Chaos Enhanced Differential Evolution in the Task of Evolutionary Control of Selected Set of Discrete Chaotic Systems

Šenkeřík, Roman; Zelinka, Ivan; Pluháček, Michal; Davendra, Donald; Kominkova, Zuzana Oplatková

doi:10.1155/2014/836484

Cited by 6 publications

(3 citation statements)

References 41 publications

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“…The observed performance of enhanced optimizer is (significantly) different, mostly the chaotic maps secured very fast progress towards function extreme, but often followed by premature convergence, thus overall statistics has given mixed results. Nevertheless, as reported in [106], the the chaos driven heuristics is performing very well [104,107], especially for some instances in the discrete domain [33,72].…”

Section: Parameter Estimationsupporting

confidence: 54%

Towards Human Cell Simulation

Spolaor

Gribaudo

Iacono

et al. 2019

Lecture Notes in Computer Science

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The faithful reproduction and accurate prediction of the phenotypes and emergent behaviors of complex cellular systems are among the most challenging goals in Systems Biology. Although mathematical models that describe the interactions among all biochemical processes in a cell are theoretically feasible, their simulation is generally hard because of a variety of reasons. For instance, many quantitative data (e.g., kinetic rates) are usually not available, a problem that hinders the execution of simulation algorithms as long as some parameter estimation methods are used. Though, even with a candidate parameterization, the simulation of mechanistic models could be challenging due to the extreme computational effort required. In this context, model reduction techniques and High-Performance Computing infrastructures could be leveraged to mitigate these issues. In addition, as cellular processes are characterized by multiple scales of temporal and spatial organization, novel hybrid simulators able to harmonize different modeling approaches (e.g., logic-based, constraint-based, continuous deterministic, discrete stochastic, spatial) should be designed. This chapter describes a putative unified approach to tackle these challenging tasks, hopefully paving the way to the definition of large-scale comprehensive models that aim at the comprehension of the cell behavior by means of computational tools.

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Section: Parameter Estimationsupporting

confidence: 54%

Towards Human Cell Simulation

Spolaor

Gribaudo

Iacono

et al. 2019

Lecture Notes in Computer Science

Self Cite

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“…An original study introduced by Zelinka's team sought to utilize hidden chaotic dynamics in pseudo-random sequences generated via chaotic map to help the differential evolution algorithm search for the best controller settings for the same chaotic system. In [75][76][77], they considered (55) with the standard parameter values of a = 1.7 and b = 0.5, and tried to stabilize desired Unstable Periodic Orbits (UPO) using the chaos-driven DE for tuning the parameters of the Extended Delay Feedback (ETDAS) control method proposed by Pyragas [78].…”

Section: Chemical Reactor Optimizationmentioning

confidence: 99%

Survey of Recent Applications of the Chaotic Lozi Map

Lozi

2023

Algorithms

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Since its original publication in 1978, Lozi’s chaotic map has been thoroughly explored and continues to be. Hundreds of publications have analyzed its particular structure and applied its properties in many fields (e.g., improvement of physical devices, electrical components such as memristors, cryptography, optimization, evolutionary algorithms, synchronization, control, secure communications, AI with swarm intelligence, chimeras, solitary states, etc.) through algorithms such as the COLM algorithm (Chaotic Optimization algorithm based on Lozi Map), Particle Swarm Optimization (PSO), and Differential Evolution (DE). In this article, we present a survey based on dozens of articles on the use of this map in algorithms aimed at real applications or applications exploring new directions of dynamical systems such as chimeras and solitary states.

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“…The same author used logistic map in the chaotic harmony search algorithm. Senkerik et al used DE for the evolutionary tuning of controller parameters for the stabilization of different chaotic systems, where the selected controlled discrete chaotic systems (Burgers map, Delayed logistic map and Lozi map) are used also as cPRNGs to drive the mutation and crossover process ( [21]). L. dos Santos Coelho and V. C. Mariani described PID controller tuned by firefly algorithm using Tinkerbell map ( [8]).…”

Section: Introductionmentioning

confidence: 99%

Study of the Influence of the Number Normalization Scheme Used in Two Chaotic Pseudo Random Number Generators Used as the Source of Randomness in Differential Evolution

Skanderova,

Fabian

2014

Preprint

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In many publications, authors showed that chaotic pseudo random number generators (PRNGs) may improve performance of the evolutionary algorithms. In this paper, we use two chaotic maps Gingerbread man and Tinkerbell as the chaotic PRNGs instead of the classical PRNG in the differential evolution. Numbers generated by this maps are normalized to the unit interval by three different methods -operation modulo, straightforward number normalization where we know minimal and maximal generated number and arctangent of the two variables x and y, where numbers x and y are generated by the Gingerbread man map and Tinkerbell map. The first goal of this paper is to show whether the differential evolution convergence speed might be affected by the way how we normalize number generated by the chaotic map. The second goal is to find out the influence of the probability distribution function of the selected chaotic PRNGs. The results mentioned below showed that the selected normalization method may improve differential evolution convergence speed, especially in the case of arctangent and straightforward number normalization, where we know the minimal and maximal generated numbers.

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Chaos Enhanced Differential Evolution in the Task of Evolutionary Control of Selected Set of Discrete Chaotic Systems

Cited by 6 publications

References 41 publications

Towards Human Cell Simulation

Towards Human Cell Simulation

Survey of Recent Applications of the Chaotic Lozi Map

Study of the Influence of the Number Normalization Scheme Used in Two Chaotic Pseudo Random Number Generators Used as the Source of Randomness in Differential Evolution

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