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Many real-life problems can be formulated as numerical optimization problems. Such problems pose a challenge for researchers when designing efficient techniques that are capable of finding the desired solution without suffering from premature convergence. This paper proposes a novel evolutionary algorithm that blends the exploitative and explorative merits of two main evolutionary algorithms, namely the Stochastic Fractal Search (SFS) and a Differential Evolution (DE) variant. This amalgam has an effective interaction and cooperation of an ensemble of diverse strategies to derive a single framework called Iterative Cyclic Tri-strategy with adaptive Differential Stochastic Fractal Evolutionary Algorithm (Ic3-aDSF-EA). The component algorithms cooperate and compete to enhance the quality of the generated solutions and complement each other. The iterative cycles in the proposed algorithm consist of three consecutive phases. The main idea behind the cyclic nature of Ic3-aDSF-EA is to gradually emphasize the work of the best-performing algorithm without ignoring the effects of the other inferior algorithm during the search process. The cooperation of component algorithms takes place at the end of each cycle for information sharing and the quality of solutions for the next cycle. The algorithm's performance is evaluated on 43 problems from three different benchmark suites. The paper also investigates the application to a set of real-life problems. The overall results show that the proposed Ic3-aDSF-EA has a propitious performance and a reliable scalability behavior compared to other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

This paper focuses on the use of differential evolution to improve the approximation properties of function approximation models based on fuzzy partitions. Two cases are considered: Fuzzy transform and Fuzzy projection, and the design of hybrid evolutionary fuzzy systems, is studied. Even though function approximation techniques based on fuzzy partitions have been well studied, few papers consider the problem of centroid selection of the basis functions. Thus, in most cases uniform fuzzy partitions are considered. By using an evolutionary algorithm a systematic approach on the selection of the partition, is provided. The optimisation problem involves the determination of the model parameters, which in our case are the fuzzy partition's membership functions' locations. The proposed method is tested on the scattered data approximation problem, in a regression sense, that is given a set of sparse data the latent function is approximated. Numerical studies on one and two-dimensional test functions demonstrate that the evolutionary algorithm based fuzzy projection displays high performance in terms of approximation error. Moreover, the proposed approach shows high approximation capabilities with a small number of basis functions. Comparison results, with uniform fuzzy partition models, neural networks and support vector machines, are provided. [ABSTRACT FROM AUTHOR]

• A novel random neighbor elite guided mutation strategy named "DE/current-to-rnbest/1", which is a general mutation framework. • Random neighbor region formed by several random individuals in the population. • Two special cases of "DE/current-to-rnbest/1": "DE/current-to-best/1" and "DE/current-to-pbest/1" • Adaptive neighbor size adjustment at the individual level based on the Cauchy distribution. • Exploring and exploiting the solution space appropriately to find global optima. Optimization problems not only become more and more ubiquitous in various fields, but also become more and more difficult to optimize nowadays, which seriously challenge the effectiveness of existing optimizers like different evolution (DE). To effectively solve this kind of problems, this paper proposes a random neighbor elite guided differential evolution (RNEGDE) algorithm. Specifically, to let individuals explore and exploit the solution space properly, a novel random neighbor elite guided mutation strategy named "DE/current-to-rnbest/1" is first proposed to mutate individuals. In this mutation strategy, several individuals randomly selected from the population for each individual to be updated along with the individual itself form a neighbor region, and then the best one in such a region is adopted as the guiding exemplar to mutate the individual. Due to the random selection of neighbors and the directional guidance of elites, this strategy is expected to direct individuals to promising areas fast without serious loss of diversity. Notably, it is found that two popular mutation strategies, namely "DE/current-to-best/1" and "DE/current-to-pbest/1", are two special cases of the proposed "DE/current-to-rnbest/1". Further, to alleviate the sensitivity of the proposed algorithm to the involved parameters, this paper utilizes the Gaussian distribution and the Cauchy distribution to adaptively generate parameter values for each individual with the mean value of the Gaussian distribution and the position value of the Cauchy distribution adaptively adjusted based on the evolutionary information of the population. With the above two techniques, the proposed algorithm is expected to effectively search the solution space. At last, extensive experiments conducted on one widely used benchmark function set with three different dimension sizes demonstrate that the proposed algorithm achieves highly competitive or even much better performance than several compared state-of-the-art peer methods. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) is one of the widely studied algorithms in evolutionary computation. Recently, many adaptive mechanisms have been proposed for DE including adaptive operator selection and adaptive parameter control. Existing studies consider the two kinds of mechanisms independently. In this paper, we first propose a unified mutation operator with learnable parameters. With different parameter settings, the unified mutation operator degenerates into various classic mutation operators. As a result, by adapting the control parameters of the unified mutation operator, we can realize parameter control and operator selection simultaneously. We then present how to use a neural network to adaptively determine the control parameters. We use natural evolution strategies to train the neural network by modeling the evolutionary process as a Markov decision process. We then embed it into three DEs including classic DE, JADE and LSHADE. Experimental studies show that by embedding the learned unified mutation operator, the performances of these backbone DEs can be improved. Particularly, by embedding the unified mutation operator, LSHADE can perform competitively among state-of-the-art EAs including the winner algorithms in the past CEC competitions. Furthermore, we verify the effectiveness of the unified mutation operator through analyzing the population diversity theoretically. [ABSTRACT FROM AUTHOR]

Wind speed forecasting plays a crucial role in reducing the risk of wind power uncertainty, which is vital for power system planning, scheduling, control, and operation. However, it is challenging to obtain accurate wind speed forecasting results since wind speed series contain complex fluctuations. In this paper, a novel wind speed forecasting model is proposed by using a genetic algorithm (GA) and long short-term memory neural network (LSTM), where GA is used for evolving the architectures and hyper-parameters of the LSTM, called EvLSTM, because there is no clear knowledge to determine these crucial parameters. In the proposed EvLSTM forecasting model, a flexible gene encoding strategy, crossover operation, and mutation operation are proposed to describe the different architectures and hyper-parameters of the LSTM during the evolutionary process. In addition, to overcome the weakness of the single method for wind speed forecasting, the ensemble EvLSTM (EnEvLSTM) is proposed by using the no negative constraint theory ensemble learning strategy, whose weight coefficients are determined by the differential evolution algorithm. The proposed EvLSTM and EnEvLSTM forecasting models are evaluated on two real-world wind farms located in Inner Mongolia, China and Sotavento Galicia, Spain. Experimental results on two forecasting horizons demonstrate the superiority of EvLSTM and EnEvLSTM in terms of three performance indices and three statistical tests. [ABSTRACT FROM AUTHOR]

[Display omitted] • A framework is proposed for population-based optimization algorithms' convergence. • DIRECT's partition and population evolutions are repeated in this framework. • The global convergence of the framework is proved. • Framework is applied successfully on three population-based optimization algorithms. Population-based optimization algorithms, such as genetic algorithm and particle swarm optimization, have become a class of important algorithms for solving global optimization problems. However, there is an issue that the global convergence is often absent for most of them. This paper proposes a partition-based convergence framework for population-based optimization algorithms to solve this troubling problem. In this framework, regular partitions and evolutions of populations are implemented alternatively. Specifically, the initial population is generated from a regular partition on the search space; after several generations of evolution of the population, the evolution result is returned to join in the regular partition again, and a new population is generated. Repeat such progress until some stop condition is satisfied. Global convergence is guaranteed for the framework. Then this convergence framework is applied to particle swarm optimization, differential evolution, and genetic algorithm. The modified algorithms are globally convergent and perform better than the original version. [ABSTRACT FROM AUTHOR]

