An Evolutionary Algorithm for Controlling Chaos: The Use of Multi-objective Fitness Functions

In this paper, we study an evolutionary algorithm employed to design and optimize a local control of chaos. In particular, we use a multi-objective fitness function, which consists of the objective function to be optimized and an auxiliary quantity applied as an additional driving force for the algorithm. Numerical results are presented illustrating the proposed scheme and showing the influence of employing such a multi-objective fitness function on convergence of the algorithm.

[1]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[2]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[3]  Athanasios Kehagias,et al.  Genetic Algorithm in Parameter Estimation of Nonlinear Dynamic Systems , 1998, PPSN.

[4]  P. Fleming,et al.  Genetic programming for dynamic chaotic systems modelling , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[5]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[6]  Mw Hirsch,et al.  Chaos In Dynamical Systems , 2016 .

[7]  Hendrik Richter,et al.  Local Control of Chaotic Systems — A Lyapunov Approach , 1998 .

[8]  Jesús Marín,et al.  Controlling chaos in unidimensional maps using macroevolutionary algorithms. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Thomas Bäck,et al.  Parallel Problem Solving from Nature — PPSN V , 1998, Lecture Notes in Computer Science.

[10]  G. Baier,et al.  Maximum hyperchaos in generalized Hénon maps , 1990 .

[11]  Chin-Teng Lin,et al.  Controlling chaos by GA-based reinforcement learning neural network , 1999, IEEE Trans. Neural Networks.

[12]  Norman H. Packard,et al.  A Genetic Learning Algorithm for the Analysis of Complex Data , 1990, Complex Syst..

[13]  Eric R. Weeks,et al.  Evolving artificial neural networks to control chaotic systems , 1997 .

[14]  S. Liberty,et al.  Linear Systems , 2010, Scientific Parallel Computing.

[15]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[16]  R. K. Dahule,et al.  Obtaining functional form for chaotic time series evolution using genetic algorithm. , 1999, Chaos.

[17]  George G. Szpiro.  Forecasting chaotic time series with genetic algorithms , 1997 .

[18]  Hendrik Richter,et al.  Optimization of local control of chaos by an evolutionary algorithm , 2000 .