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Finding multiple optimal solutions of signomial discrete programming problems with free variables

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Abstract

With the increasing reliance on mathematical programming based approaches in various fields, signomial discrete programming (SDP) problems occur frequently in real applications. Since free variables are often introduced to model problems and alternative optima are practical for decision making among multiple strategies, this paper proposes a generalized method to find multiple optimal solutions of SDP problems with free variables. By means of variable substitution and convexification strategies, an SDP problem with free variables is first converted into another convex mixed-integer nonlinear programming problem solvable to obtain an exactly global optimum. Then a general cut is utilized to exclude the previous solution and an algorithm is developed to locate all alternative optimal solutions. Finally, several illustrative examples are presented to demonstrate the effectiveness of the proposed approach.

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Authors and Affiliations

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

    Ming-Hua Lin

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

    Jung-Fa Tsai

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

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Lin, MH., Tsai, JF. Finding multiple optimal solutions of signomial discrete programming problems with free variables. Optim Eng 12, 425–443 (2011). https://doi.org/10.1007/s11081-011-9137-3

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  • DOI: https://doi.org/10.1007/s11081-011-9137-3

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