Differential Evolution with exponential crossover can be also competitive on numerical optimization

Enhancing the search ability of differential evolution through orthogonal crossover

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.

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.

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

Differential evolution (DE) is a powerful evolutionary algorithm for global optimization problems. Generally, appropriate mutation strategies and proper equilibrium between global exploration and local exploitation are significant to the performance of DE. From this consideration, in this paper, we present a novel DE variant, abbreviated to DMIE-DE, to further enhance the optimization capacity of DE by developing a dual mutations collaboration mechanism with elites guiding and inferiors eliminating techniques. More specifically, an explorative mutation strategy DE/current-to-embest with an elite individual serving as part of the difference vector and an exploitative mutation strategy DE/ebest-to-rand with selecting an elite individual as the base vector are employed simultaneously to achieve the balance between local and global performance of the whole population instead of only one mutation strategy in classical DE algorithm. The control parameters F and CR for above mutation strategies are updated adaptively to supplement the optimization ability of DMIE-DE based on a rational probability distribution model and the successful experience from the previous iterations. Moreover, an inferior solutions eliminating technique is embedded to enhance the convergence speed and compensate cost of the fitness evaluation times during the evaluation process. To evaluate the performance of DMIE-DE, experiments are conducted by comparing with five state-of-the-art DE variants on solving 29 test functions in CEC2017 benchmark set. The experimental results indicate that the performance of DMIE-DE is significantly better than, or at least comparable to the considered DE variants.

Throughout the past few decades, a variant of differential evolution (DE) algorithms have been introduced with a competitive performance on complex optimization problems. However, the DE superiority is highly dependent on its control parameters and the search operators (i.e., mutation and crossover schemes). Therefore, to obtain the optimal performance, tuning the parameters is essential. In this paper, the DE algorithm is proposed that uses a new designed mutation scaling factor to dynamically adapt the movement of the individuals in the search space toward the optimal value during the evolutionary process. The numerical experiments are conducted on thirty CEC 2014 benchmark functions on four different dimensions; 10, 30, 50, and 100. The obtained results demonstrate that the proposed algorithm is highly competitive and shows better performance than the classical DE algorithm.

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.

A dynamic clustering based differential evolution algorithm for global optimization

Differential Evolution with wavelet basis function based parameter control and dimensional interchange for diversity enhancement

Differential evolution improved with self-adaptive control parameters based on simulated annealing

With the growing demand for emission reductions and fuel efficiency improvements, alternative energy sources and energy storage technologies are becoming popular in a ship microgrid. In order to balance the two non-compatible objectives, a new differential evolution variant, which is named as SaCIDE-r, was proposed to solve the optimization problem. In this algorithm, a Collective Intelligence (CI) based mutation operator was proposed by mixing some promising donor vectors in the current population. Besides, a self-adaptive mechanism which was developed to avoid introducing extra control parameters. Further, to avoid being trapped in local optima, a re-initialization mechanism was developed. Then, we have evaluated the performances of the proposed SaCIDE-r approach by studying some numerical optimization problems of Congress on Evolutionary Computation (CEC) 2013 with D = 30, compared with seven stateof-the-art DE algorithms. Moreover, the proposed SaCIDE-r method was applied for economic scheduling of a shipboard microgrid under different cases compared with other multi-objective optimizing methods, resulting in very competitive performances. The comprehensive experimental results have demonstrated that the presented SaCIDE-r method might be a feasible solution for such a kind of optimization problem.

Differential evolution with orthogonal array‐based initialization and a novel selection strategy

Differential Evolution (DE) is widely recognized as a highly effective evolutionary algorithm for global optimization. It has proven its efficacy in tackling diverse problems across various fields and real-world applications. DE boasts several advantages, such as ease of implementation, reliability, speed, and adaptability. However, DE does have certain limitations, such as suboptimal solution exploitation and challenging parameter tuning. To address these challenges, this research paper introduces a novel algorithm called Enhanced Binary JADE (EBJADE), which combines differential evolution with multi-population and elites regeneration. The primary innovation of this paper lies in the introduction of strategy with enhanced exploitation capabilities. This strategy is based on utilizing the sorting of three vectors from the current generation to perturb the target vector. By introducing directional differences, guiding the search towards improved solutions. Additionally, this study adopts a multi-population method with a rewarding subpopulation to dynamically adjust the allocation of two different mutation strategies. Finally, the paper incorporates the sampling concept of elite individuals from the Estimation of Distribution Algorithm (EDA) to regenerate new solutions through the selection process in DE. Experimental results, using the CEC2014 benchmark tests, demonstrate the strong competitiveness and superior performance of the proposed algorithm.

An adaptive differential evolution with opposition-learning based diversity enhancement

Differential evolution (DE) algorithm is a global optimization algorithm over continuous search space. DE also has been applied in many fields, such as artificial neural networks, chemical engineering, mechanical design, robotics, signal processing, biological information, and economics. At the same time, as a powerful evolutionary algorithm for solving global numerical optimization problems, the DE algorithm has drawn more and more attention. However, how to make a proper balance between the global and local search is a burning question and to limit the optimization performance of DE. In this paper, an improved algorithm η_CODE with a new η_Cauchy operator is proposed to enhance the global and local search ability of a well-known DE variant JADE. In order to guarantee the effective performance of the proposed operator, all the fitness values are ranked through a ranking scheme based on increasing order before a new η_Cauchy operator is conducted. The pNP individuals that have better fitness are selected and carried out Cauchy disturbance operation considering the complexity of the algorithm. The Dynamic parameter mechanism is utilized to select pNP individuals that number is also adjusted dynamically in each generation. The scale factor F and crossover probability CR are obtained with Lehmer mean without using determined parameter c in JADE, which aims to balance the exploration and exploitation of the algorithm during the running time. A total of sixty benchmark functions from CEC2014 and CEC2017 on real parameter optimization are employed to prove the validity of η_CODE for solving complex high-dimensional problems. The experiments indicate that η_CODE is better than or at least comparable with several state-of-the-art DE variants, including JADE, SinDE, TSDE, AGDE, and EFADE in the global numerical optimization problems. In order to further analyze the performance of η_CODE, we also select extra two high-powered modified algorithms called EBLSHADE and LSHADESPACMA based on LSHADE to discuss advantages and disadvantages of the proposed algorithm.