A unified hyper-heuristic framework for solving bin packing problems

One-and two-dimensional packing and cutting problems occur in many commercial contexts, and it is often important to be able to get good-quality solutions quickly. Fairly simple deterministic heuristics are often used for this purpose, but such heuristics typically find excellent solutions for some problems and only mediocre ones for others. Trying several different heuristics on a problem adds to the cost. This paper describes a hyper-heuristic methodology that can generate a fast, deterministic algorithm capable of producing results comparable to that of using the best problem-specific heuristic, and sometimes even better, but without the cost of trying all the heuristics. The generated algorithm handles both one-and two-dimensional problems, including two-dimensional problems that involve irregular concave polygons. The approach is validated using a large set of 1417 such problems, including a new benchmark set of 480 problems that include concave polygons. Finding an arrangement of pieces to cut or pack inside larger objects is known as the cutting and packing problem. Besides the academic interest in this NP-hard problem, there are numerous industrial applications of its many variants. The one-dimensional (1D) and two-dimensional (2D) bin packing problems (BPPs) are particular cases of the cutting and packing problem. The 1D BPP can be applied, for example, to the assignment of commercial breaks on television and for copying a collection of files to disks (Bhatia, Hazra, & Basu, 2009). For the 2D BPP, the case of rectangular pieces is the most widely studied. However, the irregular case is seen in a number of industries where parts with irregular shapes are cut from rectangular materials. For instance, in the shipbuilding industry, plate parts with free-form shapes for use in the inner frameworks of ships are cut from rectangular steel plates, and in the garment industry, parts of clothes and shoes are cut from fabric or leather (Okano, 2002). Other applications include the optimization of layouts within the wood, sheet metal, plastics, and glass industries (Burke, Hellier, Kendall, & Whitwell, 2006). In these industries, improvements of the arrangement can result in a large saving of material (Hu-yao & Yuan-jun, 2006). Hyper-heuristics aim at automating the design of heuristic methods to solve difficult search problems and providing a more general procedure for optimizationheuristics differ from the widely-used term meta-heuristic: instead of searching within the space of solutions, they explore the space of heuristics (Vázquez-Rodríguez, Petrovic, & Salhi, 2007; Pappa et al., 2013). The idea is to …