Generalized hyper-heuristics for solving 2D Regular and Irregular Packing Problems

Abstract

The idea behind hyper-heuristics is to discover some combination of straightforward heuristics to solve a wide range of problems. To be worthwhile, such a combination should outperform the single heuristics. This article presents a GA-based method that produces general hyper-heuristics that solve two-dimensional regular (rectangular) and irregular (convex polygonal) bin-packing problems. A hyper-heuristic is used to define a highlevel heuristic that controls low-level heuristics. The hyper-heuristic should decide when and where to apply each single low-level heuristic, depending on the given problem state. In this investigation two kinds of heuristics were considered: for selecting the figures (pieces) and objects (bins), and for placing the figures into the objects. Some of the heuristics were taken from the literature, others were adapted, and some other variations developed by us. We chose the most representative heuristics of their type, considering their individual performance in various studies and also in an initial experimentation on a collection of benchmark problems. The GA included in the proposed model uses a variable-length representation, which evolves combinations of condition-action rules producing hyper-heuristics after going through a learning process which includes training and testing phases. Such hyperheuristics, when tested with a large set of benchmark problems, produce outstanding results for most of the cases. The testbed is composed of problems used in other similar studies in the literature. Some additional instances for the testbed were randomly generated.

Contrasting meta-learning and hyper-heuristic research: the role of evolutionary algorithms

“…We first describe the work of [113], where the hyper-heuristic selects heuristics for the regular and irregular two dimensional strip packing problems. In this study, the solutions are constructed by packing one item at a time.…”

“…The hyper-heuristic represents a set of mappings from states to one of the 40 heuristics. This mapping is evolved with a genetic algorithm [113]. An interesting point here is the way the fitness of the GA is calculated.…”

An effective heuristic for the two-dimensional irregular bin packing problem

“…For the 2D irregular BPP, where pieces to be placed are convex polygons, DJD has been implemented as a member of a heuristic repository in a hyper-heuristic approach (Terashima-Marín et al 2010). To our knowledge, DJT has not been implemented for the 2D irregular BPP.…”

“…Each position in the Fig. 8 Candidate rectangles when locating a piece (Terashima-Marín et al 2010) list is evaluated twice: the piece starts in the initial position and its adjacency (i.e., the common boundary between its perimeter and the placed pieces and the object edges) is computed. Then, the piece is slid down and left and the adjacency is computed again.…”

“…The benchmark instances in our study were produced by the generator proposed by Terashima-Marín et al (2010). The generated pieces are convex irregular polygons with a number of sides between 3 and 8.…”