• Using machine learning to recommend appropriate parameters and operators for differential evolution algorithm. • The fitness landscape features are used as a basis for recommending parameters for the optimization problems. • A mutation operator selector based on AdaBoost & decision tree, and a parameter selector based on BP neural network are established for the differential evolution algorithm. Due to the problems of low accuracy and increasing control parameters in the existing parameter adaptive methods of differential evolution (DE) algorithm, in this paper a mutation operator selector and a parameter selector are proposed through Fitness Landscape (FL) analysing. At first, the performance differences of the two categories of mutation operators named DE / b e s t / 1 and DE / c u r r e n t - t o - r a n d / 1 were analyzed on many test problems. Secondly, the relationship between the FL and mutation operator is founded by using ensemble learning and decision tree, and achieved a classifier named mutation operator selector. Thirdly, the relationship between the FL and algorithm parameters is founded by using a neural network, and then a classifier named parameter selector is achieved. Finally, the improved DE algorithm equip with the two selectors is tested on the CEC2017 benchmark set. The results show that the proposed improved DE algorithm is outperforms both the basis DE algorithm and other three state-of-the-arts algorithms. [ABSTRACT FROM AUTHOR]

The performance of differential evolution (DE) significantly depends on the settings of mutation strategies and control parameters. Inappropriate settings may cause an imbalance between exploration and exploitation of the algorithm, thus resulting in two extremes: premature convergence and failure to converge. In this paper, we propose a Differential Evolution using Leader-Adjoint populations (LADE), which simultaneously integrates four mutation strategies to meet the needs of exploration and exploitation at different evolutionary stages. In LADE, the population in each generation is divided into leader population and adjoint population by using a leader-adjoint model. The leader population adopts two mutation strategies with strong exploration ability to maintain the diversity and avoid premature convergence, while the adjoint population uses the other two mutation strategies with strong exploitation ability to promote convergence and avoid stagnation. In addition, the interaction and collaboration between both populations are achieved through the sharing between their individuals, thus achieving a good trade-off between exploration and exploitation. The performance of LADE is evaluated on single-objective benchmark problems of the 2017 Institute of Electrical and Electronics Engineers Congress on Evolutionary Computation (IEEE CEC2017). Experimental results indicate that LADE shows competitive convergence performance, and outperforms various state-of-the-art DE variants and two well-known metaheuristics. [ABSTRACT FROM AUTHOR]

The performance of differential evolution (DE) significantly depends on the settings of mutation strategies and control parameters. Inappropriate settings may cause an imbalance between exploration and exploitation of the algorithm, thus resulting in two extremes: premature convergence and failure to converge. In this paper, we propose a Differential Evolution using Leader-Adjoint populations (LADE), which simultaneously integrates four mutation strategies to meet the needs of exploration and exploitation at different evolutionary stages. In LADE, the population in each generation is divided into leader population and adjoint population by using a leader-adjoint model. The leader population adopts two mutation strategies with strong exploration ability to maintain the diversity and avoid premature convergence, while the adjoint population uses the other two mutation strategies with strong exploitation ability to promote convergence and avoid stagnation. In addition, the interaction and collaboration between both populations are achieved through the sharing between their individuals, thus achieving a good trade-off between exploration and exploitation. The performance of LADE is evaluated on single-objective benchmark problems of the 2017 Institute of Electrical and Electronics Engineers Congress on Evolutionary Computation (IEEE CEC2017). Experimental results indicate that LADE shows competitive convergence performance, and outperforms various state-of-the-art DE variants and two well-known metaheuristics. [ABSTRACT FROM AUTHOR]

Surrogate-assisted evolutionary algorithms (SAEAs) have gained considerable attention owing to their ability of tackling expensive optimization problems (EOPs). The surrogate model can be used to replace real fitness value with approximated one, thus greatly reducing computational cost in expensive function evaluations. However, most existing SAEAs are designed for expensive optimization with low or medium dimensions owing to the curse of dimensionality. To improve the performance for solving high-dimensional expensive optimization problems (HEOPs), a surrogate-assisted Differential Evolution with fitness-independent parameter adaptation (SADE-FI) is proposed in the paper. The SADE-FI algorithm consists of a global surrogate-assisted prescreening strategy (GSA-PS) and a local surrogate-assisted DE with fitness-independent parameter adaptation (LSA-FIDE). The main highlights of the paper can be summarized as follows: First, both global and local surrogates are employed to approximate the fitness value of candidate offspring in GSA-PS and LSA-FIDE, respectively. Second, a fitness-independent parameter adaptation mechanism is firstly incorporated into the framework of surrogate-assisted DE as an efficient parameter adaptation for surrogate-assisted search. Third, both the kernel space determination mechanism and linear population size reduction strategy are implemented to enhance the exploitation capability of LSA-FIDE. To validate the performance of SADE-FI, it was tested on expensive benchmark functions on 30D, 50D, 100D, and 200D, as well as a real-world antenna array design problem. The optimization results were compared with state-of-the-art algorithms, and the results indicate that SADE-FI has a significant performance advantage in solving HEOPs. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) is an efficient and powerful population-based search algorithm for solving numerical optimization problems in continuous spaces. It has been proven that multi-strategy DE algorithms are more effective than single-strategy DE algorithms in addressing benchmark and real-world problems. However, most multi-strategy DE variants focus on maintaining population diversity and balancing exploitation and exploration, ignoring the dynamic allocation of computational resources. Moreover, the success of these algorithms often depends on additional designed techniques, leading to increased computational complexity. In this paper, the Collaborative Resource Allocation-based Differential Evolution (CRADE) is introduced. It involves a collaborative resource allocation mechanism that utilizes the historical performance ranking of three mutation strategies to automatically allocate computational resources to various subpopulations during the search process. The parameter adaptation technique is used to adjust the associated control parameters of different mutation strategies. As a result, the most efficient mutation strategy consumes the majority of computational resources at different search stages to mitigate inefficient search under constrained resources. The performance of CRADE is evaluated on the well-known CEC2013 benchmark function set. The paper also investigates its application in the parameter identification of photovoltaic solar cells and modules. The overall results show that CRADE exhibits superior and competitive performance compared to other state-of-the-art algorithms. Consequently, CRADE has emerged as a novel and effective approach for addressing numerical optimization problems, distinguished by its excellence, practicality, and unwavering reliability. [ABSTRACT FROM AUTHOR]

