A superior linearization method for signomial discrete functions in solving three-dimensional open-dimension rectangular packing problems

This article studies the three-dimensional open-dimension rectangular packing problem (3D-ODRPP) in which a set of given rectangular boxes is packed into a large container of minimal volume. This problem is usually formulated as a mixed-integer nonlinear programming problem with a signomial term in...

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Bibliographic Details
Published in:Engineering optimization Vol. 49; no. 5; pp. 746 - 761
Main Authors: Lin, Ming-Hua, Tsai, Jung-Fa, Chang, Shu-Chuan
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 04.05.2017
Taylor & Francis Ltd
Subjects:
Computational efficiency
Containers
Discrete functions
global optimization
Integer programming
Linear programming
linearization
Mathematical models
nonlinear integer programming
Nonlinear programming
Optimization
signomial term
Three-dimensional open-dimension rectangular packing problem
Transformations
ISSN:0305-215X, 1029-0273
Online Access:Get full text
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Summary:This article studies the three-dimensional open-dimension rectangular packing problem (3D-ODRPP) in which a set of given rectangular boxes is packed into a large container of minimal volume. This problem is usually formulated as a mixed-integer nonlinear programming problem with a signomial term in the objective. Existing exact methods experience difficulty in solving large-scale problems within a reasonable amount of time. This study reformulates the original problem as a mixed-integer linear programming problem by a novel method that reduces the number of constraints in linearizing the signomial term with discrete variables. In addition, the range reduction method is used to tighten variable bounds for further reducing the number of variables and constraints in problem transformation. Numerical experiments are presented to demonstrate that the computational efficiency of the proposed method is superior to existing methods in obtaining the global optimal solution of the 3D-ODRPP.
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ISSN:0305-215X
1029-0273
DOI:10.1080/0305215X.2016.1211403