Simulated annealing for the vehicle routing problem with two-dimensional loading constraints

This paper addresses the capacitated vehicle routing problem with twodimensional loading constraints (2L-CVRP). The 2L-CVRP is a combination of the two most important problems in distribution logistics, which are loading of freight into vehicles, and the successive routing of the vehicles to satisfy customer demand. The objective is to minimize the transportation cost. All vehicles must start and terminate at a central depot, and the transported items carried by the vehicles must be feasibly packed into the loading surfaces of the vehicles. A simulated annealing algorithm to solve the problem is presented, in which the loading component of the problem is solved through a collection of packing heuristics. A novel approach to plan packing is employed. An efficient data structure (Trie) is used to accelerate the algorithm. The extensive computational results prove the effectiveness of the algorithm.