Chaos enhanced differential evolution in the task of evolutionary control of selected set of discrete chaotic systems

Evolutionary technique differential evolution (DE) is used for the evolutionary tuning of controller parameters for the stabilization of set of different chaotic systems. The novelty of the approach is that the selected controlled discrete dissipative chaotic system is used also as the chaotic pseudorandom number generator to drive the mutation and crossover process in the DE. The idea was to utilize the hidden chaotic dynamics in pseudorandom sequences given by chaotic map to help differential evolution algorithm search for the best controller settings for the very same chaotic system. The optimizations were performed for three different chaotic systems, two types of case studies and developed cost functions.Web of Science2014art. no. 83648

Synthesis of feedback control law for stabilization of chaotic system oscillations by means of analytic programming - Preliminary study

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

Adaptive strategy for neural network synthesis constant estimation

Neural Network Synthesis is a new innovative method for an artificial neural network learning and structural optimization. It is based on two other already very successful algorithms: Analytic Programming and Self-Organizing Migration Algorithm (SOMA). The method already recorded several theoretical as well as industrial application to prove itself as a useful tool of modelling and simulation. This paper explores promising possibility to farther improve the method by application of an adaptive strategy for SOMA. The new idea of adaptive strategy is explained here and tested on a theoretical experimental case for the first time. Obtained data are statistically evaluated and ability of adaptive strategy to improve neural network synthesis is proved in conclusion

Chaos enhanced differential evolution in the task of evolutionary control of discrete chaotic Lozi map

In this paper, evolutionary technique Differential Evolution ( DE) is used for the evolutionary tuning of controller parameters for the stabilization of selected discrete chaotic system, which is the two-dimensional Lozi map. The novelty of the approach is that the selected controlled discrete dissipative chaotic system is used within Chaos enhanced heuristic concept as the chaotic pseudo-random number generator to drive the mutation and crossover process in the DE. The idea was to utilize the hidden chaotic dynamics in pseudo-random sequences given by chaotic map to help Differential evolution algorithm in searching for the best controller settings for the same chaotic system. The optimizations were performed for three different required final behavior of the chaotic system, and two types of developed cost function. To confirm the robustness of presented approach, comparisons with canonical DE strategy and PSO algorithm have been performed.Grant Agency of the Czech Republic [GACR P103/15/06700S]; Ministry of Education, Youth and Sports of the Czech Republic within National Sustainability Pro- gramme [LO1303 (MSMT-7778/2014)]; European Regional Development Fund under project CEBIA-Tech [CZ.1.05/2.1.00/03.0089]; Grant of SGS of VSB-Technical University of Ostrava, Czech Republic [SP2016/175]; Internal Grant Agency of Tomas Bata University [IGA/CebiaTech/2016/007

Chaos enhanced differential evolution in the task of evolutionary control of selected set of discrete chaotic systems

Evolutionary technique differential evolution (DE) is used for the evolutionary tuning of controller parameters for the stabilization of set of different chaotic systems. The novelty of the approach is that the selected controlled discrete dissipative chaotic system is used also as the chaotic pseudorandom number generator to drive the mutation and crossover process in the DE. The idea was to utilize the hidden chaotic dynamics in pseudorandom sequences given by chaotic map to help differential evolution algorithm search for the best controller settings for the very same chaotic system. The optimizations were performed for three different chaotic systems, two types of case studies and developed cost functions.Grant Agency of the Czech Republic [GACR P103/13/08195S]; Grant of SGS [SP2014/159, SP2014/170]; VSB-Technical University of Ostrava, Czech Republic; Development of Human Resources in Research and Development of Latest Soft Computing Methods and Their Application in Practice Project - Operational Programme Education for Competitiveness [CZ.1.07/2.3.00/20.0072]; ESF; budget of the Czech Republic; European Regional Development Fund under the Project CEBIA-Tech [CZ.1.05/2.1.00/03.0089]; Internal Grant Agency of Tomas Bata University [IGA/FAI/2014/010

Analytical Programming - a Novel Approach for Evolutionary Synthesis of Symbolic Structures

This chapter discusses an alternative approach for symbolic structures and solutions synthesis and demonstrates a comparison with other methods, for example Genetic Programming (GP) or Grammatical Evolution (GE). Generally, there are two well known methods, which can be used for symbolic structures synthesis by means of computers. The first one is called GP and the other is GE. Another interesting research was carried out by Artificial Immune Systems (AIS) or/and systems, which do not use tree structures like linear GP and other similar algorithm like Multi Expression Programming (MEP), etc. In this chapter, a different method called Analytic Programming (AP), is presented. AP is a grammar free algorithmic superstructure, which can be used by any programming language and also by any arbitrary Evolutionary Algorithm (EA) or another class of numerical optimization method. This chapter describes not only theoretical principles of AP, but also its comparative study with selected well known case examples from GP as well as applications on synthesis of: controller, systems of deterministic chaos, electronics circuits, etc. For simulation purposes, AP has been co-joined with EA’s like Differential Evolution (DE), Self-Organising Migrating Algorithm (SOMA), Genetic Algorithms (GA) and Simulated Annealing (SA). All case studies has been carefully prepared and repeated in order to get valid statistical data for proper conclusions.P(ED2.1.00/03.0089), P(GA102/09/1680), S, Z(MSM7088352101

A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications

Particle swarm optimization (PSO) is a heuristic global optimization method, proposed originally by Kennedy and Eberhart in 1995. It is now one of the most commonly used optimization techniques. This survey presented a comprehensive investigation of PSO. On one hand, we provided advances with PSO, including its modifications (including quantum-behaved PSO, bare-bones PSO, chaotic PSO, and fuzzy PSO), population topology (as fully connected, von Neumann, ring, star, random, etc.), hybridization (with genetic algorithm, simulated annealing, Tabu search, artificial immune system, ant colony algorithm, artificial bee colony, differential evolution, harmonic search, and biogeography-based optimization), extensions (to multiobjective, constrained, discrete, and binary optimization), theoretical analysis (parameter selection and tuning, and convergence analysis), and parallel implementation (in multicore, multiprocessor, GPU, and cloud computing forms). On the other hand, we offered a survey on applications of PSO to the following eight fields: electrical and electronic engineering, automation control systems, communication theory, operations research, mechanical engineering, fuel and energy, medicine, chemistry, and biology. It is hoped that this survey would be beneficial for the researchers studying PSO algorithms

Multilayer perceptron network optimization for chaotic time series modeling

Chaotic time series are widely present in practice, but due to their characteristics—such as internal randomness, nonlinearity, and long-term unpredictability—it is difficult to achieve high-precision intermediate or long-term predictions. Multi-layer perceptron (MLP) networks are an effective tool for chaotic time series modeling. Focusing on chaotic time series modeling, this paper presents a generalized degree of freedom approximation method of MLP. We then obtain its Akachi information criterion, which is designed as the loss function for training, hence developing an overall framework for chaotic time series analysis, including phase space reconstruction, model training, and model selection. To verify the effectiveness of the proposed method, it is applied to two artificial chaotic time series and two real-world chaotic time series. The numerical results show that the proposed optimized method is effective to obtain the best model from a group of candidates. Moreover, the optimized models perform very well in multi-step prediction tasks.This research was funded in part by the NSFC grant numbers 61972174 and 62272192, the Science-Technology Development Plan Project of Jilin Province grant number 20210201080GX, the Jilin Province Development and Reform Commission grant number 2021C044-1, the Guangdong Universities’ Innovation Team grant number 2021KCXTD015, and Key Disciplines Projects grant number 2021ZDJS138