Standard evolutionary optimization algorithms assume that the evaluation of the objective and constraint functions is straightforward and computationally cheap. However, in many real-world optimization problems, these evaluations involve computationally expensive numerical simulations or physical experiments. Surrogate-assisted evolutionary algorithms (SAEAs) have recently gained increased attention for their performance in solving these types of problems. The main idea of SAEAs is the integration of an evolutionary algorithm with a selected surrogate model that approximates the computationally expensive function. In this paper, we propose a surrogate model based on a Lipschitz underestimation and use it to develop a differential evolution-based algorithm. The algorithm, called Lipschitz Surrogate-assisted Differential Evolution (LSADE), utilizes the Lipschitz-based surrogate model, along with a standard radial basis function surrogate model and a local search procedure. The experimental results on seven benchmark functions of dimensions 30, 50, 100, and 200 show that the proposed LSADE algorithm is competitive compared with the state-of-the-art algorithms under a limited computational budget, being especially effective for the very complicated benchmark functions in high dimensions. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms are widely used to solve multimodal optimization problems. The two main challenges faced while solving MMOPs are locating multiple optimal solutions and improving the accuracy of these solutions. In this paper, we have proposed an adaptive algorithm based on differential evolution using the distributed framework in mutation strategy and an elite archive mechanism termed Adaptive Differential Evolution with Archive to deal with these challenges. The following techniques have been proposed and integrated to locate multiple diverse optimal solutions with refined accuracy. Firstly, each individual in the population is treated as a possible exemplar and is expected to reach an optimal value by exploring the nearby search space. The search space is controlled by using an adjustable range mechanism. An adaptive mutation strategy is then used to ensure that all the good solutions or individuals of the population move to better positions. Next, an elite archive is constructed for stagnated individuals to avoid getting stuck in local optimas. The experimental results on the 20 multimodal functions from IEEE Congress on Evolutionary Computation 2013 illustrate that the performance of the proposed algorithm is better than the existing multimodal optimization algorithms in terms of finding more number of accurate solutions. [ABSTRACT FROM AUTHOR]

The combined heat and power economic dispatch (CHPED) problem is a complicated non-convex optimization problem with several constraints that has been a challenging and important task in the power system. Great efforts have been made to solve the small-scale CHPED problem, and there is considerable scope for research in the large-scale CHPED problem with lots of local optima. This paper presents a neighborhood-based differential evolution algorithm with direction induced strategy (NDIDE) to solve the large-scale CHPED problem. In NDIDE, a novel mutation strategy, named neighborhood nonelite direction induced strategy based on DE/rand/1 (DE/ldrand/1), is proposed to explore some untrodden areas of a search space using the direction information of pointing to inferior solutions within a small neighborhood. Such a strategy helps to strengthen the exploitation of some selected neighborhoods. Consequently, a good balance between exploration and exploitation abilities could be achieved. NDIDE is implemented on the CHPED systems with 7, 84, 96 and 192 units. The dispatch schedules obtained from NDIDE are feasible in three large CHPED systems and show the advantages of NDIDE in terms of cost savings and the robustness over the results obtained by three state-of-the-art differential evolution algorithms as well as recent works in this field. [ABSTRACT FROM AUTHOR]

Adversarial examples are well-designed input samples that include perturbations that are imperceptible to the human eye but easily mislead the output of deep neural networks (DNNs). Existing studies synthesize adversarial examples by leveraging simple metrics to penalize perturbations that lack sufficient consideration of the human visual system (HVS), producing noticeable artifacts. To explore why these perturbations are visible,four primary factors that affect the perceptibility of human eyes are summarized in this paper. Based on this investigation, we design a multi-factor metric MulFactorLoss for measuring the perceptual loss between benign examples and adversarial examples. To test the imperceptibility of the multi-factor metric, we propose a novel black-box adversarial attack that is referred to as GreedyFool. GreedyFool applies differential evolution to evaluate the effects of perturbed pixels on the confidence of a target DNN and introduces greedy approximation to automatically generate adversarial perturbations. We conduct extensive experiments on the ImageNet and CIFRA-10 datasets and a comprehensive user study with 60 participants. The experimental results demonstrate that MulFactorLoss is a more imperceptible metric than the existing pixelwise metrics, and GreedyFool achieves a 100% success rate in a black-box manner. [ABSTRACT FROM AUTHOR]

Multi-objective evolutionary algorithm (MOEA) based on search space decomposition (MOEA/D-M2M) is a promising framework for solving multi-objective optimization problems (MOPs). It is crucial yet challenging for an MOEA to balance convergence and diversity. Few studies have been attempted to deal with the balancing problem under the MOEA/D-M2M framework. In this paper, a two-stage hybrid learning-based MOEA, dubbed HLMEA, is proposed to address this problem. In the first stage, we propose a genetic operator with an adaptive scaling parameter in order to accelerate the convergence of the search, while the environmental selection method maintains the diversity. In the second stage, the K -means clustering method is employed within each subpopulation to construct a mating pool for each individual. In each mating pool, an adaptive method based on hypervolume is proposed to choose a suitable differential evolution operator for offspring generation. Different from the first stage, the environmental selection method used in NSGA-II is applied to select a new population. Thereafter, subpopulations are obtained by dividing the newly created population. Extensive experimental results show that HLMEA has better performance than nine state-of-the-art MOEAs. The ablation study demonstrates the effectiveness of each component of HLMEA. [ABSTRACT FROM AUTHOR]

• A novel mean-median velocity updating formula is proposed to guide individuals motion. • A new random differential mutation strategy is devised. • A back-diffusion strategy is proposed to restore the diversity of population. To accelerate the convergence speed and enhance robustness, a back-diffusion median integrated evolutionary algorithm (BMIEA) is proposed combining the advantages of particle swarm optimization (PSO) and differential evolution algorithm (DE) in this paper. The BMIEA includes three mainly optimization strategies. (1) Firstly, a new mean-median velocity updating formula is proposed to control optimal path of individuals. It can accelerate the convergence speed via reducing adverse effects of outliers on the population. (2) Secondly, a random differential mutation (RDM) inspired by the DE is devised to avoid the individuals trapping into local optimum via getting one more chance to explore optimal position while exploiting local region in each evolution. (3) Thirdly, a targeted exploration method i.e., back-diffusion operation, is proposed inspired by the duality principle to further accelerate the convergence rate and enhance robustness of algorithm. A series of simulation experiments have verified that BMIEA algorithm has revealed competitiveness compared with 13 state-of-art GOBL-based optimization algorithms. [ABSTRACT FROM AUTHOR]

Multi-objective evolutionary algorithm (MOEA) based on search space decomposition (MOEA/D-M2M) is a promising framework for solving multi-objective optimization problems (MOPs). It is crucial yet challenging for an MOEA to balance convergence and diversity. Few studies have been attempted to deal with the balancing problem under the MOEA/D-M2M framework. In this paper, a two-stage hybrid learning-based MOEA, dubbed HLMEA, is proposed to address this problem. In the first stage, we propose a genetic operator with an adaptive scaling parameter in order to accelerate the convergence of the search, while the environmental selection method maintains the diversity. In the second stage, the K -means clustering method is employed within each subpopulation to construct a mating pool for each individual. In each mating pool, an adaptive method based on hypervolume is proposed to choose a suitable differential evolution operator for offspring generation. Different from the first stage, the environmental selection method used in NSGA-II is applied to select a new population. Thereafter, subpopulations are obtained by dividing the newly created population. Extensive experimental results show that HLMEA has better performance than nine state-of-the-art MOEAs. The ablation study demonstrates the effectiveness of each component of HLMEA. [ABSTRACT FROM AUTHOR]

