Sequential Approximate Global Optimization Technique Considering Adaptive Balancing Between Global Search and Local Search

Abstract

In this study, the weighted minimum distance which is an improved measure for global search and the adaptive balancing technique which adaptively controls the weight between the global search and local search were proposed, and the Sequential Approximate Global Optimization (ASAGO) was developed by combining these two techniques. The Sequential Approximate Global Optimization (SAGO) is a method to find the global optimum by adding a sample points sequentially after generating an initial metamodel. The SAGO finds global optimum by using a combination of the global search and the local search. The global search explorers unknown design space and the local search improves the known best point. Previous studies of SAGO used fixed weight between the global search and the local search or repeated a predefined search pattern. Thus performance of the previous SAGO algorithms depends on both the characteristic of a problem and the initial sample points due to a lack of adaptability. To overcome this problem, the Adaptive Balancing technique was proposed. It controls the weight of the global search and the local search for each sequential optimization steps using the convergence history and information from the sample points. The previous studies of the SAGO used the distance to the nearest sample point or an error of a metamodel as a measure for the global search. However, in this study, the weighted minimum distance which consider not only the distance to the nearest sample point but also a response was proposed. In this study, the Adaptive Sequential Approximate Global Optimization (ASAGO) was developed by combining the weighted minimum distance and the adaptive balancing which. In addition, we examined the effect of the number of the initial sample points and user-defined parameters on the performance of the ASAGO using 10 mathematical test examples, and made recommendations on their values. Finally, by the comparison of the proposed ASAGO with the previous SAGO, excellent performance of the proposed ASAGO was demonstrated.