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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]

• A many objective evolutionary algorithm based on decomposition and moth search is proposed. • Random and adaptive weights is used to break the limitation of uniform distribution weights. • Mutual evaluation value is used to evaluate the optimal individual in the neighborhood. • Improving scale factor α in MSA is to improve the performance of the proposed algorithm. Decomposition-based multi-objective evolutionary algorithm (MOEA/D) has good performance in solving multi-objective problems (MOPs) but poor performance in solving many-objective optimization problems (MaOPs). The weight vectors in MOEA/D are relatively fixed, which results in poor performance when dealing with complex MaOPs. In this paper, random and adaptive weights are introduced into MOEA/D to break the limitation of fixed weight vectors. And the moth search algorithm (MSA) is used as an operator to improve global search ability. The updating strategies in MSA are more consistent with the neighborhood learning strategy adopted in MOEA/D. In addition, to enable MSA to find the optimal solution in the neighborhood on the MaOPs to update other individuals. This paper introduces mutual evaluation value for evaluating the optimal individual in the neighborhood, and the proposed algorithm is abbreviated as MOEA/DMS. In comparative experiments on the MaF test suite, hypervolume (HV) and inverted generational distance (IGD) are used to measure MOEA/DMS and other many-objective evolutionary algorithms (MaOEAs). The results show that MOEA/DMS has an excellent performance in dealing with MaOPs. Besides, MOEA/DMS is compared with other state-of-the-art MaOEAs on two combinatorial MaOPs. The results show that MOEA/DMS also has significant advantages in dealing with combinatorial MaOPs. [ABSTRACT FROM AUTHOR]

Dynamic multiobjective optimization problems (DMOPs) vary over time, requiring an optimization algorithm to track the position of Pareto-optimal front (PF) in a dynamic environment. To achieve that, a novel co-evolutionary algorithm based on problem analysis (CAPA) is proposed in this paper. CAPA is designed to solve DMOPs from decision space and objective space simultaneously, which is achieved by the combination of adjustable prediction (AP) and precise mapping strategy (PM). In decision space, the proposed multi-model prediction can estimate the location of new population based on the historical median points. In objective space, a novel sampling method is developed to search for sample points with better convergence or diversity. Then, mapping these sample points back to decision space based on inverse model. Through the problem analysis mechanism, the proportion of the new solutions produced by each strategy changes adaptively. CAPA is incorporated into the dynamic multiobjective evolutionary algorithm (DMOEA) based on decomposition (MOEA/D) to construct a novel algorithm. The efficacy of CAPA is validated by comparison with five state-of-the-art algorithms on 28 benchmarks. Experimental results show that CAPA has the ability to generate high quality population uniformly along PF. [ABSTRACT FROM AUTHOR]

This paper proposes an evolutionary algorithm with clustering-based selection strategies to deal with multi-objective optimization problems. In the proposed algorithm, two clustering based selection strategies, named local indicator selection and local crowding selection, have been devised to appropriately search the space. The local indicator selection is developed to select diverse and well-converged individuals for mating while the local crowding selection strategy is designed to maintain a set of evenly distributed individuals on the Pareto front for next generation of evolution. The proposed method is further enhanced by a clustering based crowding degree strategy, which is introduced to extract a uniformly distributed and convergent solutions as the final output. The performance of proposed algorithm has been evaluated on 31 benchmark problems and compared with related methods. The results clearly show the merits of proposed strategies and the proposed method could significantly outperform related methods to be compared. [ABSTRACT FROM AUTHOR]

In evolutionary multiobjective optimization, effectiveness refers to how an evolutionary algorithm performs in terms of converging its solutions into the Pareto front and also diversifying them over the front. This is not an easy job, particularly for optimization problems with more than three objectives, dubbed many-objective optimization problems. In such problems, classic Pareto-based algorithms fail to provide sufficient selection pressure towards the Pareto front, whilst recently developed algorithms, such as decomposition-based ones, may struggle to maintain a set of well-distributed solutions on certain problems (e.g., those with irregular Pareto fronts). Another issue in some many-objective optimizers is rapidly increasing computational requirement with the number of objectives, such as hypervolume-based algorithms and shift-based density estimation (SDE) methods. In this paper, we aim to address this problem and develop an effective and efficient evolutionary algorithm (E3A) that can handle various many-objective problems. In E3A, inspired by SDE, a novel population maintenance method is proposed to select high-quality solutions in the environmental selection procedure. We conduct extensive experiments and show that E3A performs better than 11 state-of-the-art many-objective evolutionary algorithms in quickly finding a set of well-converged and well-diversified solutions. [ABSTRACT FROM AUTHOR]

Multi-objective evolutionary algorithms (MOEAs) have been successfully applied in recommender systems, where the recommendation is modeled as a multi-objective optimization problem by considering both accuracy and non-accuracy metrics. However, to recommend to all users, the population individuals in most of the exiting MOEA-based recommendation algorithms are usually encoded in the form of matrix encoding, and with the increased number of users and items, it will lead to a large search space. To this end, in this paper, we propose a novel evolutionary multitasking algorithm MOREM to tackle the challenge of multi-objective recommendations, where a related auxiliary task is constructed by both user and item reduction to help solving the complex original task by knowledge transfer. Specifically, a task generation strategy for creating auxiliary task is firstly proposed to cluster users by user-rating information (i.e., user reduction), where only a part of important items (i.e., item reduction) are recommended for the central user within each cluster with the aim to greatly reduce the size of the matrix encoding. In addition, a novel knowledge transfer mechanism is proposed, which can effectively achieve knowledge migration between the two tasks. Experimental results on real-world datasets show that MOREM outperforms several state-of-the-art algorithms for multi-objective recommendations. [ABSTRACT FROM AUTHOR]

