Synergetic use of different evaluation, parameterization and search tools within a multilevel optimization platform

Abstract

This paper presents the synergetic use of different evaluation tools, parameterization schemes and search methods on the levels of a multilevel optimization platform to efficiently solve single- and multi-objective computationally demanding optimization problems. The platform is formed by a number of levels which concurrently search for optimal solutions, by regularly exchanging promising individual solutions. Each level is associated with a problem-specific evaluation tool with its own accuracy and computational cost, a parameterization scheme which determines the design variables and their mapping to generate individual solutions and a search algorithm which is either a metamodel-assisted evolutionary algorithm or a gradient-based method. The use of the multilevel platform with only one of the aforementioned features changing from level to level was presented in a previous paper by the authors. The present paper shows that the combined use of hierarchical evaluation, hierarchical parameterization and hierarchical search decreases further the computational cost by increasing the efficiency of the optimization method. This is demonstrated on function minimization and aerodynamic shape optimization problems; though only two levels are used herein, this is not a restriction and the optimization platform may accommodate any number of them.