On the parameter settings for the chaotic dynamics embedded differential evolution

This research deals with the hybridization of the two softcomputing fields, which are chaos theory and evolutionary computation. This paper aims on the investigations on the multi-chaos-driven evolutionary algorithm Differential Evolution (DE) concept. This paper is aimed at the embedding and alternating of set of two discrete dissipative chaotic systems in the form of chaos pseudo random number generators for the DE. In this paper the novel initial concept of DE/rand/1/bin strategy driven alternately by two chaotic maps (systems) is introduced. From the previous research, it follows that very promising results were obtained through the utilization of different chaotic maps, which have unique properties with connection to DE. The idea is then to connect these two different influences to the performance of DE into the one multi-chaotic concept. Repeated simulations were performed on the selected set of shifted benchmark functions in higher dimensions. Finally, the obtained results are compared with canonical DE.

This research deals with the hybridization of the two softcomputing fields, which are chaos theory and evolutionary computation. This paper aims on the experimental investigations on the chaos-driven evolutionary algorithm Differential Evolution (DE) concept. This research represents the continuation of the satisfactory results obtained by means of chaos embedded (driven) DE, which utilizes the chaotic dynamics in the place of pseudorandom number generators This work is aimed at the tuning of the complex chaotic dynamics directly injected into the DE. To be more precise, this research investigates the influence of different parameter settings for discrete chaotic systems to the performance of DE. Repeated simulations were performed on the IEEE CEC 13 benchmark functions set in dimension of 30. Finally, the obtained results are compared with canonical DE and jDE.

This research deals with the hybridization of the two softcomputing fields, which are chaos theory and evolutionary computation. This paper aims on the deeper investigations on the multi-chaos-driven evolutionary algorithm Differential Evolution (DE) concept. This research is aimed at the embedding and alternating of set of two discrete dissipative chaotic systems in the form of chaos pseudo random number generators for the DE. In this paper the novel initial concept of DE/rand/1/bin strategy driven alternately by two chaotic maps (systems) is deeply investigated in terms of determining the optimal switching moment of two different chaotic systems. From the previous research, it follows that very promising results were obtained through the utilization of different chaotic maps, which have unique properties with connection to DE. The idea is then to connect these two different influences to the performance of DE into the one multi-chaotic concept. Repeated simulations were performed on the selected shifted benchmark function in higher dimensions. Finally, the obtained results are compared with canonical DE.

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.

Differential evolution (DE) is an effective and efficient evolutionary algorithm in continuous space. The setting of control parameters is highly relevant with the convergence efficiency, and varies with different optimization problems even at different stages of evolution. Self-adapting control parameters for finding global optima is a long-term target in evolutionary field. This paper proposes a two-layered DE (TLDE) with self-adaptive control parameters combined with niching method based mutation strategy. The TLDE consists of two DE layers: a bottom DE layer for the basic evolution procedure, and a top DE layer for control parameter adaptation. Both layers follow the procedure of DE. Moreover, to mitigate the common phenomenon of premature convergence in DE, a clearing niching method is brought out in finding efficient mutation individuals to maintain diversity during the evolution and stabilize the evolution system. The performance is validated by a comprehensive set of twenty benchmark functions in parameter optimization and competitive results are presented.

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

The differential evolution (DE) algorithm is an efficient random search algorithm based on swarm intelligence for solving optimization problems. It has the advantages of easy implementation, fast convergence, strong optimization ability and good robustness. However, the performance of DE is very sensitive to the design of different operators and the setting of control parameters. To solve these key problems, this paper proposes an improved self-adaptive differential evolution algorithm with a shuffled frog-leaping strategy (SFSADE). It innovatively incorporates the idea of the shuffled frog-leaping algorithm into DE, and at the same time, it cleverly introduces a new strategy of classification mutation, and also designs a new adaptive adjustment mechanism for control parameters. In addition, we have carried out a large number of simulation experiments on the 25 benchmark functions of CEC 2005 and two nonparametric statistical tests to comprehensively evaluate the performance of SFSADE. Finally, the results of simulation experiments and nonparametric statistical tests show that SFSADE is very effective in improving DE, and significantly improves the overall diversity of the population in the process of dynamic evolution. Compared with other advanced DE variants, its global search speed and optimization performance also has strong competitiveness.

