An Efficient Quasi-Human Heuristic Algorithm for Solving the Rectangle-Packing Problem

Abstract

Rectangle-packing problem involves many industrial applications. For example, in shipping industry, various size boxes have to be loaded as many as possible in a larger container. In wood or glass industries, rectangular components have to be cut from large sheets of material. In very large scale integration (VLSI) floor planning, various chips have to be laid on the chip board, and so on. The rectangle-packing problem belongs to a subset of classical cutting and packing problems and has shown to be NP hard (Leung et al., 1990). For more extensive and detailed descriptions of packing problem, please refer to Lodi et al. (2002) and Pisinger (2002). Various algorithms based on different strategies have been suggested to solve this problem. In general, these algorithms can be classified into two major categories: non-deterministic algorithms and deterministic algorithms. The key aspect of nondeterministic algorithms, such as simulated annealing and genetic algorithm (Hopper & Turton, 1999; Bortfeldt, 2006), is to design data structure that can represent the topological relations among the rectangles. The key aspect of deterministic algorithms is to determine the packing rules, such as less flexibility first principle (Wu et al., 2002). Optimal algorithm for orthogonal two-dimensional cutting is proposed in Beasley (1985), but it might not be practical for large scale problems. In order to improve the quality of solution, some scholars combine genetic algorithm or simulated annealing with deterministic method and obtain hybrid algorithms (Liu & Teng, 1999; Leung et al., 2003). Some heuristic and meta-heuristic algorithms are also presented in literatures(Lodi et al., 1999; Hopper & Turton, 2001; Zhang et al., 2005; Burke et al., 2004). In recent years, some people began to formalize the wisdom and experience of human being and obtain the quasihuman heuristic algorithms (Huang & Jin, 1997; Huang & Xu, 1999; Wu et al., 2002; Huang et al., 2007). The “quasi-human” tries to simulate the behavior of human being in related special work such as bricklaying. Huang et al. (2007) presented a heuristic algorithm based on two important concepts, namely, the corner-occupying action and caving degree. Based on Huang et al. (2007), an efficient quasi-human heuristic algorithm (QHA) for solving rectangle-packing problem is proposed on the basis of the wisdom and experience of human being in this paper. The O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m