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Large-scale multiobjective optimization problems (LSMOPs), which optimize multiple conflicting objectives with hundreds or even thousands of decision variables, demand increasing computational resources to assure satisfactory performance as the decision variables increase. Multiobjective evolutionary algorithms are naturally scalable, but as the dimension increases, the conflict between analyzing enough solutions and the limited number of function evaluations has hindered further improvements in scalability. In this paper, we first define the scalability of multiobjective evolutionary algorithms and design an indicator to quantitatively measure the scalability. Second, to boost scalability when solving LSMOPs, we propose a scalable multiobjective optimization algorithm by transferring weights between solutions to reduce dependency on ever-increasing computational resources as the problem dimension increases. The proposed framework entails constructing a latent decision space to determine evolutionary weights for chosen representative solutions. These computed weights are then transferred to the remaining solutions, enabling evolutionary optimization to proceed without requiring additional evaluations, even as the dimensionality increases. By utilizing the knowledge gained from the source solutions, each solution is customized with an evolutionary weight scheme that not only preserves computational resources but also enhances optimization performance, thereby boosting scalability. We have conducted experiments on LSMOPs to verify the effectiveness and scalability of the proposed algorithm. The proposed method outperforms selected state-of-the-art algorithms and gains scalability boosts in situations where the dimensions increase while the function evaluation remains constant. • This paper defines the scalability of large-scale multiobjective evolutionary algorithms and introduces a novel performance indicator to measure. • We propose a scalable algorithm for LSMOPs to ensure consistent performance within specified function evaluations, regardless of dimensionality. • We design a technique to transfer learned weights between solutions without additional evaluations to enhance scalability while conserving resources. [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]

The training effect of the neural network model is directly influenced by optimization algorithms. The Barzilai-Borwein(BB) method is used in the stochastic gradient descent (SGD) and other deep learning optimization algorithms because of its outstanding performance in terms of convergence speed. In order to improve the stability of BB step size and the output quality of network model in deep learning, this paper presents two improved optimization algorithms based on the BB method: BBbound and AdaBBbound. BBbound reduces the floating BB step size by generating the upper bound of the step in the current iteration. It avoids the occasional occurrence of long steps; AdaBBbound is an adaptive gradient method based on BB method with dynamic bound. The algorithm has a fast convergence effect in the early stage, then calculates learning rate and smoothly transitions to SGD by setting the better conditions of the BB method. We analyzed the performance of the two algorithms based on the initial conditions and the learning rate change curve. Meanwhile, we tested our algorithms on popular network models such as ResNet and DenseNet. The results showed that the new optimization algorithms have achieved high stability and significantly improved the performance of the network model. [ABSTRACT FROM AUTHOR]

An optimization spiking neural P (OSN P) system is a discrete optimization model without the aid of evolutionary operators of evolutionary algorithms or swarm intelligence algorithms. However, since the processing object of OSN P systems is a spike, where information is encoded by the timing of spikes or the number of spikes in neurons, OSN P systems are limited for solving continuous optimization problems. To break this limitation, an extended numerical spiking neural (ENSN P) system is proposed based on numerical spiking neural P (NSN P) systems and multiple (ENSN P) systems, called optimization numerical spiking neural P systems (ONSN P systems or ONSNPS), are designed to solve continuous constrained optimization problems. More specifically, in ENSN P systems, the production functions are selected by probability to achieve updated parameters. In OSN P systems, a guider algorithm is introduced to finish individuals' crossover and selection. The extensively experimental results in five benchmarks, thirty-two optimization problems including five benchmark problems, seventeen manufacturing design optimization problems and ten benchmarks from CEC show that ONSN P systems in this paper outperform or are competitive to twenty-eight optimization algorithms. Finally, algorithm complexity and Holm-Bonferroni procedure based on statistical results is used to test the complexity changing when we use different dimensionality of the search space and the difference in terms of statistical performance. The testing results indicate that the time complexity of ONSN P systems grows linearly with problem dimensions and ONSN P systems are better performance than the most algorithms. [ABSTRACT FROM AUTHOR]

The rapid development of online social networks (OSNs) has enabled seamless cyberbullying activities, which not only cause psychological harm to victims but also bring disharmony to society. From the perspective of OSN platform administrators, strategic decision making towards when/how to launch an anti-cyberbullying campaign is the key to mitigating its negative impact. Hence, this paper develops a dynamic anti-cyberbullying investment solution to mitigate the adverse impact of strategic cyberbullying phenomena cost-effectively. Specifically, this paper first quantifies the payoffs of the attacker/bullying instigator and the defender/platform administrator based on a newly proposed propagation model. Then, considering the budget-constrained factor for both sides, a differential game-theoretical model is proposed to simulate each party's optimal trade-off between cost and benefit. Next, by utilizing Pontryagin Maximum/Minimum Principle, a set of necessary conditions for a Nash equilibrium strategy profile have been proposed. Based on the forward-backward sweep method, an iterative algorithm (SCR optimization algorithm) is tailored to solve the conditions numerically. Through experiments conducted under Facebook, Youtube and Twitter sub-networks, the algorithm's performance has been evaluated by inspecting its convergence speed and payoff compared with randomized profiles. Consequently, the resulting strategies are verified to exhibit superior performance in dealing with cyberbullying spreading. [ABSTRACT FROM AUTHOR]

