LAUSR

Abstract The two-echelon collaborative multiple centers vehicle routing problem (2E-CMCVRP) integrates collaboration mechanism and the vehicle routing problem. Combining k-means clustering algorithm and an improved Non-dominated Sorting Genetic Algorithm-II (Im-NSGA-II), this paper proposes a three-phase approach to simultaneously minimize the aggregate operating cost and reduce carbon dioxide emission. To ensure the initial population's quality, the sweep algorithm is integrated as modification of the standard NSGA-II. The chromosome population consists of multiple depots and corresponding customer nodes independently assessed to find local solutions, and latterly combined to yield suboptimal routes. The nodes scan principle of the sweep algorithm is employed to enforce optimization constraints, and the non-dominated sorting of the population efficiently improves the solution search accuracy. Further, the Minimum Cost-Remaining Savings (MCRS) method is used to determine appropriate profit distribution schemes, and the selection of the optimal sequential coalition is executed on the basis of the strictly monotonic path principle. Computational comparisons on benchmark instances indicate the superiority of Im-NSGA-II over NSGA-II and MOGA, and an empirical study in Chongqing, China confirms the practicability of our solution approach. The evaluation of MCRS solution's stability displays outperformance over other methods including the Shapley value model, CGA and GQP, and suitable coalition sequences are selected and assessed to improve the efficiency of logistics network optimization as well as the achievement of environment-friendly objectives.