Development of an efficient algorithm for global optimization by simplex elimination

Abstract

An efficient multi-start algorithm for global optimization is developed by introducing multi-dimensional simplexes as new expression units of attraction regions. The region elimination method generally consists of making a set of eliminated regions called attraction regions, checking adjacency between the current design point and the attraction region, and quitting local optimization for the attracted design points. The efficiency of the elimination method is considerably enhanced by supplementing general simplexes and their neighborhoods to conventional units of attraction regions of points and lines. To show the effectiveness of the proposed algorithm, mathematical problems from the literature are solved and the results are compared with several well-known multi-start algorithms. The present algorithm produces the global optimum in all problems more efficiently than the variants of the multi-start method. Several types of truss, frame, and composite material structures are optimized as engineering applications. Many local optima are found and the differences among the local optima are not negligibly small. These results suggest that an efficient and reliable global optimizer is strongly required in some fields of engineering optimization.