• A novel mean-median velocity updating formula is proposed to guide individuals motion. • A new random differential mutation strategy is devised. • A back-diffusion strategy is proposed to restore the diversity of population. To accelerate the convergence speed and enhance robustness, a back-diffusion median integrated evolutionary algorithm (BMIEA) is proposed combining the advantages of particle swarm optimization (PSO) and differential evolution algorithm (DE) in this paper. The BMIEA includes three mainly optimization strategies. (1) Firstly, a new mean-median velocity updating formula is proposed to control optimal path of individuals. It can accelerate the convergence speed via reducing adverse effects of outliers on the population. (2) Secondly, a random differential mutation (RDM) inspired by the DE is devised to avoid the individuals trapping into local optimum via getting one more chance to explore optimal position while exploiting local region in each evolution. (3) Thirdly, a targeted exploration method i.e., back-diffusion operation, is proposed inspired by the duality principle to further accelerate the convergence rate and enhance robustness of algorithm. A series of simulation experiments have verified that BMIEA algorithm has revealed competitiveness compared with 13 state-of-art GOBL-based optimization algorithms. [ABSTRACT FROM AUTHOR]

• An improved differential evolution (OMLIDE) for ELD problems is proposed. • An oppositional mutual learning strategy is used for population initialization. • Two novel mutation operators are hybridized adaptively. • Both scaling factor and crossover rate are adjusted automatically. • Benchmark functions of CEC2014 and five ELD cases are solved. The economic load dispatch (ELD) problem plays a crucial role in power system operation. In practice, the ELD problem becomes a non-convex, multi-constraint, non-linear optimization problem when considering the valve point effects, the prohibited operation zones, the ramp rate limit, and the multi-fuel options. To effectively solve this problem, this paper puts forward an improved differential evolution (DE) named OMLIDE based on opposition-mutual learning, hybrid mutation strategy, and parameters adaptive mechanism. OMLIDE differs from the traditional DE in that: (1) an opposition-mutual learning strategy is employed for population initialization to increase the probability of finding an optimal solution; (2) two novel mutation operators named DE/elite-to-ordinary/1 and DE/elite-to-ordinary/2 are hybridized and a selection probability is introduced to regulate them adaptively at different evolutionary stages; and (3) a parameters adaptive mechanism is presented to adjust the scaling factor and crossover rate. The proposed OMLIDE is first validated by the numerical benchmark functions of CEC 2014. Then it is applied to five non-convex ELD problems with valve-point effects and multi-fuel options. Simulation results demonstrate that OMLIDE provides better or highly competitive results in different terms compared with other peer algorithms. [ABSTRACT FROM AUTHOR]

Differential Evolution (DE) is an effective global optimization algorithm, and many existing adaptive variants of it have been proposed to solve engineering problems. It is well known that population feature information that refers to some mathematical statistic feature information of all individuals in the dimension of decision space, and it can reflect the features of the problem to be solved. However, the population feature information has not been fully utilized by DE's adaptive variants. As a result, those adaptive variants do not obtain promising performance in optimizing nonlinear, non-differentiable and non-separable multi-modal problems. To make adequate extraction and effective use of population feature information, we propose an adaptive differential evolution framework based on population feature information in this paper, named PFI for short. In the PFI framework, the population feature information consists of the standard deviation of fitness value and the sum of standard deviation of each dimension of population. Besides, population feature information archive is designed to store the population feature information and success parameters, and the utilization mechanism of population feature information assigns historical success parameters with high population feature similarity to the current corresponding population. Four widely used mutation strategies of DE are incorporated into the PFI framework to evaluate its performance by optimizing CEC2005, CEC2015, CEC2020 benchmark functions and two real world applications to verify the performance of the PFI framework. Experiment results have demonstrated that PFI framework can significantly improve the performance of 4 popular mutation strategies of DE. [ABSTRACT FROM AUTHOR]

• The adaptation of parameter and strategy is realized through accompanying evolution. • Accompanying population and generalized opposition-based learning enhance the population diversity. • Radial spatial projection is used for dynamic analysis of evolutionary direction. Differential evolution (DE) is an intelligent optimization algorithm inspired by biological evolution. Setting a mutation strategy and control parameters that meet the optimization requirements are the premise for DE to achieve good performance. This paper proposes a parameter and strategy adaptive differential evolution algorithm based on accompanying evolution (APSDE). Through the accompanying population, in which individuals are composed of suboptimal solutions, the mutation strategy and control parameters are optimized to realize the adaptation of the strategy and parameters of the main population. Population diversity is enhanced in evolution by generating reverse individuals. In addition, radial spatial projection technology is utilized to track the change in evolution direction with optimization. The performance of APSDE is validated under four sets of benchmark problem suites from the Institute of Electrical and Electronics Engineers (IEEE) Congress on Evolutionary Computation (CEC), and compared with state-of-the-art optimization algorithms. The results show that the proposed algorithm has better optimization performance than the competitive algorithms because of its efficient adaptive mechanism and its excellent population diversity. [ABSTRACT FROM AUTHOR]

• Differential evolution with adaptive mutation strategy based on landscape information is proposed. • Dynamic fitness landscape analysis methods are used to analyze the optimization problems. • The optimal mutation strategy selection is based on each optimization problem's dynamic fitness landscape characteristics during the evolutionary process. Differential evolution (DE) is the most efficient evolutionary algorithm widely used to solve continuous or discrete numerical optimization problems. However, the performance of DE highly depends on the choice of mutation strategy. In addition, for a given optimization problem, a different mutation strategy configuration of DE may be more effective than a single mutation strategy in searching for the optimal solution. Based on these observations, a dynamic fitness landscape-based adaptive mutation strategy selection differential evolution (DFLDE) is proposed in this paper. In DFLDE, the optimal mutation strategy selection is based on each optimization problem's dynamic fitness landscape characteristics during the evolutionary process. The CEC2017 benchmark function set is used to evaluate the performance of the proposed DFLDE algorithm. The experimental results indicate that the DFLDE is superior to the other five well-known DE variants in searching for the optimal value, convergence speed, and robustness. [ABSTRACT FROM AUTHOR]

As grade differences between concentrates increase, long-term concentrate ingredient planning (LCIP) becomes a crucial issue in ensuring continuous production and maximizing the concentrate utilization. Comparing with the existing studies, the number of LCIP ingredient stages is not deterministic and the decision variables and constraints are also will also change in accordance with the preceding ingredient list. Given these features of LCIP, this paper presents the concept of unpredictable multistage dynamic optimization (UMDO) and establishes an LCIP model that comprehensively considers production constraints, ingredient list duration, and concentrates inventories. A multistage stochastic object coding (MSOC) that establishes a mapping relationship between the coding sequence and the feasible solution space at each scheduling stage is further proposed. A multi-agent differential evolution (DE) algorithm based on the application of sequential simulation is proposed to optimize the high-dimensional population of the MSOC, enabling a globally optimal scheme in which the feasibility of the ingredient plan at each stage is ensured. Finally, the actual inventory concentration data collected from a copper industry in China are used to validate the effectiveness of the proposed planning methodology. [ABSTRACT FROM AUTHOR]

Solving nonlinear equation systems (NESs) is one of the most important tasks in numerical computing. The NESs usually have multiple roots, and quickly locating their roots in a single algorithm run with a limited number of iterations has always been the algorithm improvement direction. In order to further enhance the efficiency of the existing methods, a density clustering-based differential evolution algorithm (DCDE) for the NESs problem solving is proposed in this paper. Firstly, density-based spatial clustering of applications with noise (DBSCAN) is used to divide the population into clusters and noises, which provides a better direction for population evolution. Secondly, a cluster evaluation factor is proposed, which not only divides the clusters into excellent clusters and non-excellent clusters, but also prevents the migration of excellent clusters and maintain the diversity of populations. Then, a migration strategy and individual generation mechanism are proposed to guide non-excellent clusters to migrate to promising regions. Finally, combined with an archive technique, the individuals which satisfy the solution requirements are archived and randomly initialized to further improve population diversity. To verify the effectiveness of the proposed algorithm, comparative experimental results of the propsoed DCDE with other state-of-the-art algorithms for thirty NESs problems solving show that the proposed DCDE is the most effective algorithm to locate more roots in a single run. [ABSTRACT FROM AUTHOR]

