Variable Neighborhood Simplex Search Methods for Global Optimization Models

Abstract

Problem statement: Many optimization problems of practical interest are encountered in various fields of chemical, engineering and management sciences. They are computationally intractable. Therefore, a practical algorithm for solving such problems is to employ approximation algorithms that can find nearly optimums within a reasonable amount of computational time. Approach: In this study the hybrid methods combining the Variable Neighborhood Search (VNS) and simplex’s family methods are proposed to deal with the global optimization problems of noisy continuous functions including constrained models. Basically, the simplex methods offer a search scheme without the gradient information whereas the VNS has the better searching ability with a systematic change of neighborhood of the current solution within a local search. Results: The VNS modified simplex method has a better searching ability for optimization problems with noise. The VNS modified simplex method also outperforms in average on the characteristics of intensity and diversity during the evolution of design point moving stage for the constrained optimization. Conclusion: The adaptive hybrid versions have proved to obtain significantly better results than the conventional methods. The amount of computation effort required for successful optimization is very sensitive to the rate of noise decrease of the process yields. Under circumstances of constrained optimization and gradually increasing the noise during an optimization the most preferred approach is the VNS modified simplex method.