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 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.
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June 2001
Technical Papers
A Fuzzy Adaptive Simplex Search Optimization Algorithm
Mohamed B. Trabia, Professor,
Mohamed B. Trabia, Professor
Department of Mechanical Engineering, University of Nevada, Las Vegas, Las Vegas, NV 89154-4027
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Xiao Bin Lu, Graduate Student
Xiao Bin Lu, Graduate Student
Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, NV 89154-3005
Search for other works by this author on:
Mohamed B. Trabia, Professor
Department of Mechanical Engineering, University of Nevada, Las Vegas, Las Vegas, NV 89154-4027
Xiao Bin Lu, Graduate Student
Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, NV 89154-3005
Contributed by the Design Automation Committee for publication in the Journal of Mechanical Design. Manuscript received Oct. 1999. Associate Editor: A. Diaz.
J. Mech. Des. Jun 2001, 123(2): 216-225 (10 pages)
Published Online: October 1, 1999
Article history
Received:
October 1, 1999
Citation
Trabia, M. B., and Lu, X. B. (October 1, 1999). "A Fuzzy Adaptive Simplex Search Optimization Algorithm ." ASME. J. Mech. Des. June 2001; 123(2): 216–225. https://doi.org/10.1115/1.1347991
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