• An improved gaining-sharing knowledge-based algorithm named MSGSK is proposed. • A parameter adjustment strategy is developed to adjust relative parameters of MSGSK. • A backtracking differential mutation strategy is designed to enrich the population diversity. • A strategy selection mechanism is presented to integrate the former two strategies. • MSGSK extracts more accurate parameters for five PV models. The determination of photovoltaic (PV) model parameters has essential theoretical and practical significance for the performance evaluation, power monitoring, and power generation efficiency calculation of PV systems. In this paper, a multi-strategy gaining-sharing knowledge-based algorithm (MSGSK) is developed to determine these parameters. In our previous work, it has been demonstrated that gaining-sharing knowledge-based algorithm (GSK) is well suited for solving the concerned problem. To enhance its performance, a parameter adjustment strategy is developed to adjust the knowledge rate and knowledge ratio of GSK. Besides, a backtracking differential mutation strategy by combining the mutation scheme of differential evolution and the updating scheme of backtracking search optimization algorithm is developed to enrich the population diversity. Furthermore, a strategy selection mechanism is introduced to integrate the former two strategies to balance exploration and exploitation in different stages of the evolutionary process. The suggested MSGSK algorithm is applied to five PV cases (SDM, DDM, Photowatt-PW201, STM6-40/36, and STP6-120/36). From the experimental data, it can be observed that MSGSK extracts the PV model parameters more precisely than the basic GSK. Furthermore, it exhibits faster convergence speed and higher accuracy compared to other advanced algorithms found in the literature. [ABSTRACT FROM AUTHOR]

• Analyze DE algorithm two key issues: parameter sensitivity and search imbalance. • A complementary mutation strategy based on complementary symmetric selection and a Gaussian distribution mutation is proposed. • Data fusion-based parameter adaptation method proposed for parameter rationalization. • A novel variant of DE called DACDE is designed and results shown competitive edge. As an excellent optimization algorithm widely used to solve various practical problems, differential evolution (DE) algorithm has few parameters, yet its performance is significantly affected by these parameters. To address this issue, this paper presents a novel variant of DE called DACDE, which utilizes data fusion-based parameter adaptation and a complementary mutation strategy. Most parameter adaptation methods based on successful history only analyze the mean of parameters and ignore their degree of dispersion. In DACDE, the successful parameter distribution is recorded and described by both the mean and variance. Data fusion is then used to combine records and generate an estimated distribution, which is applied to a Gaussian distribution to generate new parameters. Inspired by opposition-based learning, we introduce a complementary mutation strategy. This strategy employs a symmetric selection mechanism to adapt to the varying search abilities required by the algorithm at different stages. The new variant is verified on 32 single-objective functions from CEC 2011 and 2014 benchmark suites, and the results show that DACDE is competitive compared to other 29 evolutionary algorithms. [ABSTRACT FROM AUTHOR]

Various variants have been proposed to improve the search ability and efficiency of Differential Evolution (DE). However, the variants ignore the impact caused by the use of accumulated historical information, resulting in unpromising performance of the search. Furthermore, the global exploration and local exploitation ability of population is affected by the population number (NP), which commonly adapts with little adaptive control or with linear descendent only. To utilize more historical population information, we propose in this paper a novel adaptive population size-based DE (APSDE) by mining historical population information, to balance global exploration and local exploitation ability. APSDE uses historical population information to mine population distribution and extract information to assign parameters to the current population. Moreover, an archive is utilized to store the historical population information, where historical successful parameter information consists of scaling factor (F), crossover rate (CR) and NP for better balancing the search ability of population. To evaluate the performance of APSDE, we conduct experiments both on the 28 benchmark functions of CEC2017, the 10 benchmark functions of CEC2020, and a real-world application - the path planning of unmanned aerial vehicles (UAVs). The experimental results have demonstrated that APSDE achieves the promising performance in both convergence accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

In association rules mining from data that have numeric-valued attributes, automatically adjusting the attribute intervals at the time of the mining process without a preprocess is very critical for preventing data loss and attribute interactions. In this paper, differential evolution and sine cosine algorithm based novel hybrid multi-objective evolutionary optimization methods are proposed for rapidly and directly mining the reduced high-quality numerical association rules by simultaneously adjusting the relevant intervals of related attributes without finding the frequent itemsets. These algorithms perform a global search and find the high-quality rules set in only one execution by modeling the rule mining task as a multi-objective problem that simultaneously meets different conflicting metrics. The algorithms proposed in this paper ensure the discovered rules to have high confidence and support and to be comprehensible. The proposed methods automate the rule mining process by directly finding the minimum intervals for the attributes and eliminating the need for minimum confidence and minimum support determined beforehand for each data set. The performances of new algorithms proposed in this study were tested with those of the state-of-the-art algorithms. The results show superiority of the proposed methods on the data sets that contain fewer attributes and higher number of instances. [ABSTRACT FROM AUTHOR]

Surrogate-assisted evolutionary algorithms (SAEAs) have been proven to be very effective in tackling low-dimensional expensive problems. However, it remains a challenge to solve high-dimensional expensive problems (HEPs) with the curse of dimensionality. Therefore, this paper proposes a surrogate-assisted improved multioperator differential evolution (SA-IMODE) algorithm to address HEPs up to 2000 dimensions. Specifically, this paper proposes a novel relationship classification model-based environment selection strategy (RCES), in which a classification model is used to distinguish between "good" and "bad" solutions to assist in environment selection. By doing this, the "unpromising" solutions are thrown away directly without evaluation to reduce the number of expensive fitness evaluations. Moreover, the solution-improvement data point and error samples are added to construct the training dataset to improve the model's prediction accuracy. Two coordinate systems are utilized to produce five types of DE operators to suit different fitness landscapes. An adaptive strategy is also used to select suitable DE operators to generate promising offspring. Furthermore, a local search mechanism is applied to refine the best solution in the current population to accelerate the algorithm's convergence. The systematic experiment results show SA-IMODE has a significant advantage over thirteen state-of-the-art algorithms on benchmark problems. [ABSTRACT FROM AUTHOR]

In this paper, we propose a T wo-stage D ifferential E volution (TDE) with novel parameter control for real parameter single objective global optimization. In the TDE algorithm, the whole evolution is divided into two stages and each stage employs a unique mutation strategy. The mutation strategy in the first stage is a novel historical-solution based mutation strategy, which can get better perception of the landscape of the objective; the mutation strategy in the second stage is an inferior-solution based mutation strategy, which can maintain better diversity of trial vector candidates while keeping better convergence speed. Furthermore, the parameter control of our TDE is novel, which means that these adaptations of control parameters are different from those in the literature: First, the adaptation schemes both for scale factor F and crossover rate CR are fitness-independent. Second, different from the fixed population size and the gradually reduced population size, the population adaptation in TDE has two different stages. Third, a stagnation indicator is proposed and a population enhancement technique can be launched if necessary when a certain individual is in the stagnation status. We examine the TDE algorithm under a relative large number of benchmarks from CEC2013, CEC2014 and CEC2017 test suites for real-parameter single objective global optimization, and the experiment results show the competitiveness of our TDE algorithm with several recently proposed state-of-the-art DE variants, e.g. it obtained 20 similar or better performance improvements out of the total 30 benchmarks 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 in comparison with the winner DE variant, the jSO algorithm, of the CEC2017 competition. [ABSTRACT FROM AUTHOR]