• A novel multi-objective scheduling model is developed for the emergency rescue planning problem. • The proposed model minimizes the fire extinguishing time, delay time, and number of fire rescue vehicles. • The factor of fire spreading speed is firstly considered in our optimization model. • A revised multi-objective discrete gravitational search slgorithm is designed to produce Pareto solutions. • An empirical case study in Heilongjiang Province, China, is applied. The implementation of emergency scheduling of priority-based rescue vehicles for extinguishing forest fires is a complex optimization problem facing with many challenges and difficulties to optimize the operational costs and to improve the efficiency to make robust decisions. The main challenges are to minimize the number of fire engines while minimizing firefighting time and firefighting delay time, simultaneously. The main difficulties to make these decisions are to consider the severity of each fire point with regards to the limited resources of vehicles. Hence, this paper motivates to develop a new multi-objective scheduling model for extinguishing the fire of forests considering rescue priority with the limited rescue resources. To make an efficient and robust solution for the proposed problem, another novelty is to propose a hybrid optimization algorithm which is a modified discrete gravitational search algorithm. To confirm the applicability of the proposed problem, an actual forest fire emergency scheduling in Heilongjiang Province, China, is simulated. The proposed hybrid optimization algorithm is tested to check the feasibility the Pareto solutions and it is compared with a set of well-known and recent algorithms to show its efficiency. Finally, after a comprehensive discussion, the results prove that this work provides an accurate and effective tool for performing the emergency scheduling for extinguishing the forest fire. [ABSTRACT FROM AUTHOR]

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

Recently, numerous unsupervised multi-view feature selection methods have been presented. However, these methods assess the significance of data features in each view individually or jointly evaluate the significance of data features across multiple views by concatenating data features from all data views. So, they disregard either inter-view or intra-view feature connections of data. Moreover, they ignore the complementary information from multiple insufficient views, each of which only captures partial information of multi-view data and is insufficient to characterize data distribution. To address these problems, this paper proposes a model named Dual-level Feature Assessment for Unsupervised Multi-view Feature Selection with Latent Space Learning (DFA-LSL). It first investigates the underlying complementary information from multiple views in a latent space while simultaneously learning latent representations for data. Compared with the original data representations, the latent representations contain the entire information of multi-view data. Then, it explores connections and distinguishing ability of features at two levels, namely the inter-view and intra-view levels, by jointly assessing the significance of features in the latent space and individually assessing the significance of features in each view concurrently. Following that, an effective optimization algorithm is presented. Extensive experiments demonstrate that the proposed work surpasses several state-of-the-art models. [ABSTRACT FROM AUTHOR]

As a new technology for model compression, self-knowledge distillation (SKD) avoids the large computational overhead of training the teacher model seen with traditional knowledge distillation. However, existing SKD methods pay attention to the knowledge transfer between deep and shallow layers of the network but ignore the mutual learning between shallow branches. This paper proposes a many-objective evolutionary self-knowledge distillation framework (MaOESKD) to guide the knowledge fusion between branches in the SKD neural network. This framework embeds an optimization module and a temporary branch into the multi-branch SKD network. The optimization module includes a many-objective adaptive weight optimization model (MaAWOM) and an many evolutionary optimization algorithm based on multi-strategy consensus mechanism (MaOEA-MCM); meanwhile, the temporary branch performs linear weighted fusion. In the MOBWOM, the weight of different branches in knowledge fusion is taken as the decision variable, and the mutual information, covariance, KL divergence between branch output features, and the total information of each branch are taken as the optimization objective. The MSCMEA integrates several state-of-the-art individual selection strategies in the field of evolutionary algorithms. It includes shift density estimation (SDE), penalized boundary intersection (PBI), balanced fitness estimation (BFE), and adaptive position transformation (APT). The accuracy of MOESKD achieves 99.70, 95.74 and 78.21 in MNIST, CIFAR-10 and CIFAR-100. [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]

As a classical unsupervised learning method, the K-means algorithm selects the cluster centers randomly and calculates the mean values of the cluster's data points to generate clusters. However, its performance is susceptible to the initial cluster centers and the sparsity of the membership matrix. To overcome these limitations, in this paper, we propose a sparse K-means clustering algorithm with anchor graph regularization (SKM-AGR) for optimizing initial cluster center sensitivity and improving membership matrix sparsity. The main idea is to use the anchor graph regularization (AGR) constrained K-means models, which effectively learn the membership matrix of data points and the membership matrix of anchors. In particular, by constructing an anchor graph, the AGR term not only discovers the internal structure information of data, but also covers the data distribution. Furthermore, an alternating optimization algorithm with fast-converging is adopted to solve the optimization problems of SKM-AGR, and the computational complexity is analyzed. Extensive clustering experiments on several synthetic and benchmark datasets show that the proposed SKM-AGR method performs better than several previous methods in most cases. [ABSTRACT FROM AUTHOR]

