Analysis of solution representation for the irregular shape packing problem

Bennell, J.A., Khaled, M. and Ramakrishnan, K. (2009) Analysis of solution representation for the irregular shape packing problem (Discussion Papers in Centre for Operational Research, Management Science and Information Systems, CORMSIS-09-14) Southampton, UK. University of Southampton

Abstract

The irregular shape-packing problem has received increasing attention over the last 15 years. An analysis of the solution methods identifies two main approaches for representing the solution. These are, representing the solution as a sequence of pieces and searching over the sequence while applying a placement heuristic to generate the layout, and representing the problem as the layout directly and searching by moving pieces over the layout. Both approaches are competitive and each new publication brings better result with respect to the benchmark data sets. These improvements can be credited to better algorithm design and the inclusion of problem specific features, but as a result it is difficult to identify the effect some of the basic design decisions have on solution quality. We intend to investigate these two approaches and establish some principles of the strengths and weaknesses and gain a better understanding of how these solution representations impact solution quality and the effectiveness of the search. The algorithms have been developed using only the basic principles of both approaches and discarding any special features found in the literature

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