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

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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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Authors and Affiliations

  1. Department of Business Management, National Taipei University of Technology, No. 1, Sec. 3, Chung-Hsiao E. Road, Taipei, 10608, Taiwan

    Jung-Fa Tsai

  2. Department of Information Management, Shih Chien University, No. 70, Ta-Chih Street, Taipei, 10462, Taiwan

    Ming-Hua Lin

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  1. Jung-Fa Tsai
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  2. Ming-Hua Lin
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Correspondence to Ming-Hua Lin.

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Tsai, JF., Lin, MH. Global optimization of signomial mixed-integer nonlinear programming problems with free variables. J Glob Optim 42, 39–49 (2008). https://doi.org/10.1007/s10898-007-9211-8

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  • DOI: https://doi.org/10.1007/s10898-007-9211-8

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