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Abstract: In this thesis we were discussing an analysis of numerical optimization algorithms from the most important aspect, that is exploration and exploitation. We focused on 2-dimensional and 3-dimensional unconstrained continuous functions, which were used to test the recently proposed metric based on attraction basins. The metric does not need any user-defined parameters. Attraction basins were expounded more profoundly and extensively. Our algorithm to calculate them consists of three steps such as making potential boundaries, filling, and then removing false boundaries from attraction basins. Results show that our algorithm is barely satisfying, depends on a particular problem function used. For example, attraction basins from Rastrigin, Schwefel, Ackley and similar functions (including all unimodal ones) were calculated accurately, while more special functions like Michalewicz, Shubert and Branin were proved to be not so easy. Further, we arbitrarly selected two algorithms, Particle Swarm Optimization and Self-adapting Differential Evolution, not for comparative study, rather to test the metric based on attraction basins. Results implied the relevance of recently proposed metric, and opened us a fruitful field for further investigation.
Keywords: exploration, exploitation, attraction basins, optimization, metaheuristic
Published in DKUM: 04.11.2020; Views: 889; Downloads: 93
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