This paper presents Adaptive Batch-ParEGO, an adaptive batch Bayesian optimization method for expensive multi-objective problems. This method extends the classical multi-objective Bayesian optimization method, sequential ParEGO, to the batch mode. Specifically, the proposed method exploits a newly proposed bi-objective acquisition function to recommend and evaluate multiple solutions. The bi-objective acquisition function takes exploitation and exploration as two optimization objectives, which are traded off by a multi-objective evolutionary algorithm. Since there's usually a certain number of limited hardware resources available in reality, we further propose an adaptive solution selection criterion to fix the number of candidate solutions in each iteration. This strategy dynamically balances exploitation and exploration by tuning the hyper-parameter in the exploitation-exploration fitness function. In addition, the expected improvement is exploited to select another candidate solution to ensure convergence and make the algorithm more robust. We verify the effectiveness of Adaptive Batch-ParEGO on three multi-objective benchmarks and a hyperparameter tuning task of neural networks compared with the state-of-the-art multi-objective approaches. Our analysis demonstrates that the bi-objective acquisition function with the adaptive recommendation strategy can balance exploitation and exploration well in batch mode for expensive multi-objective problems. All our source codes will be published at https://github.com/thuiar/Adaptive-Batch-ParEGO. [ABSTRACT FROM AUTHOR]

Multi-label classification is a machine learning task to construct a model for assigning an entity in the dataset to two or more class labels. In order to improve the performance of multi-label classification, a multi-objective feature selection algorithm has been proposed in this paper. Feature selection as a preprocessing task for Multi-label classification problems aims to choose a subset of relevant features. Selecting a small number of high-quality features decreases the computational cost and at the same time maximizes the classification performance. However extreme decreasing the number of features causes the failure of classification. As a result, feature selection has two conflicting objectives, namely, minimizing the classification error and minimizing the number of selected features. This paper proposes a multi-objective optimization algorithm to tackle the multi-label feature selection. The task is to find a set of solutions (a subset of features) in a sophisticated large-scale search space using a reference-based multi-objective optimization method. The proposed algorithm utilizes an opposition-based binary operator to generate more diverse solutions. Injection of extreme point of the Pareto-front is another component of the algorithm which aims to find feature subsets with less classification error. The proposed method is compared with two other existing methods on eight multi-label benchmark datasets. The experimental results show that the proposed method outperforms existing algorithms in terms of various multi-objective evaluation measures, such as Hyper-volume indicator, Pure diversity, Two-set coverage, and Pareto-front proportional contribution. The proposed method leads to get a set of well-distributed trade-off solutions which reach less classification error in comparing with competitors, even with the fewer number of features. [ABSTRACT FROM AUTHOR]

Multi-objective optimization problems often load in the multi-scenario environment, and they can be modeled as multi-scenario multi-objective optimization problems (MSMOs). So far, existing research on MSMOs mainly focuses on the specific method in engineering applications, and general methods are quite scarce. This paper develops an integrated information-based evolutionary framework to find a set of scenario-based non-dominated solutions for MSMOs. Sequentially, a scenario-based dominance principle evolutionary algorithm and a decomposition-based evolutionary algorithm are combined with the framework to construct two integration algorithms, respectively. Furthermore, the crucial components in both algorithms are developed under the multi-scenario environment, such as scenario-based constraint handling, scenario-based dominance concept, scenario-based crowded degree and multi-scenario decomposition method. Additionally, we design a novel comprehensive evaluation indicator for MSMOs. Finally, the proposed framework is tested on numerous artificial and engineering problems. Experiments demonstrate that the framework has superiority over four existing state-of-the-art peer competitors concerning the indicator. Two integration algorithms are able to find a set of good scenario-based non-dominated solutions. [ABSTRACT FROM AUTHOR]

• A novel membrane-inspired evolutionary framework with hybrid dynamic membrane structure is proposed to solve the multi-objective multi-task optimization problems. • A novel two-stage evolution strategy algorithm based on the membrane system is proposed as the algorithm in membrane. • The concept of information molecule concentration vector inspired by the binding process of information molecules and receptors is proposed to control the information transfer probability. • Can effectively avoid the negative transfer of knowledge and promote convergence. • Can achieve better performance than the state-of-the-art multitasking MOEAs. In recent years, many different membrane-inspired evolutionary algorithms have been proposed to solve various complex optimization problems. Considering membrane systems' powerful computing performance and parallel capability, it has outstanding potential in solving multi-task optimization problems. However, there is no research to explore the performance of membrane-inspired evolutionary algorithms in solving multi-task optimization problems. In this paper, a novel membrane-inspired evolutionary framework with a hybrid dynamic membrane structure is proposed to solve the multi-objective multi-task optimization problems. First, a novel membrane-inspired two-stage evolution strategy algorithm is proposed as the algorithm in the membrane to improve the convergence of the algorithm and the diversity of multisets. Second, the information molecule concentration vector is proposed to reduce negative information transfer. The information molecule concentration vector is inspired by the binding process of information molecules and receptors and can control the information transfer probability adaptively. Finally, comprehensive experimental results show that the proposed algorithm performs better than most advanced multi-objective evolutionary multitasking 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]

1 This paper proposes an adaptive clustering-based many-objective evolutionary algorithm. 2 A unit hypersurface is estimated to roughly reflect the characteristicsof Pareto fronts. 3 The adaptive clustering can properly fit various Pareto frontsforthe targetproblem. 4 The proposed algorithmimprovestheperformanceondifferentproblemswith various Pareto fronts. This paper proposes an adaptive clustering-based evolutionary algorithm for many-objective optimization problems (MaOPs), called MaOEA/AC. In this algorithm, an adaptive clustering strategy (ACS) is first introduced to divide the population into multiple clusters, which can properly fit various Pareto fronts (PFs) of the target MaOPs. Then, the environmental selection of MaOEA/AC is designed based on these clusters to collect the solutions with balanceable convergence and diversity. To be more detail, the similarity between solutions in ACS is appropriately measured by computing the Euclidean distance between their projections on an adaptive unit hyper-surface, whose curving rate is controlled by a parameter p. A simple yet effective estimation method is proposed to get a suitable value of p based on the distribution of the current non-dominated solution set, so that the estimated unit hyper-surface can roughly reflect the characteristics of PFs in the target MaOPs. The effectiveness of MaOEA/AC is validated by numerous experimental studies on solving test MaOPs with various PFs, which have the characteristics with convex, concave, inverted, disconnected, degenerated, and other mixed or irregular PFs. The experiments also show that MaOEA/AC has the superior performance over several recent many-objective evolutionary algorithms, when solving most of these test MaOPs. [ABSTRACT FROM AUTHOR]

