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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]

• 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]

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]

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]

• 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]

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]

Differential Evolution is a well-known stochastic algorithm in Evolutionary Computation (EC) for single-objective numerical optimization, and its powerful variants secured excellent ranks in recent competitions. These winner DE variants all employed binomial crossover which tackles the positional bias in crossover operation by treating the D parameters separately and independently, however, the binomial crossover in these winner DE variants still have bias from the spatial search perspective, and this was the reason why the QU asi- A ffine TR ansformation E volution (QUATRE) algorithm in the literature was proposed. In this paper, a novel QUATRE algorithm with novel adaptation of E volution M atrix and S election operation (QUATRE-EMS) was proposed to further improve the overall performance of the QUATRE variants for numerical optimization and the main highlights can be summarized as follows. First, the number of control parameters is reduced from three in DE to two in QUATRE-EMS by proposing an auto-generated evolution matrix. Second, a novel adaptation scheme of the evolution matrix M is proposed for a better adaptation of the landscape of the objective during evolution; Third, a new selection operation is proposed instead of employing the canonical selection operation in DE. Finally, a large test suite containing 100 benchmarks from CEC2013, CEC2014, CEC2017 and CEC2022 test suites for single-objective numerical optimization is used for algorithm validation, and total 11 state-of-the-art algorithms including our QUATRE-EMS are taken into comparison. The experimental results show the superiority of our algorithm in comparison with former QUATRE variants and several state-of-the-art DE variants. [ABSTRACT FROM AUTHOR]

Surrogate-assisted evolutionary algorithms have gained increasingly attention due to the promising search capabilities for solving computationally expensive optimization problems. However, when dealing with high-dimensional expensive optimization problems, the effectiveness of surrogate-assisted algorithms deteriorates drastically. In this paper, a novel and efficient hierarchical surrogate-assisted differential evolution (EHSDE) algorithm is proposed towards high-dimensional expensive optimization problems. To balance the exploration and exploitation during the optimization process, EHSDE utilizes a hierarchical framework. In the first phase, the best and the most uncertain offspring are identified respectively. The best offspring is prescreened by a global surrogate model which is built by using a radial basis function network with all the sample points, while the most uncertain offspring is built by the Euclidean distance between offspring and existing sample points. Subsequently, two local surrogate models, which are built by using the most promising sample points and the sample points surrounding the current best solution respectively, are utilized to accelerate the convergence speed. Moreover, experimental studies are conducted on the benchmark functions from 20D to 100D and on an oil reservoir production optimization problem. The results show that the proposed method is effective and efficient for most benchmark functions and for the production optimization problem compared with other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

The challenge of solving nonlinear equation systems is how to locate multiple optimal solutions simultaneously in a single run. To address this issue, this paper proposes a novel algorithm by combining a diversity indicator, multi-objective optimization technique, and clustering technique. Firstly, a diversity indicator is designed to maintain the diversity of the population. Then, a K-means clustering-based selection strategy is introduced to locate the promising solutions. Finally, the local search is used to accelerate the convergence of population. The experimental results on 30 nonlinear equation systems show that the proposed algorithm is better than six state-of-the-art algorithms in terms of convergence rate and success rate. [ABSTRACT FROM AUTHOR]

Multimodal optimization problems (MMOPs) aim to locate multiple global optima simultaneously, which requires a high diversity of solutions. As a diversity preservation strategy customized for evolutionary algorithms (EAs), niching has been extensively incorporated into many algorithms to deal with MMOPs. However, many existing niching techniques require pre-defined parameters to control the size or number of niches, making the algorithm sensitive to parameters. Taking individuals as nodes, the inverse distance of two individuals as edges, and the historical information of recent generations as node attributes, we can construct a population as a network, whose purpose is to divide niches through community detection without relying on sensitive parameters. Inspired by this idea, this paper proposes a network community-based differential evolution for multimodal optimization problems (NetCDE MMOPs). In NetCDE MMOPs , three strategies are proposed and work together. Firstly, the community detection-based niching (CDN) strategy constructs the population as an attribute network and automatically divides it into multiple niches without sensitive parameters. Secondly, the community elites-based updating (CEU) strategy allocates more evolutionary resources to elite individuals of communities, then predicts and updates these elites based on historical information. Finally, the poor individual remolding (PIR) strategy remolds the last-ranking individuals and guides them toward promising positions. After extensive experimentation with the widely adopted CEC'2013 test suit, the experimental results reveal the superiority of NetCDE MMOPs over many successful or recent algorithms for MMOPs. [ABSTRACT FROM AUTHOR]

