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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]

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]

• 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]

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]

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]

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]

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]

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]

• 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]

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 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]

• 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]

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]

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]

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]

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]