Global optimization of signomial mixed-integer nonlinear programming problems with free variables |
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Authors: | Jung-Fa Tsai Ming-Hua Lin |
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Institution: | (1) Department of Business Management, National Taipei University of Technology, No. 1, Sec. 3, Chung-Hsiao E. Road, Taipei, 10608, Taiwan;(2) Department of Information Management, Shih Chien University, No. 70, Ta-Chih Street, Taipei, 10462, Taiwan |
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Abstract: | 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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Keywords: | Global optimization Mixed-integer nonlinear programming Free variable Convexification |
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