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Surrogate-assisted multi-objective evolutionary algorithms have been paid much attention to solve expensive multi-objective problems in recent years. However, with the number of objectives increasing, an improper solution may be picked for expensive objective evaluation due to the accumulation error of approximated values on objective functions. Furthermore, the time to construct surrogate models for all objectives will significantly increase. Thus, in this paper, Gaussian process (GP) models are proposed for performance indicators instead of for objective functions. Furthermore, solutions are selected from either of two ways to be evaluated using the expensive objective function. When there are non-dominated solutions found so far that are approximated, they will be exactly evaluated using the objective function. Otherwise, the solution with the maximum approximation uncertainty among the current population will be evaluated using the real objective functions. The efficiency of the presented approach is validated on the DTLZ test suite with 3, 6, 10, 15, and 20 objectives, MaF benchmark problems with 3, 6, 10, 15, and 20 objectives, and a real-world optimization problem called filter design. The experimental results show that the method proposed in this paper is competitive compared to recently proposed peer algorithms for expensive many-objective problems. [ABSTRACT FROM AUTHOR]

Surrogate-assisted evolutionary algorithms (SAEAs) with prescreening model management strategies show great potential in handling expensive optimization problems (EOPs). However, their performance is highly dependent on the search strategy and surrogate model. This paper proposes an evolutionary algorithm called IDRCEA, which utilizes an individual-distribution search strategy (IDS) and a regression-classification-based prescreening mechanism (RCP) to improve the ability to solve various complex and high-dimensional EOPs. Specifically, IDRCEA first combines an individual-based search strategy and a distribution-based search strategy to enrich offspring generation. Then, a regression model and a classification model are cooperatively used to prescreen the high-level offspring. Finally, both performance-based and distribution-based infill criteria are utilized to determine the most promising offspring from the high-level group for expensive evaluation. Experimental results validate the advantages of IDRCEA over some state-of-the-art SAEAs on many complex benchmark problems and an oil reservoir production optimization problem. • Individual-based and distribution-based search strategies are used to enrich offspring generation. • Regression and classification models are cooperatively employed to pre-screen the high-level offspring. • Performance-based and distribution-based infill criteria are adopted to choose the final offspring for function evaluation. [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]

In a multi-objective particle swarm optimization (MOPSO), the selection strategies of the personal best solution (pBest) for a single particle and the global best solution (gBest) for the whole swarm are two key challenges to balance the convergence and diversity of an algorithm during its iterative process. Many selection strategies in the existing literatures were emphasized on the individual characteristics of the separate particles rather than the collective features of the whole swarm. In this paper, a novel gBest selection strategy based on a new defined virtual generational distance indicator, which is calculated from a virtual Pareto front fabricated according to the geometry of a given elite archive, is proposed for selecting the most appropriate Pareto optimal solution as the gBest with respect to the comprehensive convergence and diversity contribution to improve the search effectiveness and efficiency of a MOPSO. Besides, an adaptive pBest selection strategy based on the evolutionary state in different iterations is designed for identifying the more suitable pBest from its personal archive for each particle to strengthen the exploitation or exploration ability adaptively. The experimental results show that a MOPSO with the new gBest and pBest selection strategies outperforms ten state-of-the-art competitive algorithms on DTLZ, F, WFG and ZDT series of benchmark problems. In addition, a case study on the site selection for mobile earthquake monitoring stations is also illustrated the effectiveness of the proposed algorithm in the real-world application. [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]

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

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

Many fitness evaluations are often needed for large-scale evolutionary optimization to find the optimal solution. Therefore, evolutionary algorithms are impeded to solve computationally expensive problems. Surrogate assisted evolutionary algorithms (SAEAs) have been shown to have good capability in a finite computational budget. However, not many SAEAs, have been proposed for large-scale expensive problems. The main reason is that a proper surrogate model is challenging to be trained due to the curse of dimension. In this paper, we propose to employ the random grouping technique to divide a large-scale optimization problem into several low-dimensional sub-problems. Then a surrogate ensemble is trained for each sub-problem to assist the sub-problem optimization. The next parent population for large-scale optimization will be generated by the horizontal composition of the populations for sub-problem optimization. Furthermore, the best solution found so far for the sub-problem with the best population mean fitness value will be used to replace the best solution found so far for the large-scale problem on its corresponding dimensions, and the new solution will be evaluated using the expensive objective function. The experimental results on CEC'2013 benchmark problems show that the proposed method is effective and efficient for solving large-scale expensive optimization problems. [ABSTRACT FROM AUTHOR]

Tree-based ensemble algorithms (TEAs) have had a transformative impact in various fields. However, when they are applied to real-time critical problems such as medical analysis, existing TEAs fall short of two-fold issues. The first is the trade-off among model interpretability, accuracy, and explainability. Second, traditional TEAs perform dramatically worse when the number of contributing features to model accuracy is small in comparison to the total number of features. We address the aforementioned issues in this paper and propose a novel "eXplainable Reasonably Randomised Forest" (XRRF) algorithm. The XRRF consists of four conclusive steps: learning performance, intrinsic interpretability, model accuracy, and explainability. The proposed forest algorithm is evaluated on three real-world problems (medical analysis, business analysis, and employee churn), a hybrid artificial dataset, and twenty multidisciplinary benchmark problems with varying characteristics. The experimental results demonstrate that the XRRF outperforms the six mainstream and two cutting-edge black-box and white-box algorithms, respectively. [ABSTRACT FROM AUTHOR]