Non-parallel hyperplane classifiers have attracted many attention due to their wider applicability than parallel hyperplane classifiers, and it accelerates the training speed through separately training of each hyperplane. However, it does not consider the correlation relationship among the non-parallel hyperplanes. In addition, since these non-parallel hyperplanes are built on the same training data, there may exist correlation among them due to redundancy of the data. In this paper, we investigate the decorrelation problem of non-parallel hyperplane classifiers. We integrate non-parallel hyperplanes into a unified model and explore this relationship through a joint classifier learning approach. Taking the twin support vector machine as an example, a novel decorrelation regularization term is added into the joint problem. Additionally, an effective alternating optimization algorithm has been introduced to address this nonconvex problem. To evaluate the proposed method, a series of experiments are conducted on binary and multi-class classification datasets from the benchmark database repository. Experimental results compared to several parallel and non-parallel hyperplane based classifiers demonstrate the effectiveness of the proposed method. • A unified non-parallel SVM with decorrelation TWJCL for multi-class classification is proposed. • Compared to JCL, TWJCL achieves decorrelation in each binary classification. • Experiments show TWJCL has low correlation coefficient and good classification performance. [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]

There have been several studies in the literature that looked at bipolar fuzzy relation equations using three compositions, max-min, max-product, and max-Lukasiewicz. This paper addresses an optimization problem involving a general class of bipolar fuzzy relation equations. A point to be noted is that the constraints are formed as a system of bipolar fuzzy equations, in which the fuzzy compositions are defined by an arbitrary continuous t-norm. The paper shows that a feasible solution set consists of a finite number of closed convex cells whose lower and upper bounds are determined by corner (extreme) points. In addition, it will be illustrated that, in contrast to the (ordinary) fuzzy relational equations, corner points may neither be the minimum (maximum) nor minimal (maximal) solutions to the feasible region. The generality of the problem leads us to divide the constraints into four classes (each with a different structure) and then investigate the specific characteristics of the equations in each class. Additionally, to evaluate the feasibility of the problem in general, some necessary and sufficient conditions are presented. Due to the high computational complexity of the complete solution of FREs, six rules are introduced to reduce the size of the original problem in such a way that the effort to solve the problem is significantly decreased, followed by an algorithm for solving the current optimization problems. Accordingly, it is shown that the problem has a finite number of local optimal solutions and a global optimal solution can always be obtained by choosing a point having the minimum objective value compared to all the local optimal solutions. In the final section, we will examine an example to demonstrate how the algorithm works. • A generalized bipolar system of fuzzy relation equations programming problem has been introduced which is defined with linear objective function, bipolar fuzzy constraints and an arbitrary continuous strict t-norm. • It is proved that the feasible solution set is formed as a union of the finite number of closed convex cells whose lower and upper bounds are determined by corner (extreme) points that may be neither the minimum (maximum) nor minimal (maximal) solutions. • The constraints of the problem are categorized into four different classes, and the special characteristics of the equations in each class are investigated. • Some necessary and sufficient conditions are presented to conceptualize the feasibility of the problem. • Six rules are introduced with the aim of simplifying the original problem. [ABSTRACT FROM AUTHOR]

Convergence analysis of multi-objective optimization algorithm has been an area of vital interest to the research community. With this regard, a number of approaches have been proposed and studied. However, these studies and developed proposals cannot cope with more than 3-dimensional optimization problems. Generally speaking, interpolation planes are formed by 3-dimension data. So, when the dimensionality of the Pareto front is more than 3, the dimensionality of Pareto front will be reduced to 3 by involving principal component analysis. This may lead to some important data being missed. Due to missing data, the formed interpolation plane is usually inaccurate and uneven. This will give rise to difficulties to evaluate the distance between the Pareto front and the optimal Pareto front. Subsequently, it is not easy to evaluate exact convergence time and with this regard the existing solutions lack general. Having this in mind, this paper develops a general convergence analysis (GCAM) for evolutionary multi-objective optimization algorithm (EMOA). In this approach, two originality aspects come to existence: one associates with the interpolation plane convergence analysis while the second concerns the improved drift analysis of evolutionary algorithm. Firstly, for more than 3-dimensional space, the dimensionality of the Pareto front set becomes reduced to 3 through a locally linear embedding. This overcomes the irregular interpolation plane problem and produce a high-quality interpolation. Secondly, this study originally analyzes the convergence of EMOA by engaging an improved drift analysis. Finally, we determine the first stopping time of EMOA by analyzing the convergence metric. The experimental results demonstrate that the proposed method exhibits better performance in comparison with CAD, CAL, and CAC. Specifically, the error proportion of SMS-EMOA, AR-MOEA, SPEA2+SDE, GFM-MOEA has been decreased by 12%, 15%, 21%, 19% and 17%, respectively. [ABSTRACT FROM AUTHOR]

