Parallel Evolutionary Computation in R

Forty years have passed since Prof. Lotfi A. Zadeh introduced fuzzy set theory in his known article “Fuzzy Sets” in Information and Control, 8, 1965, sparking new development in information technology and automation. This article also formed the roots of the Fuzzy Systems Research Group, an active part of the Laboratory of Applied Mathematics, Lappeenranta University of Technology. Rough set theory, evolutionary computing, and neural computing followed, together with their combinations. This Special Issue presents 10 papers representing these areas. Many of the contributors of this Special Issue belong to the Fuzzy Systems Research Group and others work in close co-operations with this group. The first paper considers the use of linguistically expressed objectives in multicriteria decision-making in selection processes based on topological similarity M-relations between L-sets. The second presents basic ideas and fundamental concepts of rough set theory and considers properties of rough approximations. The third combines Lukasiewicz logics and modifier algebras based on Zadeh algebras, i.e., quasi-Boolean algebras of membership functions. The fourth applies Mö{o}bius transformations, known in complex analysis, to fuzzy subgroups in a topological point of view. The fifth discusses the stability of a classifier based on the Lukasiewicz structure and tests Schweizer and Sklar's implications with an extension to generalized mean to a classification task. The sixth deals with the interpretability problem of first-order Takagi-Sugeno systems and interpolation issues, developing a special two-model configuration. The seventh describes an expert system for defining an athlete's aerobic and anaerobic thresholds that successfully mimics decision-making by sport medicine professionals, with system functionality based on fuzzy comparison measures, generalized means, fuzzy membership functions, and differential evolution. The eighth applies a differential evolution algorithm-based method to training radial basis function networks with variables including centers, weights, and widths. The ninth compares two floating-point-encoded evolutionary algorithms – differential evolution and a generalized generation gap model – using a set of problems with different characteristics. The tenth proposes a new approach for monitoring break tendency of paper webs on modern paper machines, combining linguistic equations and fuzzy logic in a case-based reasoning framework. As the Guest Editor of this Special Issue, I thank the contributors and reviewers for their time and effort in making this special issue possible. I am also grateful to the JACIII editorial board, especially Prof. Kaoru Hirota, the Editors-in-Chief and Managing Editor Kenta Uchino, and the staff of Fuji Technology Press for the opportunity to participate in this work. I also thank Prof. Kaoru Hirota for organizing the reviewing of my paper.

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.

Social learning differential evolution

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.

The optimization of input variables (typically feeding trajectories over time) in fed-batch fermentations has gained special attention, given the economic impact and the complexity of the problem. Evolutionary Computation (EC) has been a source of algorithms that have shown good performance in this task. In this chapter, Differential Evolution (DE) is proposed to tackle this problem and quite promising results are shown. DE is tested in several real world case studies and compared with other EC algorihtms, such as Evolutionary Algorithms and Particle Swarms. Furthermore, DE is also proposed as an alternative to perform online optimization, where the input variables are adjusted while the real fermentation process is ongoing. In this case, a changing landscape is optimized, therefore making the task of the algorithms more difficult. However, that fact does not impair the performance of the DE and confirms its good behaviour.

The Evolutionary Computing (EC) field of Computer Science has a pool of potential optimization algorithms. They are collectively termed as Evolutionary Algorithms (EAs). The Differential Evolution (DE) algorithm is added recently to this pool. It is known for its simplicity and applicability. DE differs from other EAs by its Differential Mutation logic. There exist many strategies for this mutation logic. This paper proposes a new mutation strategy which employs a self-switching base vector selection mechanism. This self-switching mechanism uses the diversity in the population as a measure to select the base vector either randomly or the best candidate in the population. It is found from the results of the experiments carried out that the proposed mechanism works better on a standard set of benchmarking functions solving unimodal optimization problems.

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.

The Differential Evolution (DE) algorithm, under the family of Evolutionary Algorithms (EAs), is one of the powerful algorithms used for solving continuous parameter optimization challenges. The simplistic nature and robustness of the classical DE algorithm have drawn researchers' attention towards its progressive enhancement. This work reports on an investigation of the behavioral changes of the classical DE algorithm, evoked when its mutation and crossover components are fine tuned for enhancement of DE's performance. The scope of this study covers the implementation of a mutation level enhancement and a crossover level enhancement, followed by their integration. The mutation and the crossover components are augmented by incorporation of Centroid DE and Superior-Superior & Superior-Inferior DE logics, respectively. The algorithms appraised in this inquiry were classical DE, Centroid based DE(cDE), Superior-Superior based DE (ssDE), Superior-Inferior DE (siDE), Centroid Superior-Superior DE (cssDE) and Centroid Superior-Inferior DE (csiDE). These algorithms were evaluated by comparison of the values of their mean objective function (MOV), and their speed, at solving the global optimization problems in a simple benchmarking function suite with 4 functions of different categories. The study concludes that the DE algorithm shows enhancement performance with modified mutation and crossover components. However, with a trend for inconsistency for varying values of its control parameters and benchmarking problems.