• An improved MOEA/D algorithm is proposed. • Information feedback models are used to update individuals to improve algorithm performance. • Four ways of decomposing multi-objectiveproblems are used to verify the algorithm. • Large-scale multi-objective problemscan be effectively solved by the proposed algorithm. A multi-objective evolutionary algorithm based on decomposition (MOEA/D) is a classic decomposition-based multi-objective optimization algorithm. In the standard MOEA/D algorithm, the update process of individuals is a forward search process without using the information of previous individuals. However, there is a lot of useful information in the previous iteration. Information Feedback Models (IFM) is a new strategy which can incorporate the information from previous iteration into the updating process. Therefore, this paper proposes a MOEA/D algorithm based on information feedback model, called MOEA/D-IFM. According to the different information feedback models, this paper proposes six variants of MOEA/D, and these algorithms can be divided into two categories according to the way of selecting individuals whether it is random or fixed. At the same time, a new selection strategy has been introduced to further improve the performance of MOEA/D-IFM. The experiments were carried out in four aspects. MOEA/D-IFM were compared with other state-of-the-art multi-objective evolutionary algorithms using CEC 2018 problems in two aspects. The best one of the six improved algorithms was chosen to test on large-scale many-objective problems. In addition, we also use MOEA/D-IFM to solve multi-objective backpack problems. [ABSTRACT FROM AUTHOR]

• A distribution measurement indicator is proposed to measure the distribution of individuals in a population. • A distribution enhancement module is introduced to increase the distribution of the individuals. • A limit optimization variation strategy of the best individual is taken to generate local solutions. • The threshold for judging the distribution level of individuals is adjusted adaptively. In general, for the iteration process of an evolutionary algorithm (EA), there exists the problem of uneven distribution of individuals in the target space for both multi-objective and single-objective optimization problems. This uneven distribution significantly degrades the population diversity and convergence speed. This paper proposes an adaptive hybrid evolutionary immune algorithm based on a uniform distribution selection mechanism (AUDHEIA) for solving MOPs efficiently. In AUDHEIA, the individuals in the population are mapped to a hyperplane, which is correlated with the objective space and are clustered to increase the diversity of solutions. To improve the distribution of the solutions, the mapped hyperplane is evenly sectioned. With the constantly changing distribution during the iteration, a threshold as a standard for judging the distribution level is adjusted adaptively. When the threshold is not satisfied in the corresponding interval, the distribution enhancement module is activated. Then, the same number of individuals should be selected in each interval. However, sometimes, there are insufficient or no individuals in the interval during the iterative process. To obtain sufficient individuals, the limit optimization variation strategy of the best individual is adopted. Experiments show that this algorithm can escape from local optima and has a high convergence speed. Moreover, the distribution and convergence of this algorithm are superior to the peer algorithms tested in this paper. [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]

In the realm of practical problem-solving, multi-objective optimisation problems with redundant variables and indefinite objective functions (MOPRVIF) are becoming increasingly prevalent. MOPRVIF involve determining the optimal decision variables that optimise multiple objectives, leveraging the relational data of a set of variables and multiple objectives. For these problems, this paper focuses on the following two issues: one is the demand for a unified computational model to solve this problem; the other is how to improve the algorithm's deep intelligent search capability. In this regard, this paper designs a dual data-driven multi-objective optimisation method. The method used consisted of four parts: elimination of redundant variables (ERV), objective function construction (OFC), selection evolution operator (SEO), and multi-objective evolutionary algorithm (MOEA). MOEA was the main focus of the method. ERV is data preparation and variable selection according to multiple objectives. OFC involves constructing the relationship model between variables and objectives, and a high-accuracy model is important for guaranteeing reliable results. Furthermore, SEO can adjust the evolution operator during a deep search. This is an important guarantee for deep, intelligent search. MOEA combined OFC and SEO to form the final solution algorithm—Dual Data Driven Multi-Objective Evolutionary Algorithm (DDMOEA). DDMOEA was explored using two different disciplinary problems of drug compound optimisation and wild blueberry cultivation and benchmarks were selected. The first two problem domains are distinct. The first problem is more complex than the second; however, both encompass redundant variables and indefinite objective functions. Benchmarks are utilised independently to gauge the profound intelligent search capability. The experiments affirm that the dual data-driven optimization approach proposed in this paper is effective, practical, and scalable. • Provide a unified solution for optimisation problems with redundant variables and indefinite objective functions. • Propose a data-driven multi-objective optimisation algorithm. • Designing an adaptive optimiser to enhance the algorithm's depth search capability. [ABSTRACT FROM AUTHOR]

In recent years, many efficient evolutionary multitasking (EMT) algorithms have been proposed to solve multi-objective multi-task optimization problems. However, EMT algorithms often face negative transfer problems. In this paper, a novel multi-objective evolution strategy, called CT-EMT-MOES, is proposed based on a cultural transmission theory for solving multi-objective multitask optimization problems. First, two evolutionary operators inspired by cultural transmission theory are proposed. The elite-guided variation strategy can transfer the information from the current Pareto front to all individuals and guide the population to quickly converge. The horizontal cultural transmission strategy can efficiently transfer information from the source task to the target task. Second, to solve the negative transfer problem, an adaptive information transfer strategy is proposed to adaptively adjust the probability of an information transfer. Third, the proposed algorithm can gain a Pareto front with good convergence and diversity by utilizing a smaller population size and fewer computing resources. As a result, the proposed algorithm can effectively utilize the implicit similarity and complementarity between simultaneous optimized tasks to improve the overall convergence efficiency and reduce a negative transfer. Finally, comprehensive experimental results show that the proposed algorithm can achieve a better performance compared with previous state-of-the-art multi-objective EMT algorithms. [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]

• A high-performance development of evolutionary PPDM algorithm is proposed. • GPU platform is employed to accelerate association rule hiding process in big data. • Dataset scanning and fitness function evaluation phases are parallelized. • Nine large-scaled datasets are used for efficiency evaluation. • Various experiments are carried out to verify the performance of our algorithm. Privacy protection has become a predominant concern in big data analysis. Privacy-Preserving Association Rule Mining (PPARM) is a process in which original data is transformed into a sanitized version to remove sensitive patterns. Although evolutionary PPARM approaches were developed, they are inefficient because the fitness function is overwhelmingly expensive. In this paper, an efficient algorithm, GPU-based Evolutionary Privacy-Preserving (GEPP), for improving the performance of PPARM is presented. We introduce two strategies for this reason: the first one is to develop a parallel indexing machine to generate retrieval index lists by parallelizing dataset scanning between GPU blocks, and the second strategy is the parallelization of the index lists for fitness function computation using CPU/GPU platform. In the second strategy, search mechanism and fitness function steps are performed on CPU and GPU, respectively. The scalability of GEPP is evaluated in terms of GPU characteristics, e.g., blocks and threads, data characteristics, e.g., the number of transactions, items, and density ratio, and patterns characteristics, e.g., the ratio of sensitive patterns and support thresholds. Experimental results show that our parallel implementation of the proposed approach obtains a speedup up to 36.6x, on average, compared to the CPU implementation using real and synthetic large-scale transaction datasets. [ABSTRACT FROM AUTHOR]

