Heuristic algorithms for the special knapsack packing problem with defects arising in aircraft arrangement

Abstract

This paper addresses a special knapsack packing problem in which identical pieces are packed into an irregular board with unusable regions to maximize the number of pieces. This problem arises from a real-world application in which the aircraft is placed on the carrier’s deck to maximize the number of aircraft. We propose the support polygon concept to solve one of the challenges of the problem, i.e., ensure that the support points inside the piece’s interior are located within the board when the piece protrudes from the board. Many strategies for determining the piece’s location and selecting the rotation angle of the piece are proposed and compared. Based on these techniques, we propose a deterministic heuristic algorithm to solve the problem. In addition, we develop an improved version of the algorithm, called the recursive search heuristic algorithm, to get higher-quality solutions. Many experiments were conducted to test the performance of different combinations of strategies and the proposed algorithms. The computational results show that the proposed algorithms have a strong capacity for obtaining good solutions, and updating many of the best results in the benchmark instances provided by the literature.