Unsupervised Learning-Driven Matheuristic for Production-Distribution Problems
针对设施选址、生产和配送紧密耦合的复杂问题，提出一种无监督学习驱动的数学启发式方法，利用线性规划松弛解构建聚类模型并整合遗传算法，在相同计算资源下比商业求解器降低15%总成本，并在200个基准实例中获得152个最优解。
In this paper, we study a capacitated production-distribution problem where facility location, production, and distribution decisions are tightly coupled and simultaneously considered in the optimal decision making. Such an integrated production-distribution problem is complicated, and the current commercial mixed-integer linear programming (MILP) solvers cannot obtain favorable solutions for the medium- and large-sized problem instances. Therefore, we propose an unsupervised learning-driven matheuristic that uses easily obtainable solution values (e.g., solutions associated with the linear programming relaxation) to build clustering models and integrates the clustering information with a genetic algorithm to progressively improve feasible solutions. Then we verify the performance of the proposed matheuristic by comparing its computational results with those of the rolling horizon algorithm, a non-cluster-driven matheuristic, and a commercial MILP solver. The computational results show that, under the same computing resources, the proposed matheuristic can deliver better production-distribution decisions. Specifically, it reduces the total system costs by 15% for the tested instances when compared with the ones found by the commercial MILP solver. Additionally, we apply the proposed matheuristic to a related production-distribution problem in the literature and obtain 152 equivalent or new best-known solutions out of 200 benchmark test instances.