Differential evolution is a simple yet efficient heuristic originally designed for global optimization over continuous spaces that has been used in many research areas. The question how to improve its performance is still popular and during the years, many successful methods dealing with optimal setting or hybridization of the control parameters were proposed. In this paper, we propose a novel approach based on modeling of the differential evolution dynamics by complex networks. In each generation, the individuals are mapped to the nodes and the relationships between them are modeled by the edges of the graph. Thanks to this simple visualization, the interconnection between the differential evolution convergence speed and the weighted clustering coefficients has been revealed. As a consequence, we have focused on the parents selection in the mutation step where the individuals are not selected randomly as usual but on the basis of their weighted clustering coefficients. Our enhancement has been incorporated in the classical differential evolution, self-adaptive differential evolution (jDE) and differential evolution with composite trial vector generation strategies and control parameters. Finally, a set of well-known benchmark functions (including 21 functions) has been used to test and evaluate the performance of the proposed enhancement of the differential evolution. The experimental results and statistical analysis indicate that the enhanced algorithms perform better or at least comparable to their original versions and the analysis of the differential evolution dynamics with the aim of the complex network might be an effective tool to improve the differential evolution convergence in the future.

The rapid advancement of technology and the exponential growth of the global population have led to an increasing demand for data-driven solutions, giving rise to Big Data. Extracting meaningful insights from these vast datasets has significantly enhanced decision-making in fields such as healthcare, finance, and e-commerce. In particular, electroencephalography (EEG) signal analysis is crucial for diagnosing complex neurological disorders, including schizophrenia, epilepsy, and psychological conditions. However, EEG signal processing presents a major challenge due to its high dimensionality and large-scale nature, making it a Big Optimization (BigOpt) problem. Evolutionary Algorithms (EAs) have been widely employed to address BigOpt challenges, with Differential Evolution (DE) being one of the most commonly used approaches. Despite its effectiveness, DE struggles with high-dimensional and computationally expensive BigOpt tasks due to its limited exploration and exploitation capabilities. To overcome these challenges, this study proposes Self-Equation-Based Differential Evolution for Big Optimization (SSE-DEP), an enhanced DE variant that integrates three key improvements: (1) Self-Adaptive Mutation Operator: Utilizes a dynamic mutation equation pool to enhance DE’s exploration. (2) Competitive Local Search: Dynamically integrates CMA-ES and Powell’s local search to improve exploitation. (3) oldArchive Strategy: Balances exploration and exploitation to prevent premature convergence and accelerate optimization. The proposed SSE-DEP algorithm was rigorously evaluated using the IEEE Congress on Evolutionary Computation (CEC) 2014 and CEC 2017 benchmark suites for problem dimensions of 30, 50, and 100, as well as the CEC 2019 benchmark set to assess its performance across diverse optimization challenges. Comparative analyses against various self-adaptive DE variants, state-of-the-art metaheuristic algorithms, and EEG-specific optimization approaches demonstrate that SSE-DEP significantly outperforms existing methods in both benchmark and real-world EEG signal decomposition tasks.

Q-Learning-based parameter control in differential evolution for structural optimization

The differential evolution (DE) algorithm is a simple and efficient population-based evolutionary algorithm. In DE, the mutation strategy and the control parameter play important roles in performance enhancement. However, single strategy and fixed parameter are not universally applicable to problems and evolution stages with diverse characteristics; besides, the weakness of the advanced DE optimization framework, called selective-candidate framework with similarity selection rule (SCSS), is found by focusing on its single strategy and fixed parameter greedy degree (GD) setting. To address these problems, we mainly combine the multiple candidates generation with multi-strategy (MCG-MS) and the adaptive similarity selection (ASS) rule. On the one hand, in MCG-MS, two symmetrical mutation strategies, “DE/current-to-pbest-w/1” and designed “DE/current-to-cbest-w/1”, are utilized to build the multi-strategy to produce two candidate individuals, which prevents the over-approximation of the candidate in SCSS. On the other hand, the ASS rule provides the individual selection mechanism for multi-strategy to determine the offspring from two candidates, where parameter GD is designed to increase linearly with evolution to maintain diversity at the early evolution stage and accelerate convergence at the later evolution stage. Based on the advanced algorithm jSO, replacing its offspring generation strategy with the combination of MCG-MS and ASS rule, this paper proposes multi-strategy differential evolution algorithm with adaptive similarity selection rule (MSDE-ASS). It combines the advantages of two symmetric strategies and has an efficient individual selection mechanism without parameter adjustment. MSDE-ASS is verified under the Congress on Evolutionary Computation (CEC) 2017 competition test suite on real-parameter single-objective numerical optimization, and the results indicate that, of the 174 cases in total, it wins in 81 cases and loses in 30 cases, and it has the smallest performance ranking value, of 3.05. Therefore, MSDE-ASS stands out compared to the other state-of-the-art DEs.

