A global search framework for practical three-dimensional packing with variable carton orientations

  • Authors:

  • Yaohua He;Yong Wu;Robert de Souza

  • Affiliations:

  • Department of Industrial and Systems Engineering/Office of the Provost (PVO), National University of Singapore, 117576, Singapore and The Logistics Institute-Asia Pacific, National University of S ...;Department of International Business and Asian Studies, Gold Coast Campus, Griffith University, Qld 4222, Australia;The Logistics Institute-Asia Pacific, National University of Singapore, 119613, Singapore

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2012

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Abstract

This article aims to tackle a practical three-dimensional packing problem, where a number of cartons of diverse sizes are to be packed into a bin with fixed length and width but open height. Each carton is allowed to be packed in any one of the six orientations, and the carton edges are parallel to the bin edges. The allowance of variable carton orientations exponentially increases the solution space and makes the problem very challenging to solve. This study first elaborately devises the packing procedure, which converts an arbitrary sequence of cartons into a compact packing solution and subsequently develops an improved genetic algorithm (IGA) to evolve a set of solutions. Moreover, a novel global search framework (GSF), utilizing the concept of evolutionary gradient, is proposed to further improve the solution quality. Numerical experiments indicate that IGA provides faster and better results and GSF demonstrates its superior performance, especially in solving relative large-size and heterogeneous instances. Applying the proposed algorithms to some benchmarking cases of the three-dimensional strip packing problem also indicates that the algorithms are robust and effective compared to existing methods in the literature.