Smart Grid (SG) technologies are leading the modifications of power grids worldwide. The Energy Resource Management (ERM) in SGs is a highly complex problem that needs to be efficiently addressed to maximize incomes while minimizing operational costs. Due to the nature of the problem, which includes mixed-integer variables and non-linear constraints, Evolutionary Algorithms (EA) are considered a good tool to find optimal and near-optimal solutions to large-scale problems. In this paper, we analyze the application of Differential Evolution (DE) to solve the large-scale ERM problem in SGs through extensive experimentation on a case study using a 33-Bus power network with high penetration of Distributed Energy Resources (DER) and Electric Vehicles (EVs), as well as advanced features such as energy stock exchanges and Demand Response (DR) programs. We analyze the impact of DE parameter setting on four state-of-the-art DE strategies. Moreover, DE strategies are compared with other well-known EAs and a deterministic approach based on MINLP. Results suggest that, even when DE strategies are very sensitive to the setting of their parameters, they can find better solutions than other EAs, and near-optimal solutions in acceptable times compared with an MINLP approach.

Modified Differential Evolution with Locality induced Genetic Operators for dynamic optimization

Over the past few decades, various evolutionary algorithms (EAs) have been applied to the optimization design of water distribution systems (WDSs). An important research area is to compare the performance of these EAs, thereby offering guidance for the selection of the appropriate EAs for practical implementations. Such comparisons are mainly based on the final solution statistics and, hence, are unable to provide knowledge on how different EAs reach the final optimal solutions and why different EAs performed differently in identifying optimal solutions. To this end, this paper aims to compare the real-time searching behaviour of three widely used EAs, which are genetic algorithms (GAs), the differential evolution (DE) algorithm and the ant colony optimization (ACO). These three EAs are applied to five WDS benchmarking case studies with different scales and complexities, and a set of five metrics are used to measure their run-time searching quality and convergence properties. Results show that the run-time metrics can effectively reveal the underlying searching mechanisms associated with each EA, which significantly goes beyond the knowledge from the traditional end-of-run solution statistics. It is observed that the DE is able to identify better solutions if moderate and large computational budgets are allowed due to its great ability in maintaining the balance between the exploration and exploitation. However, if the computational resources are rather limited or the decision has to be made in a very short time (e.g., real-time WDS operation), the GA can be a good choice as it can always identify better solutions than the DE and ACO at the early searching stages. Based on the results, the ACO performs the worst for the five case study considered. The outcome of this study is the offer of guidance for the algorithm selection based on the available computation resources, as well as knowledge into the EA’s underlying searching behaviours.

Modified Teaching–Learning-Based Optimization algorithm for global numerical optimization—A comparative study

Differential Evolution (DE) is one of the current best evolutionary algorithms. It becomes important in many fields such as evolutionary computing and intelligent optimization. At present, DE has successfully been applied to diverse domains of science and engineering, such as signal processing, neural network optimization, pattern recognition, machine intelligence, chemical engineering and medical science. However, almost all the DE-related evolutionary algorithms still suffer from the problems such as premature convergence, slow convergence rate and difficult parameter setting. To overcome these drawbacks, we propose a novel Cloud Model-Based Differential Evolution Algorithm (CMDE) in which the pheromone and the sensitivity model of free search algorithm replaces the traditional roulette wheel selection model. The model incorporates Opposition-Based Leaning (OBL) to present an improved artificial bee colony algorithm. Experimental results verify the superiority of CMDE is over several state-of-the-art evolutionary optimizers.

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 preliminary satisfactory results obtained by means of chaos embedded (driven) DE, which utilizes the chaotic dynamics in the place of pseudorandom number generators The novelty of this work represents the experimental analysis of the chaotic dynamics directly injected into the DE. To be more precise, this research investigates the influence of parameter settings to the performance of chaos driven DE. Both settings for mutation and crossover DE control parameters and adjustable chaotic system parameters are experimentally investigated here. Repeated simulations were performed on the selected set of well-known benchmark functions in higher dimensions. Finally, the obtained results are compared with canonical DE and state-of-the art representative of basic adaptive variant jDE.

In recent years, various methods from the evolutionary computation (EC) field have been applied to electromagnetic (EM) design problems and have shown promising results. However, due to the high computational cost of the EM simulations, the efficiency of directly using evolutionary algorithms is often very low (e.g., several weeks' optimization time), which limits the application of these methods for many industrial applications. To address this problem, a new method, called surrogate model assisted differential evolution for antenna synthesis (SADEA), is presented in this paper. The key ideas are: (1) A Gaussian Process (GP) surrogate model is constructed on-line to predict the performances of the candidate designs, saving a lot of computationally expensive EM simulations. (2) A novel surrogate model-aware evolutionary search mechanism is proposed, directing effective global search even when a traditional high-quality surrogate model is not available. Three complex antennas and two mathematical benchmark problems are selected as examples. Compared with the widely used differential evolution and particle swarm optimization, SADEA can obtain comparable results, but achieves a 3 to 7 times speed enhancement for antenna design optimization.