Zuzana Kominkova Oplatkova

On the behavior and performance of chaos driven PSO algorithm with inertia weight

In this paper, the utilization of chaos pseudorandom number generators based on three different chaotic maps to alter the behavior and overall performance of PSO algorithm is proposed. This paper presents results of testing the performance and behavior of the proposed algorithm on typical benchmark functions that represent unimodal and multimodal problems. The promising results are analyzed and discussed.

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. The term symbolic regression represents a process during which measured data sets are fitted, thereby a corresponding mathematical formula is obtained in an analytical way. An output

Utilization of SOMA and differential evolution for robust stabilization of chaotic Logistic equation

This paper deals with the utilization of two evolutionary algorithms Self-Organizing Migrating Algorithm (SOMA) and Differential Evolution (DE) for the optimization of the control of chaos. This paper is aimed at an explanation on how to use evolutionary algorithms (EAs) and how to properly define the advanced targeting cost function (CF) securing fast, precise and mainly robust stabilization of selected chaotic system on a desired state for any initial conditions. The role of EA here is as a powerful tool for an optimal tuning of control technique input parameters. As a model of deterministic chaotic system, the one-dimensional discrete Logistic equation was used. The four canonical strategies of SOMA and six canonical strategies of DE were utilized. For each EA strategy, repeated simulations were conducted to outline the effectiveness and robustness of used method and targeting CF securing robust solution. Satisfactory results obtained by both heuristic and the two proposed cost functions are compared with previous research, given by different cost function designs.

Investigation on artificial ant using analytic programming

The paper deals with a alternative tool for symbolic regression - Analytic Programming which is able to solve various problems from the symbolic regression domain. In this contribution main principles of Analytic Programming are described and explained. Then follows how Analytic Programming was used for setting an optimal trajectory for an artificial ant according to Koza. An ability to create so called programs, as well as Genetic Programming or Grammatical Evolution do, is shown in that part. Analytic Programming is a superstructure of evolutionary algorithms which are necessary to run Analytic Programming. In this contribution SelfOrganizing Migrating Algorithm and Differential Evolution as two evolutionary algorithms were used to carry simulations out.

Synthesis of feedback controller for three selected chaotic systems by means of evolutionary techniques: Analytic programming

Abstract This research deals with the utilization of analytic programming for a synthesis of control law for three selected discrete chaotic systems. The novelty of the approach is that a tool for symbolic regression–analytic programming–is used for such kinds of difficult problems. The paper consists of the descriptions of analytic programming as well as chaotic systems and used cost functions. For simulations, evolutionary algorithm SOMA (Self-Organizing Migrating Algorithm) and analytic programming were used. For each case study, repeated simulations were conducted to outline the effectiveness and robustness of used methods. All repeated simulations have given satisfactory results.

Analytic programming in the task of evolutionary synthesis of a controller for high order oscillations stabilization of discrete chaotic systems

This paper deals with the utilization of a symbolic regression tool, which is Analytic Programming (AP), together with two evolutionary algorithms, the Self-Organizing Migrating Algorithm (SOMA) and Differential Evolution (DE), for the synthesis of a new control law. This synthesized chaotic controller secures the stabilization of higher periodic orbits, which represent oscillations between several values of three selected discrete chaotic systems. Selected examples were: an artificially evolutionary synthesized system, logistic equation and Henon map. The paper consists of the description of analytic programming as well as chaotic systems used, evolutionary techniques and the cost function.

Preliminary investigation on relations between complex networks and evolutionary algorithms dynamics

In this article we discuss relations between the so-called complex networks and dynamics of evolutionary algorithms. The main aim of this article is to investigate whether it is possible to model (or vizualize) evolutionary dynamics as complex networks, whose connections will represent interactions amongst the individuals during all generations. Our simulations are based on selected evolutionary algorithms (2 algorithms in 6 versions) and test functions (4 out of 17). Data obtained through the simulations were processed graphically as well as statistically.

Performance of Chaos Driven Differential Evolution on Shifted Benchmark Functions Set

This research deals with the extended investigations on the concept of a chaos-driven evolutionary algorithm Differential Evolution (DE). This paper is aimed at the embedding of set of six discrete dissipative chaotic systems in the form of chaos pseudo random number generator for DE. Repeated simulations were performed on the set of two shifted benchmark test functions in higher dimensions. Finally, the obtained results are compared with canonical DE.

Investigation on the Differential Evolution driven by selected six chaotic systems in the task of reactor geometry optimization

In this paper, Differential Evolution (DE) is used in the task of optimization of batch reactor geometry. The novality of the approach is that the six selected discrete dissipative chaotic maps are used as the chaotic pseudo random number generator to drive the mutation and crossover process in the DE. The optimized results obtained are compared with original reactor geometry and process parameters adjustment. The statistical analysis of the results given by six versions of chaos driven DE is compared with canonical DE strategy.

Extended Initial Study on the Performance of Enhanced PSO Algorithm with Lozi Chaotic Map

In this paper, it is proposed the utilization of discrete Lozi map based chaos random number generator to enhance the performance of PSO algorithm with inertia weight. Performance tests and results are presented. Results are analyzed and compared with another evolutionary algorithm. Tuning experiment was performed.