Surrogate-assisted evolutionary algorithms (SAEAs) are promising methods for addressing computationally expensive problems. This paper proposes a multiple surrogates and offspring-assisted differential evolution (MSODE) algorithm for high-dimensional expensive problems. Ensemble models consisting of multiple base models are built based on bagging. The ensemble models contribute toward reducing the variations of predictions and the uncertainty of base models. The algorithm proposes a multiple-offspring evolution strategy in which it generates multiple offspring for each parent individual to enhance the search ability of the population. The appropriate number of offspring was investigated, considering the tradeoff between optimization results and efficiency. MSODE consists of a global prescreening search, local search, and uncertainty prescreening search. The global prescreening search adopts a global ensemble to prescreen promising offspring. The local search accelerates the convergence by searching for the optimum of a local ensemble. The uncertainty prescreening search requires a number of fitness evaluations that slightly deteriorate the results. A comprehensive analysis was conducted to determine the optimal parameter settings. MSODE was compared with meta -heuristic algorithms and SAEAs on a series of benchmark problems. The results show that MSODE behaves better than most algorithms and is competitive against the best ones. [ABSTRACT FROM AUTHOR]

• In this paper, proposing a novel design of DE for Knapsack problems is reported. • A dual representation of solutions in continuous and binary is introduced. • New efficient fitness evaluation and repairing method is proposed. • Results demonstrated the efficiency of Novel DE in solving Knapsack problems. • Novel DE defined new solutions, better than best-known ones for 5 large instances. The capability of the conventional differential evolution algorithm to solve optimization problems in continuous spaces has been well demonstrated and documented in the literature. However, differential evolution has been commonly considered inapplicable for several binary/permutation-based real-world problems because of its arithmetic reproduction operator. Moreover, many limitations of the standard differential evolution algorithm, such as slow convergence and becoming trapped in local optima, have been defined. In this paper, a novel technique which makes a simple differential evolution algorithm suitable and very effective for solving binary-based problems, such as binary knapsack ones, is proposed. It incorporates new components, such as representations of solutions, a mapping method and a diversity technique. Also, a new efficient fitness evaluation approach for calculating and, at the same time, repairing knapsack candidate solutions, is introduced. To assess the performance of this new algorithm, four datasets with a total of 44 instances of binary knapsack problems are considered. Its performance and those of 22 state-of-the-art algorithms are compared, with the experimental results demonstrating its superiority in terms of both the quality of solutions and computational times. It is also capable of finding new solutions which are better than the current best ones for five large knapsack problems. [ABSTRACT FROM AUTHOR]

This study aims at investigating a scheduling problem for unloading of material ships in a large-scale steel plant. The optimization problem minimizes the cost caused by improperly delayed unloading operations of the ships for a given time horizon. The problem intends to decide the order of unloading ships and the allocation of conveyors to the ships. The solution for the practical-sized problem is NP-hard because of the dimensionality of the problem. In this paper we resolve the problem using a well-designed differential evolution algorithm (DE). In addition, a mathematical programming model is given as well for comparison. An empirical study with some comparative results from CPLXE solver and other DE variants is carried out, which shows a good potential for real-world applications. [ABSTRACT FROM AUTHOR]

In this paper, a new differential evolution (DE) algorithm is presented for solving global optimization problems by guiding the individuals adaptively to explore different decision regions and setting the control parameters properly for individuals. To consolidate algorithm efficiency and preserve population diversity, we first introduce a proration-based mutation strategy. This strategy dynamically selects promising individuals from population as guiders and proportionately allocates the individuals following them based on their fitness values and unsuccessful updates. Besides, we design a multi-segment mixed parameter setting to provide suitable parameters for individuals, considering feedback information from the population, individual requirements, and parameters' interaction. Additionally, we devise an adaptive population maintaining mechanism to refresh the population by replacing individuals with higher unsuccessful updates and removing those with poor fitness values. Unlike previous DE versions, our new algorithm dynamically and appropriately explores promising areas, refines parameter suitability, and accelerates convergence by updating and removing unpromising individuals. This enhances the algorithm search efficiency and achieves a good balance between exploration and exploitation. Finally, we evaluate the proposed algorithm's performance by comparing it with 17 typical or state-of-the-art algorithms on IEEE CEC2014 and CEC2017 test suites. Experimental results indicate that the proposed algorithm is a more promising optimizer. [ABSTRACT FROM AUTHOR]

Filter pruning has been successfully applied in convolutional neural networks (CNN) to reduce model redundancy and speed up inference. Current pruning algorithms require setting a target value for a pruned model, which is not conducive to the rapid implementation in practical application. Firstly, for a target model, it may be necessary to pay attention to multiple performances at the same time, but it is hard to keep the best trade-off among indicators. Secondly, it is time-consuming to find a suitable model by pruning in a trial-and-error way. Therefore, this paper attempts to combine the most concerning indicators into a search target, rather than producing a model that only contains some pre-defined constraint. Specifically, the multi-object differential evolution algorithm is introduced into the search process, which is used to obtain a set of sparse structures that have taken all useful indicators into account. Then select proper sub-network to retrain from search results according to actual requirements. Experiments on multiple advanced CNN networks show that our algorithm can compress different indicators while keeping comparable or better performance than prior works. On ImageNet, pruning based on ResNet50 reduces FLOPs by 60.4%, while the accuracy of top-1 and top-5 only loses 1.09% and 0.57%, respectively. [ABSTRACT FROM AUTHOR]

Over the past few years, many evolutionary algorithms have been developed to find multiple roots of the nonlinear equation system (NES). However, they can only solve one NES in a single run, ignoring the potentially useful information and solving experience derived from different NESs. To this end, an evolutionary multitasking NES optimization framework called MTNES, is proposed for the first time in this paper for solving multiple NESs simultaneously. Specifically, we first initialize multiple NES tasks in a 0-1 unified search space to establish an implicit relationship between NESs to facilitate knowledge transfer. Then, combining differential evolution and neighborhood technique, a neighborhood knowledge transfer is presented to reduce negative knowledge transfer and thus help find more roots. In addition, a novel resource reallocation mechanism is developed to release the found roots, thereby improving population diversity as well as aiding the search for more promising areas. Numerous empirical results reveal that the proposed approach can achieve a higher root rate and success rate when compared with several well-established algorithms on eighteen complex NESs. Moreover, experimental results on two real-world applications further show the potential practicability of the proposed multitasking NES-solving framework. • An evolutionary multitasking NES-solving framework MTNES is proposed. • A 0-1 unified search space is introduced to narrows the search scope and facilitate knowledge transfer. • A neighborhood knowledge transfer is presented to reduce negative knowledge transfer. • A novel resource reallocation mechanism is proposed to release the found roots. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive memetic differential evolution with multi-niche sampling and neighborhood crossover strategies for global optimization. In the proposed algorithm, a multi-niche sampling strategy is designed to sample a subpopulation for evolution at each generation. In this strategy, the entire population is firstly divided into multiple niches by employing a certain niching strategy at each generation. A subpopulation is then dynamically sampled from the resulting niches such that supporting a diverse search at the early stage of evolution while an intensive search towards the end of evolution. The above strategy will be further coupled with a neighborhood crossover, which is devised to encourage high potential solutions for exploitation while low potential solutions for exploration, thus appropriately searching the solution space. Additionally, an adaptive local search (ALS) scheme along with an adaptive elimination operation (AEO) have been designed. The ALS aims to appropriately fine-tune promising solutions in the sampled subpopulation while the AEO tends to adaptively eliminate unpromising individuals in the population during evolution. The performance of the proposed algorithm has been evaluated on CEC'2015 benchmark functions and compared with related methods. Experimental results show that our algorithm can achieve a superior performance and outperform related methods. The results also confirm the significance of devised strategies in the proposed algorithm. [ABSTRACT FROM AUTHOR]