As a population-based stochastic optimization algorithm, Gravitational Search Algorithm (GSA) has attracted numerous interests and has been applied in various applications. However, GSA has drawbacks such as uneven search and premature convergence in practical applications. This paper specifically explains the inherent characteristic of GSA in prioritizing the center position. Correspondingly, an improvement strategy of fitness normalization with mass shift is proposed, creating a situation where gravity and repulsion are mixed. Then, the global best mechanism with weights is incorporated into the particle's velocity update formula, which compensates for the difficulties in the later exploitation stage. Finally, an empirical formula for the initial gravitational constant related to the size of the solution space is proposed, which enhances the global search ability together with the former strategy. 12 shifted benchmark functions are used to construct 20 optimization problems ranging from 2 to 120 dimensions. The average performance of the proposed algorithm, other GSA and well-known algorithms are compared under the same budget. The results demonstrate that the proposed GSA not only effectively addresses the drawbacks of GSA and maintains good performance, but also exhibits strong competitiveness compared to various similar algorithms. [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]

Aiming at the problem of low data quality caused by the low quality of participants in sparse mobile crowdsensing, a participant's selection optimization algorithm based on the three-way decision is proposed in this paper. Firstly, a similarity matrix is predicted according to the correlation between Spatio-temporal cells, constructing the classification model. Secondly, the historical behavior of participants is analyzed to extract the characteristic information of the target participants for the task. Finally, with the help of the idea of the three-way decision, the high-quality and reliable candidates are selected according to the participant's characteristic information. Then the participants who perform the task are screened under the guidance of the classification model. The experimental results based on real datasets show that the algorithm proposed in this paper can effectively improve the quality of sensing data and reduce the sensing cost. [ABSTRACT FROM AUTHOR]

As one of the main research tasks in software testing, automated test case generation based on path coverage (ATCG-PC) aims to achieve maximum path coverage with a minimized set of test cases. In ATCG-PC, the correlation among the dimensions of test cases is widely utilized in academia to minimize the search efforts of the search-based algorithm. Nevertheless, the information related to target path selection is not utilized, which leads to blind decision-making by the search-based algorithm during the target path selection. Therefore, this paper proposes an enhanced scatter search strategy by using opposition-based learning. An arithmetic optimization algorithm is also proposed to solve ATCG-PC based on the enhanced scatter search strategy, namely, ESSENT. The ESSENT algorithm selects the path with the lowest path entropy among the uncovered paths as the target path, and generates new test cases that cover the target path by modifying the dimensions of the existing test cases. The performance of the ESSENT algorithm is evaluated on six iFogSim subprograms and six Stanford coreNLP subprograms. Experiment results show that the ESSENT algorithm achieves a higher convergence rate than other state-of-the-art algorithms. Furthermore, it enables maximum path coverage with fewer test cases. [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]

Dynamic multi-objective optimization problems (DMOPs) are multi-objective problems that are influenced by dynamically changing environmental parameters. Most current algorithms for solving DMOPs only respond to dynamic changes in the decision space or objective space and also ignore the impact of the type of DMOPs on the algorithm. The changes in the Pareto-optimal solution (POS) and Pareto-optimal front (POF) may affect the type of change in DMOPs. Therefore, this paper proposed an adaptive dynamic multi-objective evolutionary algorithm for type detection (TDA-DMOEA). First, the dynamic detection operator is designed to identify the types of dynamic problems. The Wilcoxon signed-rank test and Hyper Volume (HV) are used to detect the difference of POS and POF in two adjacent environments respectively. Then, different response strategies are designed to cope with different types of changes in DMOP. In particular, a multi-angle-based transfer learning method (MA-TL) with a closed kernel function is derived when faced with simultaneous changes in POS and POF. Finally, a comprehensive study of the commonly used benchmark set of DMOPs is presented, and the proposed algorithm achieves better performance in optimizing DMOPs. [ABSTRACT FROM AUTHOR]

This paper focuses on the assessment of non-complete states in complex task networks and establishes an online capability boundary assessment model based on real-time feature parameters. By utilizing multivariate heterogeneous state features for data mining and pattern recognition, we delve into virtual sample generation technology using an overall diffusion trend approach. This starts by examining the validity of sample data and analyzing the relevance of data acquired within the feature space. Building on this foundation, the overall diffusion trend method is applied to generate virtual sample input that aligns with the sampling distribution characteristics of avionics system equipment. To address non-complete state evaluation in complex task networks, we design a comprehensive model. This model involves constructing a system signal flow block diagram and a structural diagram depicting the available capacity of subsystems and the overall system tasks. The establishment of unknown function relationships in signal connections is achieved through a fusion of neural network and fuzzy logic systems. Finally, an intelligent optimization algorithm is employed to determine system parameters. Utilizing this neuro-fuzzy system in simulation, we attain real-time system responses and evaluate the output regarding the available capacity of system tasks. [ABSTRACT FROM AUTHOR]

