Adaptive coupling of differential evolution and multiquadrics approximation for the tuning of the optimization process

Abstract

Recently, the combination of global convergent stochastic search methods with approximation schemes based on radial basis functions has been introduced. This paper presents a new approach: instead of a procedural sequencing of the approximation algorithm and optimization algorithm, this optimization scheme is characterized by a direct and adaptive coupling of both algorithms. An approximation of the feasible space is constructed and updated during the progress of the evolutionary search. If the approximation fulfils particular accuracy criteria, the evolutionary search algorithm starts sampling the approximation (indirect search) instead of directly sampling the objective function. This can lead to a significant reduction of function calls, which is desirable if the function evaluation is computational expensive (e.g. involving finite element analysis steps).