A hybrid matheuristic approach for the vehicle routing problem with three-dimensional loading constraints

Abstract

This paper proposes a matheuristic algorithm based on a column generation structure for the capacitated vehicle routing problem with three-dimensional loading constraints (3L–CVRP). In the column generation approach, the master problem is responsible for managing the selection of best-set routes. In contrast, the slave problem is responsible for solving a shorter restricted route problem (CSP, Constrained Shortest Path) for generating columns (feasible routes). The CSP is not necessarily solved to optimality. In addition, a greedy randomized adaptive search procedure (GRASP) algorithm is used to verify the packing constraints. The master problem begins with a set of feasible routes obtained through a multi-start randomized constructive algorithm (MSRCA) heuristic for the multi-container loading problem (3D–BPP, three-dimensional bin packing problem). The MSRCA consists of finding valid routes considering the customers' best packing (packing first-route second). The efficiency of the proposed approach has been validated by a set of benchmark instances from the literature. The results show the efficiency of the proposed approach and conclude that the slave problem is too complex and computationally expensive to solve through a MIP.

Optimizing Heterogeneous Vehicle Routes for Urban Distribution Considering the Three-Dimensional Bin Packing Problem of Electric Meters

“…D. A. A. Rodríguez [26] introduced a mathematical algorithm based on column generation structure is proposed to solve the problem of complex and computational cost of 3L-CVRP, which cannot be solved by MIP. B. Rezaei [27] in order to further optimize the search process, a hybrid genetic search algorithm is applied as an enhanced local search and population management strategy within the algorithm framework, which significantly improves the computational efficiency.…”