The optimization of operating conditions in the polyester polymerization process is crucial for enhancing the quality of the resulting polyester. A novel multi-objective optimization algorithm, named the Interaction Adaptive RVEA (IARVEA), is presented and designed specifically to address the four-objective optimization problem in the polymerization esterification process in this paper. Three strategies are employed to guide the search for optimal solutions and approach the unknown Pareto fronts associated with this problem. Firstly, the maximum mean discrepancy distance is utilized to compare the distribution of the upper and lower solutions, subsequently determining whether an update to the reference vector is necessary. Secondly, the interaction adaptive strategy generates a reference vector based on interactive information from the current and the preceding iteration. Lastly, the projector distance is incorporated into the environment selection operator of IARVEA, which aids in achieving superior convergence properties and greater solution diversity when compared to the conventional RVEA method. Additionally, a comparative analysis is conducted between IARVEA and four other algorithms using seven benchmark test problems and the four-objective optimization problem in the polyester polymerization esterification process. The experimental results demonstrate the superiority of IARVEA over other algorithms in terms of both IGD and HV metrics. Meanwhile, the research findings have important implications for the polyester industry and related fields, offering valuable insights and guidelines for optimizing the operating conditions of the polymerization esterification process. [ABSTRACT FROM AUTHOR]

The Fireworks Algorithm (FWA) represents a relatively new algorithm that has demonstrated its competitiveness among other intelligent optimization algorithms. In most FWA variants, a simple random explosion generates sparks, accompanied by the guiding operator to explore promising search directions. However, this mechanism proves inefficient in exploiting the local landscape and effectively navigating the promising search directions. In this paper, we introduce a novel explosion technique based on orthogonal design (OD), wherein the orthogonal array is leveraged to regulate the distribution of sparks, thus enabling efficient analysis of spark information. Furthermore, we devise a two-stage mechanism for information utilization. In the initial stage, we propose an orthogonal learning (OL) prediction operator to capitalize on local optima by performing factor analysis on both the objective function value and the ranking feature information. Subsequently, in the second stage, an enhanced guiding method is deployed to determine the most promising search direction. The experimental results indicate that the proposed algorithm (OLFWA) showcases competitive performance compared to state-of-the-art FWA variants, various renowned OD-based algorithms, and other promising methods. Moreover, a comprehensive analysis of the effectiveness of each proposed strategy and their interactions has been conducted. [ABSTRACT FROM AUTHOR]

It is of necessity to select appropriate optimization algorithms from an algorithm library due to the universality of constrained multi-objective optimization problems and the suitability of intelligent optimization algorithms, which requires a rich optimization algorithm library. This paper proposes a migration-based method of enriching the algorithm library for constrained multi-objective optimization problems. After calculating the similarity between problems based on their landscape features, the proposed method calculates the migration probabilities of intelligent optimization algorithms solving similar problems based on the performance of each algorithm and the similarity between problems. According to the redundancy and compatibility of components, the algorithms with large migration probabilities enrich the algorithm library for solving the current problem. Based on the enhanced algorithm library, a Softmax regression model is trained to generate an optimal intelligent algorithm to solve the current problem. The proposed method is applied to solve a series of constrained multi-objective optimization benchmark problems and the operation optimization problems of an integrated coal mine energy system, and the experimental results verify its effectiveness and feasibility. • A method based on landscape features is proposed to determine similar problems. • A method is given to select migrated algorithms based on similarity and performance. • A method based on redundancy and compatibility is presented to enrich an IOAL. [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]

• A novel CHT is proposed based on Pareto dominance-based ranking and CDP-based ranking. • A search algorithm based on four mutation operators is proposed. • A new constrained multiobjective differential evolution algorithm is proposed. The tradeoff between objective functions and constraints is a key issue that needs to be addressed by constrained multiobjective optimization algorithms, and constraint handling techniques (CHTs) are an important technique for balancing objective functions and constraints. In this paper, a novel CHT that fuses two rankings is proposed. Specifically, each individual is assigned two rankings: one ranking calculated based on Pareto dominance (regardless of constraints) and another calculated based on the constrained dominance principle (CDP). The fitness value of an individual is the weighted sum of these two rankings, and the weight is related to the generation number and the proportion of feasible solutions in the current generation. Based on the proposed CHT, a constrained multiobjective differential evolution algorithm is proposed. To generate high-quality offspring, the proposed constrained multiobjective differential evolution algorithm combines four mutation operations as core components of the search algorithm. The proposed algorithm is compared with eight state-of-the-art algorithms in experiments with five test suites, and the experimental results show that the proposed algorithm performs significantly better than the eight state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