Abstract Differential evolution (DE) is a simple yet powerful evolutionary algorithm that has been used to solve various complex optimization problems in numerous engineering fields. However, DE has some problems, such as premature convergence and sensitivity to parameter settings. To improve the performance of DE and extend its application, an adaptive differential evolution with the Lagrange interpolation argument algorithm (ADELI) is proposed in this paper. To accelerate the convergence speed of DE, a local search with Lagrange interpolation (LSLI) is introduced into DE. LSLI performs a local search in the neighborhood of the best individual in the current generation to enhance the exploitation capability of DE. Meanwhile, an adaptive argument strategy is presented to adaptively determine whether to use LSLI in terms of its performance in the previous generation, which can balance the global exploration capability and the local exploitation capability of ADELI. To verify the feasibility and effectiveness of ADELI, 30 test functions in the CEC 2014 benchmark sets with different dimensions were simulated. Moreover, a path synthesis problem was also optimized. The results demonstrated that ADELI considerably outperforms other EAs in most functions and obtains the most accurate solution among the compared algorithms in the application of path generation. [ABSTRACT FROM AUTHOR]

Abstract: Motivated by the recent success of diverse approaches based on differential evolution (DE) to solve constrained numerical optimization problems, in this paper, the performance of this novel evolutionary algorithm is evaluated. Three experiments are designed to study the behavior of different DE variants on a set of benchmark problems by using different performance measures proposed in the specialized literature. The first experiment analyzes the behavior of four DE variants in 24 test functions considering dimensionality and the type of constraints of the problem. The second experiment presents a more in-depth analysis on two DE variants by varying two parameters (the scale factor F and the population size NP), which control the convergence of the algorithm. From the results obtained, a simple but competitive combination of two DE variants is proposed and compared against state-of-the-art DE-based algorithms for constrained optimization in the third experiment. The study in this paper shows (1) important information about the behavior of DE in constrained search spaces and (2) the role of this knowledge in the correct combination of variants, based on their capabilities, to generate simple but competitive approaches. [ABSTRACT FROM AUTHOR]

Abstract: Evolutionary algorithms (EAs) have been applied with success to many numerical and combinatorial optimization problems in recent years. However, they often lose their effectiveness and advantages when applied to large and complex problems, e.g., those with high dimensions. Although cooperative coevolution has been proposed as a promising framework for tackling high-dimensional optimization problems, only limited studies were reported by decomposing a high-dimensional problem into single variables (dimensions). Such methods of decomposition often failed to solve nonseparable problems, for which tight interactions exist among different decision variables. In this paper, we propose a new cooperative coevolution framework that is capable of optimizing large scale nonseparable problems. A random grouping scheme and adaptive weighting are introduced in problem decomposition and coevolution. Instead of conventional evolutionary algorithms, a novel differential evolution algorithm is adopted. Theoretical analysis is presented in this paper to show why and how the new framework can be effective for optimizing large nonseparable problems. Extensive computational studies are also carried out to evaluate the performance of newly proposed algorithm on a large number of benchmark functions with up to 1000 dimensions. The results show clearly that our framework and algorithm are effective as well as efficient for large scale evolutionary optimisation problems. We are unaware of any other evolutionary algorithms that can optimize 1000-dimension nonseparable problems as effectively and efficiently as we have done. [Copyright &y& Elsevier]

Abstract: This paper proposes a novel and unconventional Memetic Computing approach for solving continuous optimization problems characterized by memory limitations. The proposed algorithm, unlike employing an explorative evolutionary framework and a set of local search algorithms, employs multiple exploitative search within the main framework and performs a multiple step global search by means of a randomized perturbation of the virtual population corresponding to a periodical randomization of the search for the exploitative operators. The proposed Memetic Computing approach is based on a populationless (compact) evolutionary framework which, instead of processing a population of solutions, handles its statistical model. This evolutionary framework is based on a Differential Evolution which cooperatively employs two exploitative search operators: the first is based on a standard Differential Evolution mutation and exponential crossover, and the second is the trigonometric mutation. These two search operators have an exploitative action on the algorithmic framework and thus contribute to the rapid convergence of the virtual population towards promising candidate solutions. The action of these search operators is counterbalanced by a periodical stochastic perturbation of the virtual population, which has the role of “disturbing” the excessively exploitative action of the framework and thus inhibits its premature convergence. The proposed algorithm, namely Disturbed Exploitation compact Differential Evolution, is a simple and memory-wise cheap structure that makes use of the Memetic Computing paradigm in order to solve complex optimization problems. The proposed approach has been tested on a set of various test problems and compared with state-of-the-art compact algorithms and with some modern population based meta-heuristics. Numerical results show that Disturbed Exploitation compact Differential Evolution significantly outperforms all the other compact algorithms present in literature and reaches a competitive performance with respect to modern population algorithms, including some memetic approaches and complex modern Differential Evolution based algorithms. In order to show the potential of the proposed approach in real-world applications, Disturbed Exploitation compact Differential Evolution has been implemented for performing the control of a space robot by simulating the implementation within the robot micro-controller. Numerical results show the superiority of the proposed algorithm with respect to other modern compact algorithms present in literature. [Copyright &y& Elsevier]