Recently, multi and many-objective evolutionary algorithms (MOEAs) embedded with clustering techniques to enhance their environmental selection show promising performance for tackling multi and many-objective optimization problems (MOPs) with irregular Pareto fronts (PFs). However, the similarity metric used for clustering cannot reflect the diversity of solutions fairly when it is measured based on the direction distances of solutions to an ideal point. Consequently, it may mislead the environmental selection when solving MOPs with convex PFs. To alleviate this issue, this paper suggests an MOEA using clustering with a flexible similarity metric to run the environmental selection. In our approach, we first use a simple yet effective method to roughly predict the concavity or convexity of the target problem. Then, a flexible reference point is set to define the direction distances of solutions, which can properly measure the similarity between solutions and fairly show their diversity for solving MOPs with various PF shapes. After that, we use a hierarchical clustering method with this flexible similarity metric to run the environmental selection on all solutions, which will properly classify them into N clusters (N is the population size). Finally, in each cluster, one solution with the best convergence value will survive to compose the new population. When compared to twenty-seven competitive MOEAs in solving nineteen benchmark MOPs and sixteen real-world engineering MOPs with various PF shapes, the experimental results demonstrate that the proposed algorithm has significant advantages. [ABSTRACT FROM AUTHOR]

A key issue in evolutionary constrained optimization is how to achieve a balance between feasible and infeasible solutions. The quality of generated solutions in decomposition-based multi-objective evolutionary algorithms (MOEAs) depends strongly on the weights' setting. To fully utilize both the promising feasible and infeasible solutions, this paper proposes two-type weight adjustments based on MOEA/D for solving highly constrained many-objective optimization problems (CMaOPs). During the course of the search, the number of infeasible weights is dynamically reduced, to guide infeasible solutions with better convergence to cross the infeasible barrier, and also to lead infeasible solutions with better diversity to locate multiple feasible subregions. Feasible weights are evenly distributed and keep unchanged throughout the evolution process, which aims to guide the population to search Pareto optimal solutions. The effectiveness of the proposed algorithm is verified by comparing it against six state-of-the-art CMaOEAs on three sets of benchmark problems. Experimental results show that the proposed algorithm outperforms compared algorithms on majority problems, especially on highly constrained optimization problems. Besides, the effectiveness of the proposed algorithm has also been verified on an antenna array synthesis problem. [ABSTRACT FROM AUTHOR]

Due to the fixed and monotonous search direction, the performance of decomposition-based multiobjective evolutionary algorithms (MOEAs) highly depends on the Pareto front (PF) shape. Recent studies have highlighted the complementary effect of the ideal and nadir points. They roughly employed both as the reference points to diversify the search direction. However, few works investigate whether two points are equally important. This paper thereby proposes a novel decomposition-based MOEA, where the ideal point is consistently considered as the global reference point while the nadir point is conditionally employed as the local one. We show that the nadir point may aid the ideal point in some cases and be recognized as a redundant one in others. More specifically, an assignment strategy is suggested to determine the necessity of using a local reference point for each subproblem, by considering whether the solution found by the nadir point and corresponding weight vector can improve the quality of the population. Experimental results finally verify the effectiveness of the proposed algorithm on 57 benchmark test problems with various PF shapes. In comparison with the state-of-the-art decomposition-based MOEAs, the proposed algorithm is promising to bring a more refined search and prevent redundant search behaviors. [ABSTRACT FROM AUTHOR]

Instance selection, as an important data pre-processing task, is widely used in supervised classification. Recently, a series of instance selection algorithms with different techniques have been suggested. Among them, evolutionary algorithms (EAs) have shown competitive performance. However, when the size of instance set is large, these EA-based algorithms may face great challenges on search efficiency and computational cost. To this end, in this paper, a multi-objective evolutionary algorithm based on length reduction, termed as LRIS, is proposed for large-scale instance selection, where a length reduction strategy is suggested to recursively shorten the length of each individual in the population, and improve the computational efficiency of LRIS greatly. Specifically, in the proposed length reduction strategy of LRIS, each gene in the individuals has a probability of being deleted, whose probability is obtained according to the importance of the corresponding instance in the instance set and the importance of the corresponding gene in the population. Then, two evolutionary operators (e.g. crossover and mutation) based on the length reduction strategy are developed to generate offspring population from the reduced population. In addition, an individual repairing operator is also designed to repair the length of over-reduced individuals. Experimental results on 12 large-scale data sets have demonstrated the efficiency and the effectiveness of the proposed LRIS in comparison with the state-of-the-art EA-based instance selection algorithms. [ABSTRACT FROM AUTHOR]

Hybridization in context to Evolutionary Computation (EC) strives to combine operators, components, and the best merits of different EC paradigms, to form a new evolutionary algorithm that enjoys a statistically superior performance, compared to its ancestors, over a wide range of application-specific optimization problems. In this paper, we propose a simple yet powerful amalgam composed of a modified Cultural Algorithm (CA) that is supported with an Enhanced Levy Flight Search (ELFS) to guide the search and further promote the harmony between the explorative and exploitative capacities of the conventional techniques. The novel amalgam, denoted by q-a CA + m IS, utilizes a balanced search scheme where it employs an adapted Influence Function (IF) with a novel quality function that establishes a harmony between the Knowledge Sources (KSs) in the Belief Space (BS), and between the BS and other components in the hybrid to produce the most suitable knowledge needed for a certain search mode. The CA framework is reinforced with an updated Selection Function (SF) that employs a successful selection strategy that uses the extended situational knowledge for the future selection of individuals. The proposed algorithm is tested using more than 50 benchmark functions that are taken from the IEEE CEC'06, and the IEEE CEC'19 competitions on constrained real-parameter optimization. Moreover, three well-known engineering design problems are used to test the validity of the algorithm for the solution of complex real-life problems. The comparative study indicates that the q-a CA + m IS algorithm was able to obtain a statistically superior performance and scalability behavior over most of the considered functions in comparison with other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