More and more studies have demonstrated that circRNAs can be used as markers of various diseases due to their inherent stability. Numerous computational methods, especially artificial intelligence approaches, have been applied to the prediction of circRNA-disease associations. However, the objective functions of these prediction methods are usually single and standard. The single objective function hardly reflects the characteristics of the prediction problem, and leads to low prediction accuracy. There has never been a method to design a set of objective functions for the circRNA-disease prediction problem and solve it by using intelligent optimization algorithms. In this paper, a method ICDMOE is proposed to identify circRNA-disease associations via a multi-objective evolutionary algorithm. A solution space is defined and four objective functions are designed based on matrix factorization and modularity of similarity networks. An improved decomposition-based multi-objective evolutionary algorithm (MOEA/D) is also employed to solve these objective functions. In the MOEA/D, an adaptive penalty-based boundary intersection strategy is proposed, which not only ensures convergence, but also guarantees the diversity of solutions in the Pareto front. Finally, the experimental results show that ICDMOE has better performance than pure matrix factorization-based methods, non-adaptive MOEA/D-based methods and other prediction methods. Furthermore, we find that the predicted disease-circRNAs can be confirmed by existing studies, miRNA regulations and expression profiles, etc. These indicate that ICDMOE can provide good candidates for biomedical experiments. [ABSTRACT FROM AUTHOR]

The distribution characteristic of populations is one of the main characteristics of population. The pattern of distribution characteristics determines the probability law of individual values. At the same time, the initialization of the population lays a foundation for the iterative process of the swarm intelligence optimization algorithm. To reveal the influence of population distribution characteristics on the swarm intelligence optimization algorithm, this paper proposes a variety of search strategies based on the populations with different distribution characteristics and analyzes the influence of population distribution characteristics on optimization process by comparing the test results of the optimization algorithm after implementing these strategies. First, a new population generator is designed that can transform the same initial population into a population with uniform and central peaking distributions. On this basis, the two kinds of populations are applied to the global and local search stages of the optimization process, and four different search strategies are formed. Among them, the global and local search strategies based on a uniformly distributed population are the traditional methods. Finally, the performance of the optimization algorithm using different search strategies is evaluated through 29 test problems from the CEC2017 benchmark for 10, 30, 50 and 100 dimensions. In addition, the algorithms are applied to solve the TSP problem. For CEC2017 in 100D, only 13 of the 29 test functions achieve the best optimization effect by using the traditional method, while the other 16 test functions achieve better search results by using the other three search strategies. The analysis shows that the population distribution characteristics have a great influence on the population optimization algorithm. The performance of the algorithm with different population distribution combination strategies is statistically superior to the traditional algorithm with a uniform distribution population, as revealed in the test functions ranging from 38.7% to 62.9% for different dimensions. By reconstructing populations with different distribution characteristics, the overall efficiency of the swarm intelligence optimization algorithm can be greatly improved. [ABSTRACT FROM AUTHOR]

• The algorithm named AMSMO is proposed for high-dimensional and computationally expensive problems. • The real-time auto-selection of kernels approach for building the most promising RBF is proposed. • The new distance- and objective-based criterion is proposed for the global search. • The dynamic search criterion is used to make the algorithm explore at the early search stage and exploit at the final stage. • A cluster-based restart criterion that aims at refining the training data for surrogate models is proposed. Surrogate-assisted evolutionary algorithms (SAEAs) have been widely used for solving computationally expensive optimization problems. However, the performance of SAEAs deteriorates drastically for high-dimensional problems since the accuracy of surrogates may decrease to an insupportably low level in high dimensions which profoundly affect subsequent evolution optimization. To overcome this issue, this paper proposes an adaptive multi-surrogate and module-based optimization algorithm named AMSMO. Unlike existing algorithms that adopt sole surrogate models, AMSMO develops a real-time autoselection of kernels approach for building the most promising RBF. AMSMO makes use of five modules to promote the optimization quality, including: a. global search module; b. local search module; c. semi-local search module; d. convergence module; e. restart module. Specifically, we provide a novel distance- and objective-value-based criterion for global search. The semi-local search module applies a dynamic search criterion that makes the algorithm explore at the early search stage and exploit at the final stage. A cluster-based restart criterion is proposed to address the stagnation of optimization. Several benchmark functions with dimensions varying from 30 to 100 and computationally intensive practical simulation–optimization problems are adopted to validate the proposed algorithm. The empirical experiments demonstrate that the proposed algorithm outperforms other state-of-the-art algorithms in most cases. [ABSTRACT FROM AUTHOR]

Evolutionary Algorithm is a mature global optimization method with high robustness and wide applicability. It can effectively address complex problems that are difficult to be solved by traditional optimization algorithms. In evolution, it is still uncertain which gene parent can produce offspring through competition and eventually become an excellent individual of the last generation population. Inspired by the fact that gene sequencing can discover biological gene defects, this paper proposes a dynamic multi-objective evolutionary algorithm based on gene sequencing and gene editing (GSGE). The gene sequencing algorithm is designed using support vector machine (SVM), and correlation coefficient, as the result of sequencing, has also been verified. Combining stratified sampling and multi-population strategy, a prediction strategy that can use all chromosome information is designed. The new gene editing strategy edits individual genes to optimize the Pareto optimal front (PF) distribution, for the first time different types of genes can match different optimization strategies, which greatly improves the distribution of the population without affecting the convergence. The comparison experiment between GSGE and the state of the art algorithms is performed on 25 test functions and the Pareto optimal set (PS) curves obtained by dimension reduction fully demonstrate the significant advantages of GSGE. • Gene sequencing using support vector machine was designed for gene classification. • A prediction strategy that can use all chromosome information is designed. • A novel gene editing strategy was designed to achieve direct assign values to genes. [ABSTRACT FROM AUTHOR]

