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This research deals with the comparison of the two modern approaches for evolutionary algorithms, which are the adaptivity and complex chaotic dynamics. This paper aims on the investigations on the chaos-driven Differential Evolution (DE) concept. This paper is aimed at the embedding of discrete dissipative chaotic systems in the form of chaotic pseudo random number generators for the DE and comparing the influence to the performance with the state of the art adaptive representative jDE. This research is focused mainly on the possible disadvantages and advantages of both compared approaches. Repeated simulations for Lozi map driving chaotic systems were performed on the simple benchmark functions set, which are more close to the real optimization problems. Obtained results are compared with the canonical not-chaotic and not adaptive DE. Results show that with used simple test functions, the performance of ChaosDE is better in the most cases than jDE and Canonical DE, furthermore due to the unique sequencing in CPRNG given by the hidden chaotic dynamics, thus better and faster selection of unique individuals from population, ChaosDE is faster. © 2016 Author(s).

This research deals with a synthesis of control law for selected discrete chaotic system - logistic equation by means of analytic programming. The novelty of the approach is that a tool for symbolic regression - analytic programming - is used for the purpose of stabilization of higher periodic orbits - oscillations between several values of chaotic system. The paper consists of the descriptions of analytic programming as well as used chaotic system and detailed proposal of cost function used in optimization process. For experimentation, Self-Organizing Migrating Algorithm (SOMA) with analytic programming and Differential evolution (DE) as second algorithm for meta-evolution were used.