• A surrogate model based on IRL is suggested, which applies the max-margin method to approximate the reward function. • Under different dynamic environments, IRL learns the reward function and helps accelerate the convergence of the algorithm. • On the basis of learned reward function, IRL-DMOEA generates promising non-dominated solutions during the evolutionary process. Due to the widespread interest in dynamic multiobjective optimization in real-world applications, more and more approaches exploiting machine learning are deployed to tackle this type of problems. Unfortunately, recent works do not make full use of the data obtained during the optimization process, which could be benefit for model training thereby mining the dynamic characteristics of the underlying problem. To address this issue, this paper proposes a dynamic multiobjective evolutionary algorithm driven by inverse reinforcement learning to solve the dynamic multiobjective optimization problems. IRL is widely used to recover the unknown reward function, making it possible to perform at an expert level. The notable features of the proposed algorithm mainly consist of data-driven evolutionary technique, which uses inverse reinforcement learning as a surrogate-assisted model for model training. This design makes full use of the surrogate management strategy based on inverse reinforcement learning to optimize the reward function within a reinforcement learning framework. At the same time, the algorithm can generate a promising policy based on limited training data during the optimization process to achieve better algorithm evolution and guide the search. The experimental results on the benchmark problems validate that the proposed algorithm is effective in dealing with dynamic multiobjective optimization. [ABSTRACT FROM AUTHOR]

• The traditional two-archive algorithm is improved. CA and DA no longer only focus on the convergence and diversity of the objective space, but also extend to the decision space. • We propose a fitness scheme that combines the convergence of the objective space and the crowding distance of the decision space (COCD) to improve the convergence and diversity of the population. • We use different neighborhood criteria in the two archives to improve the convergence and diversity of the population in the decision space. This paper proposes a two-archive algorithm with decomposition and fitness allocation for multi-modal multi-objective optimization problems which have more than one Pareto-optimal solution set corresponding to the same objective vector. The general framework of the proposed method uses two archives, the convergence archive (CA) and the diversity archive (DA), which focus on the convergence and diversity of population, respectively. Both archives are based on a decomposition-based framework. In CA, the population update strategy adopts a fitness scheme, which is designed according to the change state of population during evolution, combining the convergence of the objective space with the diversity of the decision space. In DA, we use the crowding distance strategy to ensure the diversity of the decision space. Moreover, different neighborhood criteria are used to ensure the convergence and diversity of population for two archives. The algorithm is shown to not only locate and maintain a larger number of Pareto-optimal sets, but also to obtain good diversity and convergence in both the decision and objective spaces. In addition, the proposed algorithm is empirically compared with five state-of-the-art evolutionary algorithms on two series of test functions. Comparison results show that the proposed algorithm has better performance than the competing algorithms. [ABSTRACT FROM AUTHOR]

For many-objective problems, how to maintain the diversity and convergence of the distribution of the solution set over Pareto front (PF) has always been the research emphasis. In the iteration process, the state of population is critical to improve the level of evolution. Therefore, this paper will use two convergence and diversity indicators to further strengthen the usage of evolutionary state information and propose a dynamic learning strategy. In addition, a dynamic learning strategy based many-objective evolutionary algorithm (MaOEA) is proposed, called dynamic learning evolution algorithm (DLEA), which continuously changes the direction of learning: convergence and diversity in the iteration process. The purpose is to make the algorithm prefer to convergence in the early iteration and prefer to diversity when it is close to PF in the late iteration, so that the convergence and diversity of the final solution set can be well maintained. And then, the performance of DLEA is measured by two indicators. Meanwhile, DLEA will be compared with four state-of-the-art algorithms on the DTLZ and MaF, and its performance will be verified on a many-objective combinatorial problem. And the experimental results and Friedman test show that DLEA has great advantages. [ABSTRACT FROM AUTHOR]

• The niche-based density estimation and angle-based selection strategy are devised. • Individuals with poor diversity are identified by niche-based density estimation. • Individuals with worse convergence are removed via angle-based selection. • NAEA can be easily extended to constrained many-objective optimization problems. It is well known that balancing population diversity and convergence plays a crucial role in evolutionary many-objective optimization. However, most existing multiobjective evolutionary algorithms encounter difficulties in solving many-objective optimization problems. Thus, this paper suggests niche-based and angle-based selection strategies for many-objective evolutionary optimization. In the proposed algorithm, two strategies are included: niche-based density estimation strategy and angle-based selection strategy. Both strategies are employed in the environmental selection to eliminate the worst individual from the population in an iterative way. To be specific, the former estimates the diversity of each individual and finds the most crowded area in the population. The latter removes individuals with weak convergence in the same niche. Experimental studies on several well-known benchmark problems show that the proposed algorithm is competitive compared with six state-of-the-art many-objective algorithms. Moreover, the proposed algorithm has also been verified to be scalable to deal with constrained many-objective optimization problems. [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]

Constrained multi-objective optimization problems (CMOPs) are difficult to handle because objectives and constraints need to be considered simultaneously, especially when the constraints are extremely complex. Some recent algorithms work well when dealing with CMOPs with a simple feasible region; however, the effectiveness of most algorithms degrades considerably for CMOPs with complex feasible regions. To address this issue, this paper proposes a multi-stage evolutionary algorithm, where constraints are added one after the other and handled in different stages of evolution. Specifically, in the early stages, the algorithm only considers a small number of constraints, which can make the population efficiently converge to the potential feasible region with good diversity. As the algorithm moves to the later stages, more constraints are considered to search the optimal solutions based on the solutions obtained in the previous stages. Furthermore, a strategy for sorting the constraint-handling priority according to the impact on the unconstrained Pareto front is proposed, which can accelerate the convergence of the algorithm. Experimental results on five benchmark suites and three real-world applications showed that the proposed algorithm outperforms several state-of-the-art constraint multi-objective evolutionary algorithms when dealing with CMOPs, especially for problems with complex constraints. [ABSTRACT FROM AUTHOR]