As a rule-based expert system, good interpretability is one of the prominent advantages and characteristics of the belief rule base (BRB) system, and consistency is one of the important indicators of interpretability. However, the modeling of the BRB system in current research and applications usually focuses only on accuracy but ignores rule consistency. In this paper, the concept and connotation of consistency in the BRB system are first discussed. On this basis, a dynamic measurement formula of rule consistency is designed to determine whether a pair of rules is consistent and thus identify inconsistent rules. Then, an optimization process of inconsistent rules is proposed, in which expert experience or optimization algorithms can be utilized as the optimization tool. In particular, a conflict degree-based sorting method is presented to determine the optimization sequence of inconsistent rules. The proposed measurement and optimization process of rule consistency in the BRB system is validated by two cases, namely, pipeline leakage detection and remaining useful life estimation. The experimental results show that the process can effectively identify and eliminate inconsistencies in the BRB system and further ensures the effectiveness and interpretability of BRB systems in practical applications. • Illustrate the concept of rule consistency in the BRB system. • Propose a dynamic measurement formula of rule consistency under different criteria. • Calculate similarity of premise parts and similarity of conclusion parts by three measures. • Propose a conflict degree-based method to determine the inconsistent rules optimization order. [ABSTRACT FROM AUTHOR]

Graph data are widely available in complex network systems. Numerous community detection algorithms have been investigated to study graph problems wherein the network topology offers abundant behavioral and functional information. In real scenarios, networks are extremely susceptible to external perturbations, primarily because of sparse topological information. Consequently, maintaining robust community detection performance when confronted with intricate network attacks or perturbations is challenging. Previous anti-graph perturbation methods have typically been adjusted to specific perturbation types, leading to the degradation or failure of these defences when confronted with other types of attack. Accordingly, a unified robust framework that leverages extreme adversarial attacks is proposed in this paper. Specifically, a novel graph perturbation module is introduced into the model to generate extreme undirected or directed perturbations through dynamic updating; this ensures that the model can fit the attacked network well. The proposed framework derives a unified perturbation formulation capable of simultaneously attacking symmetric and asymmetric networks. Furthermore, this framework can be applied to many existing non-negative matrix factorization-based community detection methods. Extensive experiments on artificial and real-world networks demonstrate that the proposed framework significantly improves the robustness of detection tasks, particularly in noisy networks. • A unified robust network embedding framework is proposed for CD to enhance the robustness against structural perturbations. • Two versions of the proposed NMF-based model are proposed for the directed and undirected graph data. • An efficient optimization algorithm is devised to construct network perturbation matrices for the extreme global attacks. [ABSTRACT FROM AUTHOR]

To improve the utilization of infrastructure resources and reduce the cost of operators in the future 6G network construction, a 6G shared base stations optimization model is proposed in this paper, which is a bi-level multiobjective optimization problem (BLMOP). In such a BLMOP, the tower company is responsible for the construction of base stations at the upper level, while operators share the base station resources of the tower company at the lower level. In addition, we also propose two strategies to solve the optimization efficiently. First, we use surrogate models to fit lower-level Pareto fronts (PF), then the degree of lower-level optimality constraint violation is converted to distance between the candidate solutions and the approximate lower level PF. So the BLMOP is transformed to a single-level constrained multi-objective optimization problem. Second, to accelerate the current lower-level optimization, we migrate the modified population from the adjacent lower-level optimization tasks. These two strategies effectively reduce the computational overhead. Compared with three existing works, the proposed method has achieved the best or comparable results on 7 benchmark problems and 5 generated test instances with less computation overhead, whose efficiency has been confirmed. [ABSTRACT FROM AUTHOR]

Distributed optimization has a wide variety of applications, such as economic dispatch in power systems, social welfare maximization, optimal power flow, where distributed nodes work cooperatively to achieve a minimized global objective function, where the information exchanges among distributed and networked nodes play an important role. However, such information exchanges often suffer from inevitable energy and bandwidth constraints due mainly to their distributed and networked nature. Event-triggered distributed optimization provides an effective means to address this issue. However, designing an event-triggered distributed optimization algorithm with both fast convergence and resource efficiency is challenging. In this paper, a distributed zero-gradient-sum algorithm with a dynamic event-triggered scheme is presented for distributed discrete-time optimization. The triggering threshold is composed of an exponential decaying term and a positive dynamic auxiliary variable. The linear convergence is established theoretically. Finally, this algorithm is applied to an economic dispatch problem to verify the theoretical findings and to demonstrate the effectiveness and superiority of the proposed algorithm. • A discrete-time optimization algorithm is designed based on the dynamic ETS and ZGS. • The proposed algorithm is proved to linearly converge to the global minimizer. • The more efficient communication is proved in theory and verified by simulation. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicles (UAVs) searching for a moving target is a complex search optimization problem that aims to find a path with maximum probability of observing the target. However, as the area where the target may be located increases in size, existing methods tend to cause easy entrapment into local optima, resulting in poor performance. Hence, we propose a Convex Combination Multiple Populations Competitive Swarm Optimization algorithm (CDCSO) in this paper. First, we suggest applying the multiple population strategy to enhance the search ability of the algorithm. The population of interest is divided into two subgroups that each conduct the CSO. Second, we propose a novel convex combination update strategy to coordinate the two subgroups to search jointly for the global optimal solution. At each iteration, this strategy allows the two subgroups to compete and learn from each other, which prevents the population from falling into the local optimum. We then designed new scenarios containing 3 to 6 probability areas to investigate the performance of our proposed algorithm in multiple and complex scenarios. Results: To demonstrate the effectiveness and stability of the proposed algorithm, we compared it with several swarm optimization algorithms from different perspectives. Experimental results showed that the proposed algorithm has superior performance in following and intercepting a high-probability area. To further demonstrate the generality of the convex combination update strategy, we evaluated the strategy in several developed particle swarm optimization algorithms. The results demonstrated that the convex combination update strategy can be integrated into other algorithms to better address the moving target search problem. [ABSTRACT FROM AUTHOR]

