Hierarchical Evolutionary Algorithms and Noise Compensation via Adaptation

Hierarchical Evolutionary Algorithms (HEAs) are Nested Algorithms composed by two or more Evolutionary Algorithms having the same fitness but different populations. More specifically, the fitness of a Higher Level Evolutionary Algorithm (HLEA) is the optimal fitness value returned by a Lower Level Evolutionary Algorithm (LLEA). Due to their algorithmic formulation, the HEAs can be efficiently implemented in Min-Max problems. In this chapter the application of the HEAs is shown for two different Min-Max problems in the field of Structural Optimization. These two problems are the optimal design of an electrical grounding grid and an elastic structure. Since the fitness of a HLEA is given by another evolutionary algorithm (LLEA), it is noisy. This noise, namely Hierarchical Noise (HN) is distributed according to an asymmetrical and non-Gaussian probability function. A preliminary analysis of the HN is performed and a set of adaptive rules are then carried out in order to robustly handle this kind of noise. The Adaptive Higher Level Evolutionary Algorithm (AHLEA) is thus proposed. The AHLEA works on the sample size, the population size, and the survivor selection scheme in order to ensure the reliability of the optimization process in presence of the HN. The analysis of a benchmark problem proves the effectiveness of the adaptive rules carried out and the tests for grounding grids and elastic structures show the applicability of the AHEAs to real world problems.

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