Global optimization of signomial mixed-integer nonlinear programming problems with free variables

Mixed-integer nonlinear programming (MINLP) problems involving general constraints and objective functions with continuous and integer variables occur frequently in engineering design, chemical process industry and management. Although many optimization approaches have been developed for MINLP probl...

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Bibliographic Details
Published in:Journal of global optimization Vol. 42; no. 1; pp. 39 - 49
Main Authors: Tsai, Jung-Fa, Lin, Ming-Hua
Format: Journal Article
Language:English
Published: Boston Springer US 01.09.2008
Springer Nature B.V
Subjects:
Algorithms
Computer Science
Design engineering
Mathematics
Mathematics and Statistics
Methods
Nonlinear programming
Operations Research/Decision Theory
Optimization
Optimization techniques
Real Functions
Solutions
Studies
Variables
Global optimization
Mixed-integer nonlinear programming
Convexification
Free variable
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:Mixed-integer nonlinear programming (MINLP) problems involving general constraints and objective functions with continuous and integer variables occur frequently in engineering design, chemical process industry and management. Although many optimization approaches have been developed for MINLP problems, these methods can only handle signomial terms with positive variables or find a local solution. Therefore, this study proposes a novel method for solving a signomial MINLP problem with free variables to obtain a global optimal solution. The signomial MINLP problem is first transformed into another one containing only positive variables. Then the transformed problem is reformulated as a convex mixed-integer program by the convexification strategies and piecewise linearization techniques. A global optimum of the signomial MINLP problem can finally be found within the tolerable error. Numerical examples are also presented to demonstrate the effectiveness of the proposed method.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-007-9211-8