Differential evolution is one of the most promising evolutionary algorithms for real-parameter single-objective optimization. It has usually been hybridized with another competitive algorithm, the CMA-ES to boost the overall performance in the recent CEC competitions. In this paper, we compare the performance of a recently proposed domain transform-based differential evolution with the CEC competition winners on the CEC2025 benchmark functions. A new performance evaluation method, the U-score approach which could measure both the speed and accuracy of stochastic optimizers is adopted in the comparison. The results show that the domain transform-based differential evolution achieves the best performance against the winners which are usually hybrid methods. This study indicates that a pure DE could also be competitive to or even outperform hybrid algorithms. Besides guaranteeing the performance, it also simplifies algorithmic designs.

The parameter adaptation enhanced differential evolution (DE) algorithm has demonstrated promising performance for noiseless optimization. However, its efficiency degrades when confronted with noise in a noisy environment, which makes the fitness comparison for adaptation unreliable. To deal with the issue and improve the performance, this article proposes a fuzzy logic system (FLS)-assisted parameter adaptation for noisy optimization, inspired by the strength of FLS in handling uncertainties. The proposed FLS is fully informed by search feedback from both the objective and solution spaces, as well as their correlation, allowing for a more comprehensive estimation of parameters. Experimental studies confirm the superiority of the proposed method in noisy environments over adaptation methods that solely rely on fitness comparison. The constructed fully informed FLS-assisted noisy DE exhibits state-of-the-art performance compared to other evolutionary algorithms.

Although a significant advancement of differential evolution (DE) for global optimization has been witnessed in the past two decades, the problems of premature convergence and stagnation are still open questions that hinder the performance. Both are likely to occur on complicated multimodal functions, but the phenomena differ. Premature convergence refers to a rapid loss of population diversity when attracted to a local minimum while stagnation happens even though the population is diverse. To deal with these problems, this article proposes a domain transform (DT) methodology. Different from existing fitness analysis which mainly utilizes the original fitness landscape information, DT yields a transformed fitness landscape with transform operation to the frequency domain and inverse transform operation back to the solution domain, between which the first few highest frequencies are removed. With the deletion operation, the transformed fitness landscape becomes smoother and facilitates the escape from local minima and stagnation on complicated multimodal functions. Simulation results show that DT significantly improves the population successful update rate and population convergence. The constructed DTDE algorithm consequently exhibits remarkable improvements on the baseline algorithm and outperforms several state-of-the-art DE variants. DT has also been extended for noisy optimization and it performs better than the baseline, the classic resampling method, state-of-the-art DE variants, as well as several popular noisy evolutionary optimization algorithms.

Different from the classic differential evolution (DE) and many of its variants, collective information powered DE (CIPDE) is characterized by the utilization of collective information of population in the mutation and crossover processes of DE. This paper proposes a restart mechanism for CIPDE, to improve its robustness for solving the 100-digit challenge on single objective numerical optimization. Restart based CIPDE (rCIPDE) restarts the population when the unsuccessful update of the population exceeds a threshold value. Simulations on the challenge show that the restart mechanism enhances the performance on five out of the total 10 benchmark functions. According to the competition rule, rCIPDE achieves a total score of 85 (10 marks on each of F1-F7 and F10, 2 marks on F8 and 3 marks on F9).

Differential evolution (DE) is recognized as a simple but powerful algorithm in the family of evolutionary algorithms. Over the past two decades, many advanced DE variants with significantly improved performance have been proposed. However, the variants may only achieve the best performance on a certain type of functions. Moreover, a specific optimizer may not always be suitable for the whole optimization process. To overcome these weaknesses, this paper proposes a multiple variants coordination (MVC) framework with two mechanisms, namely, the multiple variants adaptive selecting mechanism and the multiple variants adaptive solutions preserving mechanisms (MV-APM). In MVC, the evolution process is divided into nonoverlap segments with equal numbers of generations. Each segment includes the learning generations (LGs) and executing generations (EGs). In LG, all the candidate DE optimizers are utilized independently. The best performing optimizer is determined and then utilized in EG in the same segment. Furthermore, MV-APM maintains the population by adaptively preserving promising solutions generated by multiple optimizers. Numerical experiments on the CEC2014 benchmark suit show that the proposed MVC framework can significantly improve the performance of the baseline algorithms and the resulted algorithm significantly outperform the start-of-the-art and up-to-date DEs. Moreover, as a general framework, MVC can also be applied to coordinate multiple improved DE variants to further enhance their performance.

Differential evolution (DE) is a simple yet powerful evolutionary algorithm for both single objective and multiobjective optimizations (MOPs). In nature, good parents are more likely to produce good offspring, because genes from good individuals propagate throughout the population. Inspired by this phenomenon, a two-step subpopulation strategy is proposed, in which individuals in the current population are sorted based on evaluation metrics, and are divided into superior and inferior subpopulations. The inferior subpopulation evolves to generate offspring. If the generated offspring has better evaluation metric values than individuals in the superior subpopulation, they will replace the latter and be used as vectors for mutation strategies. The proposed strategy is incorporated into several advanced DE variants for both single-objective optimization (SOP) and MOPs to verify its effectiveness. Experiments are conducted on 25 single objective, 5 bi-objective, and 4 tri-objective Deb, Thiele, Laumanns and Zitzler (DTLZ) benchmark problems. Results indicate that the proposed subpopulation strategy is capable of improving the performance of both single objective and multiobjective algorithms. The application of the proposed approach is demonstrated by solving a microwave circuit design problem with stringent requirements. The better performance achieved by the proposed approach in quality of solutions, convergence rate, and diversity is verified by the performance comparison with competitive optimization algorithms in the literature.