In this paper, a feature selection (FS) method is proposed to identify key quality features (KQFs) in complex manufacturing processes. We propose a multi-objective binary particle swarm optimization algorithm, called MPBPSO, with three new components to optimize a bi-objective FS model of maximizing the geometric mean (GM) measure and minimizing the number of selected features. First, MPBPSO uses a modified probability-based solution update (PSU) mechanism which utilizes a flipping vector to update particles. A mutation operator with three basic operations, i.e., add, eliminate, and interchange, is also utilized in MPBPSO to improve the exploration performance. Second, a strategy combining the Pareto dominance concept with a distance measure is proposed for MPBPSO to update p b e s t (personal best position). Finally, a selection strategy based on the roulette wheel selection is proposed to determine the g b e s t (global best position) from the non-dominated set during iterations. The experimental results on four datasets have shown that the proposed FS method can identify a small number of KQFs that have good predictive ability for product quality. Further analysis indicates that MPBPSO obtains better search performance than eight benchmark optimization algorithms and the new components in MPBPSO are effective for improving its search performance. • Quality feature selection is addressed by a multi-objective optimization model. • A multi-objective binary PSO algorithm is proposed for the model. • Probability-based mechanism is combined with mutation for updating solutions. • New pbest update and gbest selection strategies are proposed. • Experiments verify the effectiveness of the model and optimization algorithm. [ABSTRACT FROM AUTHOR]

Protein structure prediction (PSP) from its primary sequence is a challenging task in computational biology. PSP is an optimization problem that determines the stable or native structure with minimum free energy. Several researchers have applied various heuristic algorithms and/or their variants to solve this problem. However, the mechanism to select a particular algorithm is not known a priori. Fitness landscape analysis (FLA) is a technique to determine the characteristics of a problem or its structural features based on which the most appropriate algorithm can be recommended for solving the problem. The aim of this study is two-fold while considering the PSP problem. Firstly, the structural features are determined by using the standard FLA techniques and secondly, the performance of some of the well-known optimization algorithms are analyzed based on the structural features as an illustration of the usefulness of the former research agenda. In this paper, we determine structural features of the PSP problem by analyzing the landscapes generated by using the quasi-random sampling technique and city block distance. Comprehensive simulations are carried out on both artificial and real protein sequences in 2D and 3D AB off-lattice model. Numerical results indicate that the complexity of the PSP problem increases with protein sequence length. We calculate the Pearson correlation coefficient between the FLA measures, separately for 2D and 3D off-lattice model and significant differences are identified among the measures. Six well-known real-coded optimization algorithms are evaluated over the same set of protein sequences and the performances are subsequently analyzed based on the structural features. Finally, we suggest the most appropriate algorithms for solving different classes of PSP problem. [ABSTRACT FROM AUTHOR]

The paper presents a novel paradigm of the original particle swarm concept, based on the idea of having two types of agents in the swarm; the “explorers” and the “settlers”, that could dynamically exchange their role in the search process. The explorers’ task is to continuously explore the search domain, while the settlers set out to refine the search in a promising region currently found by the swarm. To obtain this particle task differentiation, the numerical coefficients of the cognitive and social component of the stochastic acceleration as well as the inertia weight were related to the distance of each particle from the best position found so far by the swarm, each of them with a proper distribution over the swarm. This particle task differentiation enhances the local search ability of the particles closer to gbest and improves the exploration ability of the particles as the distance from gbest increases. The originality of this approach is based on the particle task differentiation and on the dynamical adjustment of the particle velocities at each time step on the basis of the current distance of each particle from the best position discovered so far by the swarm. To ascertain the effectiveness of the proposed variant of the PSO algorithm, several benchmark test functions, both unimodal and multi-modal, have been considered and, thanks to its task differentiation concept and adaptive behavior feature, the algorithm has demonstrated a surprising effectiveness and accuracy in identifying the optimal solution. [ABSTRACT FROM AUTHOR]