A differential evolution algorithm with ternary search tree for solving the three-dimensional packing problem

Abstract

The three-dimensional packing problem, which is a strongly NP-hard problem and extremely difficult to solve in practice, is a typical issue in container loading. The container loading problem (CLP) is a combinatorial optimization problem with complex constraints. Its solution process is complicated, and the amount of computation is large. Although some studies used exact algorithms, they could not obtain the optimal solution in a reasonable time. Therefore, heuristic algorithms and intelligent optimization algorithms have become the preferred choice for solving the three-dimensional container loading problem (3D-CLP). Differential evolution algorithm (DE) is an efficient intelligent optimization algorithm, which has remarkable effect in dealing with optimization problems. In this paper, we propose a novel technique that combines a differential evolution algorithm with a ternary search tree model (TSTDE) to solve the 3D-CLP. TSTDE utilizes the ternary tree model to generate a set of suboptimal solutions as the initial population of DE. The improved differential evolution algorithm is used to search the feasible solution of the problem. In this paper, we used the Bischoff and Ratcliff instances to test the TSTDE algorithm, and the results solving the 3D-CLP were compared with those of other advanced algorithms. The experimental results verified the feasibility and superiority of TSTDE in handling the 3D-CLP.