A clustering-based extended genetic algorithm for the multidepot vehicle routing problem with time windows and three-dimensional loading constraints

Abstract

Since the multidepot vehicle routing problem with time windows and three-dimensional loading constraints (MDVRPTW-TDLC) is a multiconstraint and combinatorial optimization problem, this study proposes a resource sharing scheme on the basis of customer clustering to achieve a balance of spatial resource spatial distributions, thereby reducing the operating costs in a collaborative multidepot logistics network. Moreover, this study proposes a vehicle compartment partition strategy based on cargo characteristics such as type and sizes to increase vehicle loading rates, after which the proposed MDVRPTW-TDLC is formulated as a bi-objective mixed-integer programming model to minimize the total operating costs while maximizing the average loading rate of vehicles. Subsequently, a two-stage hybrid algorithm combining a three-dimensional (3D) k-harmonic means clustering algorithm and extended nondominated sorting genetic algorithm-II (ENSGA-II) is developed to find the Pareto optimal solutions and solve the MDVRPTW-TDLC optimization model, followed by an introduction of the 3D k-harmonic means clustering algorithm to cluster customers, thereby reducing computational complexity. The proposed ENSGA-II, integrating the improved Clarke–Wright savings algorithm and NSGA-II is then used to obtain the final optimal solutions, followed by the application of a selective exchange mechanism between the clustering algorithm and ENSGA-II to enhance the global and local optimization capability, enabling fast and efficient computation of optimal solutions. Based on our investigations revealed through an algorithm comparison using the multiobjective harmony search algorithm, multiobjective evolution algorithm, multiobjective particle swarm optimization, monarch butterfly optimization, Runge Kutta optimizer, and Harris hawks optimization, ENSGA-II demonstrates better performance in reaching high-quality objective function values. Finally, a real-world case study of Chongqing City, China is employed to verify the efficiency of the proposed model and optimization algorithm, after which a comparison of the optimization results among different vehicle compartment partition strategies demonstrates the efficiency of the proposed method. We also discuss 16 scenarios with and without the vehicle compartment partition strategy with computational results showing an improved vehicle loading rate and reduced logistics operating costs with the adopted vehicle compartment partition strategy. Therefore, our results confirm that the proposed MDVRPTW-TDLC can facilitate the sustainable development of logistics operations, and providing decision support for constructing intelligent logistics systems smart cities.