A Fuzzy Adaptive Simplex Search Optimization Algorithm

Document Type

Article

Publication Date

6-2001

Publication Title

Journal of Mechanical Design

Volume

123

Issue

2

First page number:

216

Last page number:

225

Abstract

Most optimization algorithms use empirically-chosen fixed parameters as a part of their search strategy. This paper proposes to replace these fixed parameters by adaptive ones to make the search more responsive to changes in the problem by incorporating fuzzy logic in optimization algorithms. The proposed ideas are used to develop a new adaptive form of the simplex search algorithm whose objective is to minimize a function of n variables. The new algorithm is labeled Fuzzy Simplex. The search starts by generating a simplex with n + 1 vertices. The algorithm then repeatedly replaces the point with the highest function value by a new point. This process has three components: reflecting the point with the highest function value, expanding, and contracting the simplex. These operations use fuzzy logic controllers whose inputs incorporate the relative weights of the function values at the simplex points. Standard minimization test problems are used to evaluate the efficiency of the algorithm. The Fuzzy Simplex algorithm generally results in a faster convergence. Robustness and sensitivity of the algorithm are also considered. The Fuzzy Simplex algorithm is also applied successfully to several engineering design problems. The results of the Fuzzy Simplex algorithm compare favorably with other available minimization algorithms.

Keywords

Adaptive computing systems; Adaptive systems; Fuzzy algorithms; Fuzzy logic; Nonlinear programming; Optimisation; Search engines — Programming; Search problems

Disciplines

Applied Mathematics | Computer-Aided Engineering and Design | Computer Sciences | Mechanical Engineering | Non-linear Dynamics | Theory and Algorithms

Language

English

Permissions

Use Find in Your Library, contact the author, or interlibrary loan to garner a copy of the item. Publisher policy does not allow archiving the final published version. If a post-print (author's peer-reviewed manuscript) is allowed and available, or publisher policy changes, the item will be deposited.

Publisher Citation

A Fuzzy Adaptive Simplex Search Optimization Algorithm Mohamed B. Trabia and Xiao Bin Lu, J. Mech. Des. 123, 216 (2001), DOI:10.1115/1.1347991

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