Differential Evolution (DE) has established itself as a leading population-based stochastic optimization technique, widely acclaimed for its conceptual simplicity and effectiveness in handling continuous real-parameter problems. Notwithstanding its broad applicability, the canonical DE framework and many refined variants continue to grapple with two longstanding issues: premature convergence and erosion of population diversity, which become particularly pronounced in complex, multi-modal optimization scenarios. These shortcomings often originate from a suboptimal trade-off between exploratory and exploitative behaviors, ineffective mutation operators during stagnant phases, and diversity preservation approaches that tend to disrupt promising search trajectories. To mitigate these limitations, we present the Dynamic Hybrid Adaptive Differential Evolution (DMADE) algorithm, which introduces three principal innovations: first, a dual-phase parameter adaptation mechanism that employs Gaussian-inspired base components and adaptive perturbations to dynamically regulate exploration-exploitation balance; second, a centroid-driven mutation strategy that utilizes population distribution features to rejuvenate trapped solutions; and third, a diversity enhancement technique grounded in potential energy theory, incorporating dynamic interaction sensing and gradient-based relocation. Empirical studies conducted on the CEC2014, CEC2017, and CEC2022 test suites indicate that DMADE consistently outperforms state-of-the-art DE algorithms in terms of solution precision, convergence rate, and algorithmic stability. The method’s robustness is further substantiated through extensive statistical testing and component-wise ablation experiments, affirming its efficacy in overcoming core challenges prevalent in contemporary evolutionary optimization.
Differential Evolution (DE), a population-driven stochastic optimization technique, has garnered significant interest among researchers across diverse disciplines because of its simple approach, high resilience, and few control parameters. However, numerous existing DE variants frequently encounter limitations when tackling intricate optimization problems, especially due to premature convergence weakness. To mitigate these deficiencies, the paper proposes an adaptive differential evolution with a deeply informed mutation strategy and historical information for numerical optimization (ADEDH), the main contributions of which can be outlined as follows: Firstly, a bi-stage parameter control strategy is proposed to achieve a better balance between exploration and exploitation. Secondly, a deeply informed mutation strategy is implemented, which uses the historical population to mirror the objective landscape and help guide the evolution. Thirdly, a diversity enhancement strategy based on historical information is proposed to tackle the premature convergence weakness. ADEDH is evaluated against nine outstanding competitors under a vast testing framework, containing CEC2013, CEC2014, and CEC2017 test suites. Additionally, the feasibility of ADEDH is further validated through its application to the parameter identification problem of a photovoltaic model. Experimental results demonstrate that ADEDH diversifies the population, attains superior solution precision, and achieves better stability.
Differential evolution (DE), known for its simplicity and robustness, has been widely applied to various real-world optimization tasks. However, DE still suffers from premature convergence and evolutionary stagnation. Premature convergence often results from insufficient population diversity, whereas stagnation typically arises from a lack of global search landscape. To address these issues, this paper proposes A Hybrid Differential Evolution with Discrete Cosine Transform-Based Mutation Strategy and Dynamic Diversity Mechanism (HDCT-DE). First, the discrete cosine transform is used to map inferior individuals from the solution domain to the frequency domain, eliminating fitness landscape components associated with local optima to help DE escape local optima and avoid stagnation. Second, the cumulative variance contribution ratio is used as a diversity indicator to dynamically regulate population diversity and alleviate premature convergence. Then, an Archimedean spiral-based perturbation strategy is embedded in the crossover operation to mitigate evolutionary stagnation. Finally, a novel parameter generation mechanism is proposed, which incorporates frequency-domain-transformed inferior individuals to construct trial vectors. Performance evaluation on 100 benchmark functions from CEC2013, CEC2014, CEC2017, and CEC2022 shows that HDCT-DE outperforms state-of-the-art DE and evolutionary algorithm variants. In addition, a photovoltaic model parameter estimation problem is used to verify the algorithm’s effectiveness on real-world tasks. Experiments show that HDCT-DE significantly alleviates evolutionary stagnation and improves population convergence.
Substituted MnAs0.97P0.03 manganese arsenide is prepared, and its structural, magnetic, and magnetocaloric properties are studied. At 260 K, an abrupt decrease in the magnetization of the sample is observed, which is interpreted as a ferromagnetic–paramagnetic transition. The magnetostructural phase transition is accompanied by the magnetocaloric effect, which is observed in magnetic fields up to 13.5 T.
Owing to its fast convergence speed and high optimization accuracy, differential evolution (DE) has become one of the benchmark algorithms for solving continuous optimization problems. However, when tackling complex optimization problems such as high-dimensional and multimodal tasks, DE often suffers from evolutionary stagnation, insufficient global search capability, and premature convergence. To address these challenges, this paper proposes Differential Evolution with a Variance Contribution Ratio-Based Diversity Enhancement Mechanism (DE-VCR). The proposed algorithm incorporates the following three major improvements. First, an infinity-norm-based parameter generation and update mechanism is designed, which exploits information from the current best individual to guide adaptive control parameter adjustment. Second, a gamma-distribution-based mutation strategy is proposed to enhance global exploration by transforming low-fitness individuals. Finally, a population diversity enhancement mechanism based on the variance contribution ratio is introduced and combined with principal component analysis to effectively alleviate evolutionary stagnation. To evaluate the performance of DE-VCR, extensive experiments are conducted on 376 benchmark problems from the CEC2013, CEC2014, CEC2017, and CEC2022 test suites, with comparisons against various state-of-the-art DE variants and other evolutionary algorithms. The experimental results demonstrate that DE-VCR exhibits strong competitiveness in terms of optimization accuracy. In addition, the algorithm shows good practicality and robustness in real-world applications such as parameter estimation of photovoltaic power systems.
