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Global optimization of mixed-integer polynomial programming problems: A new method based on Grobner bases theory

Credit to Download: 1 | Page Numbers 13 | Abstract Views: 139
Year: 2017
COI code: IIEC14_057
Paper Language: English

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Authors Global optimization of mixed-integer polynomial programming problems: A new method based on Grobner bases theory

  Ali papi - MSc, Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
  armin Jabbarzadeh - Assistant Professor, Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
  Adel Aazami - PhD Candidate, Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

Abstract:

Mixed-integer polynomial programming (MIPP) problems are one class of mixed-integer nonlinear programming (MINLP)problems where objective function and constraints are restricted to the polynomial functions. Although the MINLP problem is NPhard, in special cases such as MIPP problems, an efficient algorithm can be extended to solve it. In this research, we propose an algorithm for global optimization of the MIPP problems, in which, first, the MIPP is reformulated as a multi-parametric programming by considering integer variables as parameters. Then, the optimality conditions of resulting parametric programming give a parametric polynomial equations system (PES) that is solved analytically by Grobner bases (GB) theory. After solving PES, the parametric optimal solution as a function of the relaxed integer variables is obtained. A simple discrete optimization problem is resulted for any non-imaginary parametric solution of PES, which the global optimum solution of MIPP is determined by comparing their optimal value. Some numerical examples are provided to clarify proposed algorithm and extend it for solving the MINLP problems. Finally, a performance analysis is conducted to demonstrate the practical efficiency of the proposed method.

Keywords:

Mixed-integer polynomial programming (MIPP), parametric programming, Polynomial equations system (PES), Grobner bases theory

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COI code: IIEC14_057

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papi, Ali; armin Jabbarzadeh & Adel Aazami, 2017, Global optimization of mixed-integer polynomial programming problems: A new method based on Grobner bases theory, 14th International Industrial Engineering Conference, تهران, انجمن مهندسي صنايع ايران - دانشگاه علم و صنعت ايران, https://www.civilica.com/Paper-IIEC14-IIEC14_057.htmlInside the text, wherever referred to or an achievement of this article is mentioned, after mentioning the article, inside the parental, the following specifications are written.
First Time: (papi, Ali; armin Jabbarzadeh & Adel Aazami, 2017)
Second and more: (papi; Jabbarzadeh & Aazami, 2017)
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Type: state university
Paper No.: 20366
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