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Differential Evolution (DE) stands out as an exceptional intelligent evolutionary algorithm, acclaimed for its simplicity in implementation and the ability to optimize without necessitating differentiable conditions. However, a significant pitfall of DE lies in its susceptibility to getting trapped in local minima, leading to algorithmic stagnation and substantial performance impairments. To counteract the shortcoming, the A daptative D ifferential E volution with D iversity M aintenance and R estart M echanism (ADE-DMRM) is proposed. This approach integrates three primary innovations. Firstly, the algorithm controls the number of generations that individuals stay in the external archive based on the successful evolution rate, thereby optimizing the mutation strategy to effectively maintain population diversity. Secondly, ADE-DMRM proposes a novel restart mechanism in which the current stagnant individuals are identified by combining a stagnation tracker and a diversity assessment indicator and then regenerated using a dimension-learning-based approach. Thirdly, wavelet basis functions and Cauchy distributions are employed for scaling factor implementation across different stages, while the dimension change information of successfully evolved individuals is harnessed to refine the adaptive parameter control scheme. Finally, comprehensive experiments were undertaken on the CEC2013, CEC2014, and CEC2017 test sets, assessing accuracy, convergence speed, the efficacy of each module, and time complexity. The results confirm that ADE-DMRM is an efficient single-objective optimization algorithm that outperforms current advanced variants. • An adaptive DE with Diversity Maintenance and Restart Mechanism is proposed. • The external archive is selectively optimized based on the successful rate of the population. • A novel restart mechanism is proposed to avoid premature convergence. • Wavelet basis functions and Cauchy distributions are employed in generating F. [ABSTRACT FROM AUTHOR]

Differential evolution is one of the most powerful stochastic real-parameter optimization algorithms currently, and its performance depends heavily on control parameters and mutation strategy. In recent years, methods to select favorable parameters control and mutation strategy when solving various optimization problems have attracted increasing attention. To choose an appropriate mutation strategy and control parameters for a given optimization problem, in this paper, a Adaptive Differential Evolution Algorithm Based on Deeply-Informed Mutation Strategy and Restart Mechanism (ADEDMR) is proposed, and the ADEDMR algorithm has the following characteristics: First, a deeply-informed mutation strategy is proposed, which takes into account the information of suboptimal solutions discarded by selection and inherits the advantages of the powerful "DE/target-pbest/1/bin", aiming to obtain a better perceptual landscape of the target function and improve the candidate diversity of the trial vector. Second, according to the evolution process, the segmentation method is used to control F , which alleviates the scaling of F in the wrong direction, and makes the newly generated F fit more accurately. Third, a new population restart mechanism is adopted to further enhance population diversity by adaptively enhancing the search ability of hopeless individuals and randomly replacing some inferior individuals with wavelet walks. To evaluate the performance of our proposed algorithm, comparative experiments are conducted on 72 benchmark functions from the CEC2014, CEC2017 and CEC2022 test suites. Experimental results show that the proposed ADEDMR has higher convergence accuracy, better optimization ability when solving high-dimensional complex functions, and is competitive with six recent strong DE variants. [ABSTRACT FROM AUTHOR]

