Successive Twinkling Simplex Search Optimization Algorithms

Abstract

Abstract Simplex algorithms have been proven to be a reliable nonlinear programming pattern search algorithm. The effectiveness of simplex however reduces when the solved problem has large number of variables, several local minima, or when initial guess is not readily available. Recent results obtained by introducing a technique of random selection of the variables in optimization processes, encouraged studying the effect of this idea on the Nelder & Mead version of the simplex algorithm to improve its semi-global behavior. This paper proposes several enhancements to the simplex. The algorithm is run for several attempts. Each attempt uses the final answer of the previous attempt as an initial guess. At each attempt, the search starts by generating a simplex with n+1 vertices. A random subset of the variables is involved in the movement (reflection, expansion, contraction, shrinking) of the simplex. This process is called twinkling. The paper presents several variations of twinkling the simplex. The random nature of the algorithm lends itself to problems with large dimensionality or complex topography. The algorithm is applied successfully to several engineering design problems. The results compare favorably with both regular simplex and genetic algorithms.