• Importance of the constraint handling operator even for box-constrained problems. • Use of percentage of solutions generated outside the domain as performance measure. • Re-purposing of stochastic objective function f0 for studying algorithmic effects. • Popular EC algorithms generate significant amounts of infeasible solutions. • Distribution of percentages of solutions generated outside the domain is nontrivial. This paper investigates how often the popular configurations of Differential Evolution generate solutions outside the feasible domain. Following previous publications in the field, we argue that what the algorithm does with such solutions and how often this has to happen is important for the overall performance of the algorithm and interpretation of results. Based on observations therein, we conclude that significantly more solutions than what is usually assumed by practitioners need to undergo some sort of 'correction' to conform with the definition of the problem's search domain. A wide range of popular Differential Evolution configurations is considered in this study. Conclusions are made regarding the effect the Differential Evolution components and parameter settings have on the distribution of proportions of infeasible solutions generated in a series of independent runs. Results shown in this study suggest strong dependencies between proportions of generated infeasible solutions and every aspect mentioned above. Further investigation of the distribution of proportions of generated infeasible solutions is required. [ABSTRACT FROM AUTHOR]

Many domination-based multi-objective evolutionary algorithms (MOEAs) are designed for constrained multi-objective optimization problems (CMOPs). However, they still face the challenge of balancing the feasibility, convergence and distribution. This paper tackles this issue by proposing a multi-objective differential evolution algorithm based on domination and a mechanism of constraint-handling switching (MODE-CHS). In constraint-handling switching, if there are no feasible solutions in the population, the population evolves by constraint-handling; otherwise, the population evolves without handling constraints. This mechanism enhances the rate of population convergence to the maximum while obtaining the feasible solutions. Furthermore, in MODE-CHS, the feasible solutions are saved to an external archive and evolve together with the population to explore the feasible region. Meanwhile, to enhance the distribution, the offspring of the external archive also participates in the individual-update procedure of the population. 27 bench-mark test problems and two real-world problems are used for the performance comparison of the proposed algorithm with other five state-of-the-art algorithms. In the experiment, the proposed algorithm, MODE-CHS, is shown to produce satisfactory solutions for most of the tested functions, where other five MOEAs perform relatively worse. The experiment results demonstrate MODE-CHS is very competitive for solving CMOPs. [ABSTRACT FROM AUTHOR]

In differential evolution algorithm (DE), it is a widely accepted method that selecting individuals with higher fitness to generate a mutant vector. In this case, the population evolution is under a fitness-based driving force. Although the driving force is beneficial for the exploitation, it sacrifices performance on the exploration. In this paper, a n ovelty-hybrid- f itness d riving force is introduced to trade off contradictions between the exploration and the exploitation of DE. In the new proposed DE, named as NFDDE, both fitness and novelty values of individuals are considered when choosing individuals to create mutant vectors. In addition, two adaptive scaling factors are proposed to adjust the weights of the fitness-based driving force and the novelty-based driving force, respectively, and then distinct properties of the two driving forces can be effectively utilized. At last, to save computational resources, some individuals with lower novelty are deleted when the population has converged to a certain extent. The comprehensive performance of NFDDE is extensively evaluated by comparisons between it and other 9 state-of-art DE variants based on CEC2017 test suite. In addition, distinct properties of the newly introduced strategies and involved parameters are further confirmed by a set of experiments. [ABSTRACT FROM AUTHOR]

Differential Evolution (DE) is one of the most effective approaches in Evolutionary Computation to tackling complex black-box optimization, however, the overall performance of a DE variant is heavily dependent on its mutation strategy and the associated parameter control schemes. According to the "No free Lunch theorem", every mutation strategy has its own fatal defect, therefore, DE variant with a single mutation strategy can not tackle all optimization problems. Furthermore, DE variant with ensemble of mutation strategies usually needs more parameter control schemes, which inevitably decreases the practicality of it. Here in this paper, a novel Cooperative Strategy based DE (CS-DE) with population diversity enhancement is proposed, and the CS-DE algorithm has the following contributions: First, a cooperative strategy pool containing two similar mutation strategies is advanced in the algorithm, and the two mutation strategies share the same parameter control. Second, a novel grouping strategy is proposed, then the two mutation strategies can be chosen in an adaptive manner by different individuals in generating trial vectors during the evolution. Third, novel adaptation schemes for the three control parameters F , CR and PS as well as a stagnation based re-initialization mechanism are also proposed in our CS-DE algorithm. 58 benchmarks from the CEC2013 and CEC2014 test suites are employed in algorithm validation, and experiment results show the competitiveness of the CS-DE algorithm with several state-of-the-art DE variants. [ABSTRACT FROM AUTHOR]

Solving nonlinear equation systems using evolutionary algorithms involves solving two key problems. One problem is how to efficiently optimize the nonlinear equations derived from the physical features, and the other problems is how to locate more than one optimal solution in a single trial. To address these two problems, an improved dynamic tri-objective differential evolution method is proposed in this paper. First, we transform a given system with any type and number of nonlinear equations into a dynamic tri-objective optimization problem, which targets the first problem. Second, we develop a self-adaptive ranking multi-objective differential evolution, which targets the second problem. In addition, a probability distribution-based local search is introduced, which aims to identify the optimal solutions with a high level of accuracy. Based on previous studies of numerical optimizations with multiple solutions, each component is elaborately proposed and developed, so it is more suitable for a nonlinear equation system. Experiments were conducted on 30 numerical examples collected from real-world applications. The statistical results are encouraging, showing that the performance of the proposed approach is better than that of eight state-of-the-art evolutionary algorithms, with respect to root ratio and success rate metrics. [ABSTRACT FROM AUTHOR]