This paper proposes a new decision variable classification-based cooperative coevolutionary algorithm, which uses the information of decision variable classification to guide the search process, for handling dynamic multiobjective problems. In particular, the decision variables are divided into two groups: convergence variables (CS) and diversity variables (DS), and different strategies are introduced to optimize these groups. Two kinds of subpopulations are used in the proposed algorithm, i.e., the subpopulations that represent DS and the subpopulations that represent CS. In the evolution process, the coevolution of DS and CS is carried out through genetic operators, and subpopulations of CS are gradually merged into DS, which is optimized in the global search space, based on an indicator to avoid becoming trapped in local optimum. Once a change is detected, a prediction method and a diversity introduction approach are adopted for these two kinds of variables to get a promising population with good diversity and convergence in the new environment. The proposed algorithm is tested on 16 benchmark dynamic multiobjective optimization problems, in comparison with state-of-the-art algorithms. Experimental results show that the proposed algorithm is very competitive for dynamic multiobjective optimization. [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]

Constrained multi-objective optimization problems (CMOPs) require a delicate balance between satisfying constraints and optimizing objectives. Existing constrained multi-objective evolutionary algorithms (CMOEAs) often struggle to balance convergence, diversity, and feasibility, especially when dealing with CMOPs that have complex feasible regions. This paper proposes a multi-task-based self-organizing mapping evolutionary algorithm (MTSOM) to tackle this challenge, which includes a main and auxiliary task. Two populations independently optimize two tasks without considering constraints in the early stage. Subsequently, in the middle stage, both tasks explore the distribution structure of the population in parallel by employing a novel constraint-to-constraint self-organizing mapping (SOM) approach. In the late stage, the main task fully considers feasibility, while the auxiliary task focuses solely on the highest priority constraints. This approach enables rapid convergence toward feasible regions. To evaluate MTSOM's effectiveness, we conducted a series of experiments on five benchmark suites. Results indicate that MTSOM is competitive when compared to other state-of-the-art CMOEAs. Additionally, our proposed constraint-to-constraint SOM is superior in handling complex CMOPs. [ABSTRACT FROM AUTHOR]

The application of semantic technologies, particularly ontologies, in the realm of multi-objective evolutionary algorithms is overlook despite their effectiveness in knowledge representation. In this paper, we introduce MOODY, an ontology specifically tailored to formalize these kinds of algorithms, encompassing their respective parameters, and multi-objective optimization problems based on a characterization of their search space landscapes. MOODY is designed to be particularly applicable in automatic algorithm configuration, which involves the search of the parameters of an optimization algorithm to optimize its performance. In this context, we observe a notable absence of standardized components, parameters, and related considerations, such as problem characteristics and algorithm configurations. This lack of standardization introduces difficulties in the selection of valid component combinations and in the re-use of algorithmic configurations between different algorithm implementations. MOODY offers a means to infuse semantic annotations into the configurations found by automatic tools, enabling efficient querying of the results and seamless integration across diverse sources through their incorporation into a knowledge graph. We validate our proposal by presenting four case studies. • A semantic model is proposed for consolidating multi-objective optimization knowledge. • A knowledge graph is presented, as well as the tools to include new RDF data. • The model allows for semantic reasoning on evolutionary algorithm configurations. • The proposal is validated on three use cases with data from experiments. • Moody enables knowledge-based recommendations of configurations for algorithms. [ABSTRACT FROM AUTHOR]

Various evolutionary algorithms have been proposed for tackling many-objective optimization problems over the past three decades. However, these algorithms still suffer from the loss of selection pressures due to the existence of dominance resistance. To tackle this issue, this paper proposes a relative non-dominance matrix, based on which a fitness formula is defined. Empirical analyses show that solutions with smaller fitness values are likely to dominate more other solutions in the future evolutionary process, and play a vital role in enhancing the convergence toward to the true Pareto fronts. Additionally, to further ensure the diversity, k -means clustering strategy is combined with the relative non-dominance matrix for a new design of the environmental selection, where parameter k in the clustering strategy is adjusted adaptively. The proposed algorithm is extensively tested with four state-of-art algorithms on WFG, MaF and DTLZ test suites. Empirical comparisons demonstrate the competitiveness of the proposed algorithm regarding to the convergence, diversity and spread. [ABSTRACT FROM AUTHOR]

• We devise a reinforcement learning-based framework to relocate the POS more adaptively. • Based on different severity degree of environmental changes, three change response methods are integrated to predict the POS. • The proposed algorithm learns the dynamic environment and determines the appropriate prediction-based strategy. Dynamic Multi-objective Optimization Problem (DMOP) is emerging in recent years as a major real-world optimization problem receiving considerable attention. Tracking the movement of Pareto front efficiently and effectively over time has been a central issue in solving DMOPs. In this paper, a reinforcement learning-based dynamic multi-objective evolutionary algorithm, called RL-DMOEA, which seamlessly integrates reinforcement learning framework and three change response mechanisms, is proposed for solving DMOPs. The proposed algorithm relocates the individuals based on the severity degree of environmental changes, which is estimated through the corresponding changes in the objective space of their decision variables. When identifying different severity degree of environmental changes, the proposed RL-DMOEA approach can learn better evolutionary behaviors from environment information, based on which apply the appropriate response mechanisms. Specifically, these change response mechanisms including the knee-based prediction, center-based prediction and indicator-based local search, are devised to promote both convergence and diversity of the algorithm under different severity of environmental changes. To verify this idea, the proposed RL-DMOEA is evaluated on CEC 2015 test problems involving various problem characteristics. Empirical studies on chosen state-of-the-art designs validate that the proposed RL-DMOEA is effective in addressing the DMOPs. [ABSTRACT FROM AUTHOR]