Differential Evolution (DE) is one of the most effective methods for single-objective numerical optimization, however, the former state-of-the-art DE variants ignore the huge differences among the individuals in the population. To take full advantage of different individuals in the population, in this paper, a dynamic Hierarchical Population based Differential Evolution (HPDE) with novel diversity metric is proposed, and the HPDE algorithm has the following innovations: Firstly, the individuals in the hierarchical population are dynamically divided into two layers, the layer of elites, and the layer of ordinary individuals. Moreover, the ordinary layer individuals are further divided into secondary elites and inferior individuals. The individuals in the two layers employed different mutation strategies and the corresponding parameter control schemes. Secondly, a novel hierarchical population based mutation strategy is firstly proposed in our HPDE algorithm and the individuals in the elite layer employ the novel mutation strategy aiming at scouting the landscape of the objective while the ordinary individuals employ an improved "DE/target- p best/1/bin" strategy aiming at getting a better balance between exploration and exploitation of the solution space. Thirdly, a N ovel P arameter C ontrol technique, namely NPC technique, is employed in the adaptation of control parameters during the evolution. Fourthly, a new metric of population diversity is proposed and premature convergence can be avoided by maintaining better population diversity. To evaluate the performance of our HPDE algorithm, intensive experiments are conducted on 88 benchmark functions from the CEC2013, CEC2014 and CEC2017 test suites, and the results show the competitiveness of our HPDE with six recent state-of-the-art DE variants, e.g. it obtained 28 similar or better performance improvements out of the total 30 benchmarks on 30D optimization in comparison with the winner algorithm, the LSHADE algorithm, of the CEC2014 competition and it also obtained 19 similar or better performance improvements out of the total 30 benchmarks on 30D optimization in comparison with the winner DE variant, the jSO algorithm, of the CEC2017 competition. Furthermore, the novel HPDE algorithm is utilized to estimate the parameters of the photovoltaic model, and the experiment results support its superiority as well. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a novel fitness-value-independent Differential Evolution to tackle complex real-parameter single-objective optimization. There were three innovations in the algorithm: First, dimension improvements based adaptation schemes for control parameters F and C R were advanced in this paper. Different from those fitness value improvements based parameter control in the recent winner DE variants, our algorithm has fitness-value-independent characteristic, therefore, it can be applied in much wider optimization scenarios especially for those that the exact fitness values of the objectives are unavailable. Second, a combined parabolic–linear reduction scheme for population size is employed in the algorithm based on the observation that the slower reduction of population size at the earlier stage of the evolution usually helps to get better perception of the objectives while a linear reduction of population size in the later stage helps to get better exploitation. Third, an indicator is proposed to monitor the diversity of the population and a corresponding population enhancement technique is launched when the diversity is detected bad. The first two innovations have the P arameter a daptive characteristic of the DE algorithm while the third innovation refers to p opulation e nhancement t echnique, therefore, we name our algorithm "the PaDE-pet algorithm". Then, the algorithm is validated under a larger test suite containing 88 benchmarks from CEC2013, CEC2014 and CEC2017 test suites for real-parameter single objective optimization, which may avoid over-fitting problem in comparison with employing a test suite containing a small number of benchmarks. The experiments support the superiority of the novel PaDE-pet algorithm in comparison with several recently proposed powerful DE variants. • A black-box model reflecting complex optimization without available fitness values. • The model reveals the fitness-value-dependent weakness of recent winner DE variants. • A novel fitness-value-independent DE algorithm was proposed to tackle the model. • New adaptation schemes for control parameters and population enhancement technique. • To avoid over-fitting, a larger test suite is employed in algorithm validation. [ABSTRACT FROM AUTHOR]

Abstract Differential Evolution (DE) variants have been proven to be excellent algorithms in tackling real-parameter single objective numerical optimization because they have secured the front ranks of these competitions for many years. Nevertheless, there are still some weaknesses, e.g. (1) improper control parameter adaptation schemes; and (2) defect in a given mutation strategy., existing in some state-of-the-art DE variants, which may result in slow convergence and worse optimization performance. Therefore, in this paper, a novel Parameter adaptive DE (PaDE) is proposed to tackle the above mentioned weaknesses and the PaDE algorithm has three advantages: (1) A grouping strategy with novel adaptation scheme for C r is proposed to tackle the improper adaptation schemes of C r in some state-of-the-art DE variants; (2) A novel parabolic population size reduction scheme is proposed to tackle the weakness in linear population size reduction scheme; (3) An enhanced time stamp based mutation strategy is proposed to tackle the weakness in a former mutation strategy. The novel PaDE algorithm is verified under 58 benchmarks from two Congress on Evolutionary Computation (CEC) Competition test suites on real-parameter single objective numerical optimization, and experiment results show that the proposed PaDE algorithm is competitive with the other state-of-the-art DE variants. [ABSTRACT FROM AUTHOR]

Optimization demands are ubiquitous in science and engineering. The key point is that the approach to tackle a complex optimization problem should not itself be difficult. Differential Evolution (DE) is such a simple method, and it is arguably a very powerful stochastic real-parameter algorithm for single-objective optimization. However, the performance of DE is highly dependent on control parameters and mutation strategies. Both tuning the control parameters and selecting the proper mutation strategy are still tedious but important tasks for users. In this paper, we proposed an enhanced structure for DE algorithm with less control parameters to be tuned. The crossover rate control parameter Cr is replaced by an automatically generated evolution matrix and the control parameter F can be renewed in an adaptive manner during the whole evolution. Moreover, an enhanced mutation strategy with time stamp mechanism is advanced as well in this paper. CEC2013 test suite for real-parameter single objective optimization is employed in the verification of the proposed algorithm. Experiment results show that our proposed algorithm is competitive with several well-known DE variants. [ABSTRACT FROM AUTHOR]

Differential Evolution (DE) is a simple but powerful population-based stochastic optimization algorithm. Owing to its simplicity, easy implementation and excellent performance, DE has been wildly applied in scientific and engineering areas. However, there are still some inconveniences and weaknesses in DE algorithm, such as the inconveniences in the choice of proper control parameters and the defects existing in a given mutation strategy. In this paper, a new DE variant, called Parameters with Adaptive Learning Mechanism Differential Evolution (PALM-DE), is proposed to tackle the inconvenience in control parameter selection as well as to enhance a former mutation strategy. The new variant is verified on 44 commonly used real-parameter single objective benchmark functions selected from CEC2013 and CEC2014 competitions. Several recently proposed well-known DE variants are also contrasted in the paper, and the experiment results show that the proposed PALM-DE algorithm is competitive in comparison with these DE variants. An attempt to enhance the performance of PALM-DE by employing linear population size reduction is also presented, and the performance is still competitive. [ABSTRACT FROM AUTHOR]