• The concept and verification method of affine invariance are presented. • Six algorithms are employed to analyze their affine invariances. • PSO, OFA and DE are affine invariant, GWO, SCA and BOA are not affine invariant. • Multiple experimental comparisons are executed to verify algorithms' affine invariance. An algorithm whose performance depends on the objective function being aligned with a privileged coordinate system is a poor choice in general because it is unlikely that the optimal orientation will be known in advance. In this paper, a property of meta -heuristic algorithms, named affine invariance, is introduced to verify whether the algorithm is depended on the privileged coordinate system or not. The concept of affine invariance is described in detail, and some classical algorithms, efficient in most test and actual problems, are proved to be affine invariant. While some recent algorithms in the literature are proved to be not affine invariant. As a conclusion, particle swarm optimization (PSO), differential evolution (DE) and optimal foraging algorithm (OFA) are affine invariant, while grey wolf optimizer (GWO), sine cosine algorithm (SCA) and butterfly optimization algorithm (BOA) are not affine invariant. Furthermore, comparison tests are designed to support the theoretical analysis results. In these tests, same random numbers and initial population are used to avoid the influence of randomness, thus, the conclusion is reliable. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) has been recognized as one of the most effective algorithms for solving numerical optimization problems. In this paper, we propose a tri-population differential evolution (TPDE) to further enhance the search capability of DE. More specifically, the parent population is partitioned into three sub-populations with different emphasises at each iteration based on a newly proposed zonal-constraint stepped division (ZSD) mechanism, which determines the size of each sub-population according to not only individual's fitness value but also the evolutionary process. To make the best of information provided by elite individuals and play their leading role on other individuals, three elite-guided mutation strategies are presented for each sub-population. Moreover, three sets of adaptive control parameters including the scale factor F and crossover rate CR are configured for three mutations according to Gaussian distribution model, Cauchy distribution model and a triangular wave function respectively. The design of mutation strategies and control parameters for each sub-population is based on the principle of balancing the global exploration and local exploitation capabilities. To evaluate the performance of TPDE, comparative experiments are conducted based on 59 benchmark functions from CEC2014 and CEC2017 test suites. The results indicate that the proposed TPDE is significantly better than, or at least comparable to the recent nine state-of-the-art DE variants. [ABSTRACT FROM AUTHOR]

Penalty function is well-known for constrained evolutionary optimization. An open question in the penalty function is how to tune the penalty coefficient. This paper proposes an adaptive fuzzy penalty method to address this issue, where the coefficient is adjusted at both the individual level and the population level. At the individual level, each individual chooses a penalty coefficient from a predefined domain according to some fuzzy rules. At the population level, the domain of the crisp output is adjusted adaptively by using population information. To enhance the population diversity, an effective mutation scheme is developed. Due to its numerous merits, differential evolution is used to design a search algorithm. By the above processes, a constrained optimization evolutionary algorithm called AFPDE is proposed. Since the objective function value and the degree of constraint violation are normalized, AFPDE is less problem-dependent than the seminal work of the fuzzy penalty method. AFPDE introduces a lower penalty value in the early stage of AFPDE while a higher one in the later stage. Thus, it can escape local optima in the infeasible region. Experiments on three well-known benchmark test sets and two mechanical design problems validate that AFPDE is competitive. [ABSTRACT FROM AUTHOR]

The paper describes the problem of bias in parameter adaptation in Differential Evolution and other Evolutionary Algorithms. Based on the newly proposed Expected Fitness Improvement metric, the shift towards exploitation is demonstrated. The generalized Lehmer mean and Linear Bias Reduction are for the first time proposed to control the parameter adaptation bias for the fitness improvement based L-SHADE and distance based Db-L-SHADE algorithms. The experiments are performed on the benchmark functions of the Institute of Electrical and Electronics Engineers (IEEE) Congress on Evolutionary Computation (CEC) 2017 competition on real-parameter optimization. The influence of the modified scaling factor and crossover rate adaptation is evaluated using Friedman ranking procedure and Mann–Whitney statistical test. The usage of Lehmer mean and Linear Bias Reduction is shown to deliver statistically better results for high-dimensional functions and improve the exploration properties of the search algorithm in the long-term perspective. To support the statements made, the search process is additionally analyzed using diversity measures and cluster analysis techniques. [ABSTRACT FROM AUTHOR]

• Two new mutation strategies to enhance the DE performance are proposed. • A new adaptive approach to key control parameters are defined. • The proposed approach has superior classiffication accuracy. • The proposed algorithm's performance is acceptable in feature subset selection. In classification problems, normally there exists a large number of features, but not all of them contributing to the improvement of classification performance. These redundant features make the classification problem time consuming and often result in poor performance. Feature selection methods have been proposed to reduce the number of features, minimize computational cost, and maximize classification accuracy. As a wrapper-based approach, evolutionary algorithms have been widely applied in feature subset selection tasks. However, some of them trap into local minima, especially when the number of features increases, while others are not efficient in computational time. This paper proposes a Modified Differential Evolution (DE) approach to Feature Selection (MDEFS) by utilizing two new mutation strategies to create a feasible balance between exploration and exploitation and maintain the classification performance in an acceptable range concerning both the number of features and accuracy. Some modifications are made to the standard DE crossover and its key control parameters to enhance the proposed algorithm's capabilities further. The proposed method has been compared to several state-of-the-art methods utilizing standard datasets from the UCI repository and results of the experiments demonstrate the superiority of the proposed approach. [ABSTRACT FROM AUTHOR]

Differential Evolution (DE) was a powerful population-based evolutionary algorithm for global optimization, and it achieved great success in both evolutionary computation competitions and engineering applications. Despite the excellent performance of the state-of-the-art DE variants, there are still two main weaknesses existing within them: one is the weakness in a given mutation strategy and the other is the weakness in the corresponding parameter control (of the mutation strategy). By reviewing the existing mutation strategies in the recent state-of-the-art DE variants, it can be seen that all of them have insufficient use of the knowledge obtained during the evolution because the historical information of the population is not taken into consideration, which inevitably leads to a bad perception of the landscapes of the objectives. Moreover, the adaptations of the control parameters including F and CR in these state-of-the-art DE variants are interlaced with one another. A bad F and a good CR may produce a good trial vector candidate, then the bad F is of misuse in the parameter control and vice versa. In this paper, a novel DE variant, called Hip-DE, meaning the latest fashion of DE, with historical population based mutation strategy was proposed to tackle the above mentioned weaknesses. Moreover, novel parameter adaptive mechanisms for control parameters F and CR as well as a platform based step-decrease scheme of population size were proposed to enhance capacity of the mutation strategy. By incorporating these three advancements, the novel Hip-DE algorithm secured an overall better performance on the tested benchmarks in comparison with the recent proposed state-of-the-art DE variants. [ABSTRACT FROM AUTHOR]

In the last decade, the decomposition-based multiobjective optimization evolutionary algorithm (MOEA/D) has displayed promising performance when dealing with multiobjective optimization problems (MOPs). However, for some complex MOPs, the conventional MOEA/D often leads to the loss of population diversity in the iterative process, and the convergence performance of the population is weakened in the mean time. In this paper, a novel MOEA/D, based on improved multiple adaptive dynamic selection strategies and elite archive strategy (MOEA/D-IMA), is proposed to improve the population diversity and convergence. First, a novel differential evolution (DE) operator is constructed, which constitutes an operator pool with other DE operators. According to the search information of the current population, an adaptive dynamic selection strategy is proposed, which is used by MOEA/D-IMA to select a suitable DE operator to replace the simulated binary crossover (SBX) operator. Second, a parameter adaptive dynamic selection strategy is proposed to enhance the robustness of MOEA/D-IMA by using the information of population evolution state. Third, an elite archive strategy is introduced to improve the convergence and diversity of the population where mutual dominance of individuals and their aggregation distance is employed. Finally, the proposed MOEA/D-IMA is compared with several state-of-the-art algorithms on three suits of 18 test problems. Experimental results indicate that the proposed MOEA/D-IMA can significantly improve the optimization performance when coping with MOPs. [ABSTRACT FROM AUTHOR]