• We propose a knee based evolutionary algorithm, named MMO-EvoKnee, which incorporates MCDM strategy into solving MMOPs. The proposed algorithm can find a complete set of global knee solutions accurately instead of an entire Pareto front and Pareto sets. • The EvoKnee selection aims to find target global knee solutions and boundary individuals in the objective space. After that, the other three procedures would turn the search direction into the decision space for multiple equivalent optimal knee and boundary solutions. • The Knee Multimodal Solutions Selection focuses on searching for well-converged knee solutions. Furthermore, the Maximum Spanning Subset Selection can accurately identify a complete set of global knee solutions from overcrowded solutions, which can relieve the burden for decision makers. Recently, many advanced multimodal multi-objective evolutionary algorithms (MMOEAs) have been presented to solve multimodal multi-objective optimization problems (MMOPs). However, most of these approaches struggle not only to find the entire Pareto sets and Pareto front, but also ignoring the problem of Multi-Criteria Decision Making (MCDM) to be handled at a later stage. As a matter of fact, it is a very eclectic and challenging burden for decision makers to choose some trade-off optimal solutions from an enormous collection of non-dominated Pareto-optimal individuals. In this paper, we propose a knee based evolutionary algorithm, named MMO-EvoKnee, which incorporates MCDM strategy into solving MMOPs. The proposed algorithm is designed to search for a complete set of global knee solutions instead of an entire Pareto front and Pareto sets. Firstly, the EvoKnee Selection is adopted to find target global knee solutions and boundary individuals. Secondly, the Knee Multimodal Solutions Selection focuses on decision space exploitation to obtain well-converged multiple Pareto-optimal knee solutions. Thirdly, the Maximum Spanning Subset Selection is designed to accurately identify a complete number of knee solutions from overcrowded Pareto regions. Fourthly, the Boundary Multimodal Solutions Selection can find and maintain well-diversified and well-converged boundary solutions. As a result, MMO-EvoKnee can consistently find all knee solutions of interest quickly, and it relieves the burden for decision makers. Finally, the performance of the proposed algorithm is evaluated on thirteen benchmark MMOPs. The experiment results clearly show that the proposed MMO-EvoKnee provides a competitive edge over the chosen state-of-the-art MMOEAs. [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]

• We propose two novel variants of low-rank update for evolution strategies. • We analyze the algorithms properties and the connections to other variants. • We evalaute the algorithms' performances on BBOB COCO benchmarks. The covariance matrix adaptation evolution strategy (CMA-ES) is one of the most successful evolutionary algorithms. CMA-ES incrementally learns the variable metric by evolving a full covariance matrix. Yet, it suffers from high computational overload. In this paper, we propose two efficient variants of CMA-ES, termed mutation matrix adaptation (MMA-ES) and exponential MMA-ES (xMMA-ES). These variants are derived by taking the first order approximation of the update of the covariance matrix in CMA-ES. Both variants avoid the computational costly matrix decomposition while keeping the simplicity of the update scheme of CMA-ES. We analyze the properties and connections of MMA-ES and xMMA-ES to other variants of evolution strategies. We have experimentally studied the proposed algorithms' behaviors and performances. xMMA-ES and MMA-ES generally outperform or perform competitively to CMA-ES. We have investigated the performance of MMA-ES with the BiPop restart strategy on the BBOB benchmarks. The experimental results validate the performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

• Propose to divide the whole population into heterogeneous CL subpopulation and DMS subpopulation respectively mainly responsible for exploitation and exploration. • Propose to classify the DMS subpopulation sub-swarms search level and construct a new adaptive nonlinear decrease inertia weight formula. • Propose to introduce the non-uniform mutation operator in the DMS subpopulation and introduce a Gaussian mutation operator in the global optimal experiences of the whole population. • The performance of the proposed HCLDMS-PSO algorithm is compared with other 8 state-of-the-art PSO variants and 11 evolutionary algorithms on two classical benchmark optimization problems (CEC2005 and CEC2017) and a real-world engineering problem. In this paper, a heterogeneous comprehensive learning and dynamic multi-swarm particle swarm optimizer with two mutation operators (HCLDMS-PSO) is presented. In addition, a comprehensive learning (CL) strategy with the global optimal experience of the whole population is conducted to generate an exploitation subpopulation exemplar. However, a modified dynamic multi-swarm (DMS) strategy is specially designed to construct the exploration subpopulation exemplar. In the canonical DMS strategy, it is unfavorable for different sub-swarms to use the same linear decreasing inertia weight parameter. We first propose classifying the DMS sub-swarms at the search level and then constructing a novel nonlinear adaptive decreasing inertia weight for different sub-swarms, introducing a non-uniform mutation operator to enhance its exploration capability. Finally, the gbest of the whole population also adopts a Gaussian mutation operator to avoid falling into the local optimum. The particles of the two subpopulations will update their velocity independently without crippling one another to prevent a loss of diversity. The performance of HCLDMS-PSO is compared with those of 8 other PSO variants and 11 evolutionary algorithms on two classical benchmark optimization problems and a real-world engineering problem. Experimental results demonstrate that the HCLDMS-PSO improves the convergence speed, accuracy, and reliability on most optimization problems. [ABSTRACT FROM AUTHOR]

• Propose a mechanism combining key features of Linkage Tree Genetic Algorithm (LTGA) and Multifactorial Optimization (MFO). • Propose a method for building the linkage tree based on unified search space to exploit both information between problem variables and transfer knowledge of independent tasks. • Propose an assortative mating mechanism to enhance the compatibility between the main features of MFO and LTGA. • Introduce a crossover operator to keep the key advantages of MFO and LTGA as well as maintain population diversity. • Demonstrate the effectiveness of the proposed algorithm on two benchmark problems. Linkage Tree Genetic Algorithm (LTGA) is an effective Evolutionary Algorithm (EA) to solve complex problems using the linkage information between problem variables. LTGA performs well in various kinds of single-task optimization and yields promising results in comparison with the canonical genetic algorithm. However, LTGA is an unsuitable method for dealing with multi-task optimization problems. On the other hand, Multifactorial Optimization (MFO) can simultaneously solve independent optimization problems, which are encoded in a unified representation to take advantage of the process of knowledge transfer. In this paper, we introduce Genetic Algorithm (MF-LTGA) by combining the main features of both LTGA and MFO. MF-LTGA is able to tackle multiple optimization tasks at the same time, each task learns the dependency between problem variables from the shared representation. This knowledge serves to determine the high-quality partial solutions for supporting other tasks in exploring the search space. Moreover, MF-LTGA speeds up convergence because of knowledge transfer of relevant problems. We demonstrate the effectiveness of the proposed algorithm on two benchmark problems: Clustered Shortest-Path Tree Problem and Deceptive Trap Function. In comparison to LTGA and existing methods, MF-LTGA outperforms in quality of the solution or in computation time. [ABSTRACT FROM AUTHOR]

