Range reduction techniques for improving computational efficiency in global optimization of signomial geometric programming problems

► We integrate range reduction techniques for SGP problems to decrease CPU time. ► Proposed algorithm reaches an approximate global solution. ► Numerical experiments are presented to demonstrate the advantages. Many global optimization approaches for solving signomial geometric programming problems...

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Bibliographic Details
Published in:European journal of operational research Vol. 216; no. 1; pp. 17 - 25
Main Authors: Lin, Ming-Hua, Tsai, Jung-Fa
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 2012
Elsevier
Elsevier Sequoia S.A
Subjects:
Algorithms
Applied sciences
Approximation
Computational efficiency
Efficiency
Exact sciences and technology
Geometry
Global optimization
Integer programming
Inverse problems
Linearization
Mathematical models
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization
Optimization algorithms
Piecewise linear function
Programming
Range reduction
Reduction
Signomial geometric programming
Studies
Transformations
Range reduction
Global optimization
Piecewise linear function
Signomial geometric programming
Non convex programming
Inverse transformation
Global optimum
Mixed integer programming
Non linear programming
Convex programming
Optimization
Geometric programming
Computation time
Point process
Linearization techniques
Problem solving
Signomial function
Piecewise linearization
Piecewise-linear techniques
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:► We integrate range reduction techniques for SGP problems to decrease CPU time. ► Proposed algorithm reaches an approximate global solution. ► Numerical experiments are presented to demonstrate the advantages. Many global optimization approaches for solving signomial geometric programming problems are based on transformation techniques and piecewise linear approximations of the inverse transformations. Since using numerous break points in the linearization process leads to a significant increase in the computational burden for solving the reformulated problem, this study integrates the range reduction techniques in a global optimization algorithm for signomial geometric programming to improve computational efficiency. In the proposed algorithm, the non-convex geometric programming problem is first converted into a convex mixed-integer nonlinear programming problem by convexification and piecewise linearization techniques. Then, an optimization-based approach is used to reduce the range of each variable. Tightening variable bounds iteratively allows the proposed method to reach an approximate solution within an acceptable error by using fewer break points in the linearization process, therefore decreasing the required CPU time. Several numerical experiments are presented to demonstrate the advantages of the proposed method in terms of both computational efficiency and solution quality.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2011.06.046