Differential evolution (DE) is one of the most successful evolutionary algorithms (EAs) for global numerical optimization. Like other EAs, maintaining population diversity is important for DE to escape from local optima and locate a near-global optimum. Using a multi-population algorithm is a representative method to avoid early loss of population diversity. In this paper, we propose a multi-population DE algorithm (MPDE) which manipulates multiple sub-populations. Different sub-populations in MPDE exchange information via a novel mutation operation instead of migration used in most multi-population EAs. The mutation operation is helpful to balance the fast convergence and population diversity of the proposed algorithm. Moreover, the performance of MPDE is further improved by an adaptive parameter control scheme designed based on the multi-population approach. Each sub-population in MPDE evolves with its own set of control parameters, and a learning strategy is used to adaptively adjust the parameter values. A set of benchmark functions is used to test the proposed MPDE algorithm. The experimental results show that MPDE performs better than, or at least comparably, to the classical single population DE with fixed parameter values and three existing state-of-the-art DE variants.

This work investigates the performance of Differential Evolution (DE) and its opposition-based version (ODE) on large scale optimization problems. Opposition-based differential evolution (ODE) has been proposed based on DE; it employs opposition-based population initialization and generation jumping to accelerate convergence speed. ODE shows promising results in terms of convergence rate, robustness, and solution accuracy. A recently proposed seven-function benchmark test suite for the CEC-2008 special session and competition on large scale global optimization has been utilized for the current investigation. Results interestingly confirm that ODE outperforms its parent algorithm (DE) on all high dimensional (500D and 1000D) benchmark functions (F1-F7). Furthermore, authors recommend to utilize ODE for more complex search spaces as well. Because results confirm that ODE performs much better than DE when the dimensionality of the problems is increased from 500D to 1000D. All required details about the testing platform, comparison methodology, and also achieved results are provided.

In this paper, we study a problem of the control parameter settings in Differential Evolution algorithm and test novel variant of the algorithm called Co- BiDE. Although Differential Evolution with basic setting (i.e. CR = 0:5; F = 0:5) works quite well, it starts to fail on rotated functions. In general, we want to improve the convergence of algorithm primarily on rotated functions. It is done by adapting crossover parameter CR whereas parameter F is fixed to 0.5. There is a recommendation to set CR = 1 for rotated functions. It means that trial vectors are essentially composed from mutant. However, it is not easy task to set the parameters appropriately for solving optimization problem but it is crucial for obtaining good results. Moreover, the quality of points produced in evolution is highly aected by the coordinate system. In CoBiDE, the authors proposed new coordinate system based on the current distribution of points in the population. We test these two approaches by running both algorithms on six pairs of rotated and non-rotated functions from CEC 2013 benchmark set in two levels of dimension space. This experimental study aims to reveal if such algorithm's setting is invariant under a rotation.

Differential Evolution (DE) is a very simple but powerful Evolutionary Algorithm (EA) for real-world applications. There are two aspects affecting the overall optimization performance significantly, one is parameter control scheme and the other is trial vector generation strategy. As all the control parameters are employed in generating trial vectors, from this perspective of view, the trial vector generation strategy dominates the overall optimization performance. Therefore, trial vector generation strategies are often designed first, and then the corresponding parameter control schemes are well-tuned thereafter. Both of them constitute the main body of a new DE variant. Here in the paper, a novel DE variant with a new designed trial vector generation strategy as well as novel parameter control scheme is proposed to tackle freight trains scheduling problem. By incorporating both a time-stamp mechanism of the external archive and a novel parameter control scheme, the new algorithm can secure better optimization performance not only on man-made benchmarks but also on real-world applications. Both the man-made benchmarks from Congress on Evolutionary Computation (CEC) test suite and the real-world freight train scheduling problem are employed in the validation of the new DE variant. The experiment results show that it is competitive with other state-of-the-art DE techniques for these optimization problems.