A Fuzzy Adaptive Simplex Search Optimization Algorithm

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.