Application of multiple equilibrium point search in gradient systems to mixed-integer programming
✍ Scribed by Kazuaki Masuda; Kenzo Kurihara
- Publisher
- Wiley (John Wiley & Sons)
- Year
- 2009
- Tongue
- English
- Weight
- 802 KB
- Volume
- 92
- Category
- Article
- ISSN
- 1942-9533
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✦ Synopsis
Abstract
This paper proposes a solution to mixed‐integer programming by using a gradient system and searching for multiple equilibrium points in the system. The method is available when the objective function of a problem is continuous and differentiable. In order to find feasible solutions of a mixed‐integer programming problem by gradient systems, discrete decision variables are treated as continuous ones. We demonstrate a systematic way to build the kind of gradient systems in which equilibrium points are embedded at feasible solutions of a mixed‐integer problem. For numerical computation, the multiple equilibrium points search method we have already proposed is available and its adjustments to improve efficiency and certainty for mixed‐integer programming are also proposed in this paper. Results for some problems show the effectiveness of our method: high ability of thorough search and high quality of derived solutions. © 2009 Wiley Periodicals, Inc. Electron Comm Jpn, 92(8): 53–63, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecj.10037