the advancement of autonomous delivery robot (ADR) technology, there is a growing deployment of ADRs for last-mile delivery purposes. In this paper, we have studied a new collaborative passenger and freight transportation problem involving buses and ADRs, namely, the bus and ADR collaborative delivery problem (BACDP). In this scenario, a bus route transports several ADRs, which carry multiple parcels, to distribution regions for door-to-door delivery, each ADR boards a bus to reach the sub-region and then boards another bus to return to the distribution center. We have proposed a mathematical model for BACDP, which can be decomposed into a master problem and a sub-problem. and the condition that the optimal solution to the master problem is also the optimal solution to the original problem has been proved. To tackle the BACDP effectively, we designed a novel three-stage iterative method, guided by adaptive late acceptance hill-climbing heuristics (ALAHH). Specifically, at the first stage, the k-means++ and Hamiltonian graph-guided algorithms are used to cluster customers; at the second stage, the variable neighborhood search plans the ADRs’ routes; at the third stage, we utilize the solver to address subproblems, and the evaluation and invocation mechanism is proposed to achieve the efficient utilization of solvers. Extensive experiments have been conducted on synthetic instances of varying scales to investigate the efficiency of ALAHH. The experimental results demonstrate that the objective values and the computation time are significantly lower than those of SA and LAHC, and our algorithm has achieved the best solutions for 16 problems to date. Additionally, the impacts of two key parameters and mechanisms have been analyzed, and further validation of the robustness of the algorithm parameters and the effectiveness of the mechanisms.