In realistic numerical optimization problems, the efficiency of the algorithm is a crucial consideration. Fitness landscape approximation is beneficial for improving the search efficiency in evolutionary algorithms, but this method increases the computational cost significantly with an increase in the dimension. This paper proposes a quantum-inspired algorithm with dimension decomposition and fitness landscape approximation. The high-dimensional problem space is transformed into a low-dimensional projection space for fitness landscape approximation through mapping transformation. Linear approximation for the fitness landscape is performed in the transformed multiple 1D projected spaces. In accordance with two different diversity-retaining strategies, reference sampling points with different characteristics are selected to perform two-point linear approximation. Candidate points in the projection space are estimated and then synthesized as candidate solutions in the problem space. Then, candidate solutions are used in an appropriate population reconstruction mechanism to improve the performance of the algorithm. The proposed algorithms are implemented on benchmark functions abstracted from real-world optimization problems and compared with several algorithms. Experimental results on errors, success rates, and their rankings show the superiority of the proposed approach with the solution diversity priority with regard to effectiveness, adaptability, and stability. [ABSTRACT FROM AUTHOR]

Balancing multiple objectives and various constraints is crucial for effectively solving constrained multi-objective optimization problems (CMOPs). Excessive focus on either convergence or feasibility may not result in favorable outcomes of the algorithm. To confront this challenge, this paper proposes a cooperative evolutionary algorithm named SaE-CMO, which aims to achieve a harmonious balance between convergence and feasibility by extracting valuable information from both feasible and infeasible regions. To achieve this, SaE-CMO employs a dual-population approach to enhance search progress, consisting of a main population, Population1, and an auxiliary population, Population2. These two populations complement each other to achieve optimal results. A newly proposed self-adaptive epsilon method is employed in both Population1 and Population2, using different comparison criteria to select next population from mating pools, respectively. Population2 can retain some solutions that are well-constrained but poorly converged, thereby preserving information about both the constrained and the unconstrained Pareto front. This property enables Population2 to assist Population1 in maintaining diversity in certain complex CMOPs. To verify the effectiveness of SaE-CMO, we conduct experiments on three benchmark test instances and four real-world CMOPs with some related state-of-the-art constrained multi-objective optimization algorithms, experimental results prove that the proposed algorithm outperforms the compared algorithms. [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]

Allowing the population size to variate during the evolution can bring advantages to evolutionary algorithms (EAs), retaining computational effort during the evolution process. Dynamic populations use computational resources wisely in several types of EAs, including genetic programming. However, so far, a thorough study on the use of dynamic populations in Geometric Semantic Genetic Programming (GSGP) is missing. Still, GSGP is a resource-greedy algorithm, and the use of dynamic populations seems appropriate. This paper adapts algorithms to GSGP to manage dynamic populations that were successful for other types of EAs and introduces two novel algorithms. The novel algorithms exploit the concept of semantic neighbourhood. These methods are assessed and compared through a set of eight regression problems. The results indicate that the algorithms outperform standard GSGP, confirming the suitability of dynamic populations for GSGP. Interestingly, the novel algorithms that use semantic neighbourhood to manage variation in population size are particularly effective in generating robust models even for the most difficult of the studied test problems. [ABSTRACT FROM AUTHOR]

Multi-objective optimization problems with interval parameter (IMOPs) are among the most critical optimization problems in practical applications. However, in contrast to deterministic multi-objective optimization, few studies have addressed IMOPs. Moreover, the uncertainty in such problems makes the convergence and diversity of the algorithm more challenging. Therefore, this paper proposes an interval multi-objective optimization algorithm based on elite genetic strategy (EG-IMOEA). First, existing interval dominance relations cannot comprehensively determine which of the two intervals is better when their midpoints are equal but their upper and lower limits are unequal. Therefore, a conditional-based interval confidence dominance relation is proposed that considers both the average level of convergence and value of the minimum lower limit of intervals. The interval crowding distance (ICD) applied to multiple objectives is then defined to evaluate the solutions more completely. Furthermore, an elite genetic strategy for crossover and mutation is proposed to generate better offspring. The proposed algorithm was evaluated on nine benchmark test problems and compared with the typical algorithm as well as state-of-the-art algorithms. The results showed that this algorithm outperformed the comparison algorithms in terms of convergence, diversity, imprecision, and uniform distribution. [ABSTRACT FROM AUTHOR]

Many-objective problems refer to the optimization problems containing more than three conflicting objectives. To obtain a representative set of well-distributed non-dominated solutions close to Pareto front in the objective space remains a challenging problem. Many papers have proposed different Multi-Objective Evolutionary Algorithms to solve the lack of the convergence and diversity in many-objective problems. One of the more promising approaches uses a set of reference points to discriminate the solutions and guide the search process. However, this approach was incorporated mainly in Multi-Objective Evolutionary Algorithms, and there are just some few promising adaptations of Particle Swarm Optimization approaches for effectively tackling many-objective problems regarding convergence and diversity. Thus, this paper proposes a practical and efficient Many-Objective Particle Swarm Optimization algorithm for solving many-objective problems. Our proposal uses a set of reference points dynamically determined according to the search process, allowing the algorithm to converge to the Pareto front, but maintaining the diversity of the Pareto front. Our experimental results demonstrate superior or similar performance when compared to other state-of-art algorithms. [ABSTRACT FROM AUTHOR]

Abstract Achieving a balance between convergence and diversity in many-objective optimization is a great challenge. This paper suggests an evolutionary algorithm based on a region search strategy to deal with different kinds of benchmark problems. In the proposed algorithm, each solution is associated with a region, and the region search strategy is applied to constrain the updating process; this strategy will enhance the diversity of population without losing convergence. A new normalization procedure is used for dealing with scaled problems. Moreover, the comparison of two solutions is based on both dominance relation and perpendicular distance; the result shows the algorithm's reliability for solving both convex and concave problems. The performance of the proposed algorithm is validated by several well-known benchmark problems with different properties. Seven state-of-the-art algorithms are compared and the experimental results demonstrate that the introduced algorithm performs the best on almost all benchmark problems. Furthermore, the proposed strategy depicts a high computational efficiency for solving the problems with a high dimension of objectives. [ABSTRACT FROM AUTHOR]

Abstract It is well known that maintaining a good balance between convergence and diversity is crucial to the performance of multiobjective optimization algorithms (MOEAs). However, the Pareto front (PF) of multiobjective optimization problems (MOPs) affects the performance of MOEAs, especially reference point-based ones. This paper proposes a reference-point-based adaptive method to study the PF of MOPs according to the candidate solutions of the population. In addition, the proportion and angle function presented selects elites during environmental selection. Compared with five state-of-the-art MOEAs, the proposed algorithm shows highly competitive effectiveness on MOPs with six complex characteristics. [ABSTRACT FROM AUTHOR]