This paper presents a new novel evolutionary approach named QUasi-Affine TRansformation Evolutionary (QUATRE) algorithm, which is a swarm based algorithm and use quasi-affine transformation approach for evolution. The paper also discusses the relation between QUATRE algorithm and other kinds of swarm based algorithms including Particle Swarm Optimization (PSO) variants and Differential Evolution (DE) variants. Comparisons and contrasts are made among the proposed QUATRE algorithm, state-of-the-art PSO variants and DE variants under CEC2013 test suite on real-parameter optimization and CEC2008 test suite on large-scale optimization. Experiment results show that our algorithm outperforms the other algorithms not only on real-parameter optimization but also on large-scale optimization. Moreover, our algorithm has a much more cooperative property that to some extent it can reduce the time complexity (better performance can be achieved by reducing number of generations required for a target optimum by increasing particle population size with the total number of function evaluations unchanged). In general, the proposed algorithm has excellent performance not only on uni-modal functions, but also on multi-modal functions even on higher dimension optimization problems. [ABSTRACT FROM AUTHOR]

Differential Evolution (DE) is one of the most popular and powerful branches of evolutionary algorithm family. However, even many state-of-the-art DE-based variants still exist weakness such as improper parameter adaptation and population stagnation during the later stage of evolution. To mitigate these deficiencies, differential evolution with fitness-difference based parameter control and hypervolume diversity indicator (FDHD-DE) is proposed in this paper. Firstly, a semi-adaptive adaptation scheme for control parameters is proposed, in which the generation of scale factor and crossover rate is modified by dividing into two stages, thus enhancing the efficiency of parameter adaptation. Secondly, a novel fitness-based weighting strategy is proposed to improve the performance of existing success history-based adaptation by employing a novel approach of utilizing fitness information. Finally, a hypervolume-based diversity indicator and corresponding dimension exchange strategy are proposed to alleviate the problem of population stagnation. The performance of FDHD-DE is verified on the 88 benchmark functions from Congress on Evolutionary Computation (CEC) 2013, CEC 2014, and CEC 2017 test suites on 10D, 30D and 50D and a real-world application. The experiment results are compared with several state-of-art DE variants, and the results show that FDHD-DE has better performance, both in terms of solution accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

Differential Evolution (DE), as a powerful population-based stochastic optimization algorithm, has attracted the attention of researchers from various fields due to its advantages such as simple operation, strong robustness, and few control parameters. However, many existing DE variants often suffer from drawbacks such as premature convergence and stagnation when solving complicated optimization problems. In view of the aforementioned issues, this paper proposes an adaptive DE with opposition learning-based diversity enhancement (OLBADE). The main contributions can be summarized as follows: Firstly, a new adaptive parameter control is proposed with a non-linear weighting strategy incorporating into the framework of parameter adaptation. Secondly, a donor vector perturbation strategy is introduced to complement existing strategy for increasing population diversity. Thirdly, a novel stagnation indicator is proposed, and then opposition learning strategy is employed to renew stagnated individuals in the population when stagnation occurs. OLBADE is compared with five excellent DE variants under a large test-bed containing CEC2013, CEC2014, CEC2017 and CEC2022 test suites to verify its effectiveness. In addition, OLBADE is applied in parameter identification problem of photovoltaic model to verify its feasibility. Experimental results demonstrate that OLBADE achieves higher solution accuracy, faster convergence speed and better stability. • A hybrid method combining the logistic and sine functions is used for the adjustment of F. • A donor vector perturbation strategy is introduced. • A diversity enhancement mechanism based on opposition learning is proposed. • To avoid over-fitting, a larger test suite is employed in algorithm validation. [ABSTRACT FROM AUTHOR]

Optimization problems exists extensively in real life, especially in science and engineering. Over the past decades, various optimization techniques have been developed to solve complex optimization problems in different areas especially that are unable to be solved by traditional methods. QUasi-Affine TRansformation Evolutionary (QUATRE) algorithm is a new novel evolution structure for global optimization, which is a swarm based algorithm and use quasi-affine transformation approach for evolution. Nevertheless, there are still some weaknesses in these QUATRE variants. This paper presents a novel E-QUATRE algorithm in which an automatically generated evolution matrix with self-adaptive mechanism and an adaptive control parameter F are proposed for the enhancement of the QUATRE algorithm. Moreover, this paper also discusses the relationship between QUATRE algorithm, Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithm, all of which are also famous swarm based Stochastic Algorithms (SAs). Algorithm validation is conducted under CEC2013 test suite on single-objective numerical optimization, and E-QUATRE algorithm is compared with several famous Particle Swarm Optimization (PSO) variants, Differential Evolution (DE) variants and QUATRE variants. The experiment results indicate that the proposed E-QUATRE algorithm has a better performance than these swarm based algorithms with fixed population. [ABSTRACT FROM AUTHOR]