It is a challenge to balance the convergence and the diversity in multi-objective optimization problems. In this paper, a new two-stage based evolutionary algorithm (MOEA/TS) is proposed, where the convergence and the diversity are handled in two independent phases. In the first stage, the convergence is accelerated by using the gradient information of constrained sub-problems. In the second stage, the diversity is improved by adopting the dominance based multi-objective evolutionary algorithm. The comparative experiments are presented in terms of two performance indicators for benchmark test problems. The results indicates that MOEA/TS has the competitive performance. [ABSTRACT FROM AUTHOR]

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

Pareto dominance-based multi-objective evolutionary algorithms (PDMOEAs) encounter scalability issues due to the lack of selection pressure as the dimensionality of objective space increases. In addition, PDMOEAs combat difficulties in achieving the proper balance between convergence and diversity. To overcome this issue, recently, additional convergence-related metrics have been proposed for PDMOEAs to improve their performance by enhancing the selection pressure towards the true Pareto front; however, these approaches have limitations. To address the drawbacks of the previous approaches, in this paper, we propose an adaptive neighborhood based evolutionary algorithm with pivot-solution based selection (Pi-MOEA) to tackle multi- and many-objective optimization problems. The proposed Pi-MOEA approach identifies a set of pivot-solutions to improve the convergence performance. An adaptive neighborhood is designed among the individuals, and the average ranking method is employed to identify the pivot-solutions within the neighborhood. In addition, to preserve the population diversity, density estimation based on Euclidean distance is adopted in Pi-MOEA. The performance of the Pi-MOEA is investigated extensively on 26 test problems from three popular benchmark problem suites by comparing them with seven state-of-the-art algorithms. The experimental results show that the Pi-MOEA algorithm performs considerably better when compared with state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Surrogate models are widely used to model the high computational cost problems such as industrial simulation or engineering optimization when the size of sampled data for modeling is greatly limited. They can significantly improve the efficiency of complex calculations by modeling original expensive problems with simpler computation-saving functions. However, a single surrogate model cannot always perform well for various problems. On this occasion, hybrid surrogate models are created to improve the final performances on different problems by combining advantages of multiple single models. Nevertheless, existing hybrid methods work by estimating weights for all alternative single models, which limits the efficiency when more single models are adopted. In this paper, we propose a novel hybrid surrogate model quite different from former methods, named the Deep Residual Surrogate model (DRS). DRS does not merge all alternative single surrogate models directly by weights, but by assembling selected ones in a multiple layers structure. We propose first derivate validation (FDV) to recurrently select the single surrogate model adopted in each layer from all candidates. Experimental results on multiple benchmark problems demonstrate that DRS has better performances than existing single and hybrid surrogate models in both prediction accuracy and stability with higher efficiency. [ABSTRACT FROM AUTHOR]

In this paper, a novel approach to the self-organization of hierarchical prototype-based classifiers from data is proposed. The approach recursively partitions the data at multiple levels of granularity into shape-free clusters of different sizes, resembling Voronoi tessellation, and naturally aggregates the resulting cluster medoids into a multi-layered prototype-based structure according to their descriptive abilities. Different from conventional classification models, it is nonparametric and entirely data-driven, and the learned model can offer a high-level of transparency and interpretability thanks to the underlying prototype-based nature. The system identification process underpinning the approach is driven by the aim of separating data samples of different classes into nonoverlapping multi-granular clusters. Its associated decision-making process follows the "nearest prototype" principle and hence, the rationales of the subsequent decisions made can be explicitly explained. Experimental studies based on popular benchmark classification problems, as well as on a practical application to remote sensing image classification, demonstrate the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

More training instances could lead to better classification accuracy. However, accuracy could also degrade if more training instances mean further noises and outliers. Additional training instances arguably need additional computational resources in future data mining operations. Instance selection algorithms identify subsets of training instances that could desirably increase accuracy or at least do not decrease accuracy significantly. There exist many instance selection algorithms, but no single algorithm, in general, dominates the others. Moreover, existing instance selection algorithms do not allow direct controlling of the instance selection rate. In this paper, we present a simple and generic cluster-oriented instance selection algorithm for classification problems. Our proposed algorithm runs an unsupervised K Means Clustering algorithm on the training instances and with a given selection rate, selects instances from the centers and the borders of the clusters. On 24 benchmark classification problems, when very similar percentages of instances are selected by various instance selection algorithms, K Nearest Neighbours classifiers achieve more than 2%–3% better accuracy when using instances selected by our proposed method than when using those selected by other state-of-the-art generic instance selection 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]

Few-Shot Class-Incremental Learning (FSCIL)presents an extension of the Class Incremental Learning (CIL)problem where a model is faced with the problem of data scarcity while addressing the Catastrophic Forgetting (CF)problem. This problem remains an open problem because all recent works are built upon the Convolutional Neural Networks (CNNs)performing sub-optimally compared to the transformer approaches. Our paper presents Robust Transformer Approach (ROBUSTA)built upon the Compact Convolutional Transformer (CCT). The issue of overfitting due to few samples is overcome with the notion of the stochastic classifier, where the classifier's weights are sampled from a distribution with mean and variance vectors, thus increasing the likelihood of correct classifications, and the batch-norm layer to stabilize the training process. The issue of CFis dealt with the idea of delta parameters, small task-specific trainable parameters while keeping the backbone networks frozen. A non-parametric approach is developed to infer the delta parameters for the model's predictions. The prototype rectification approach is applied to avoid biased prototype calculations due to the issue of data scarcity. The advantage of ROBUSTAis demonstrated through a series of experiments in the benchmark problems where it is capable of outperforming prior arts with big margins without any data augmentation protocols. [ABSTRACT FROM AUTHOR]

The hardly dominated boundary (HDB) is a common feature of multi-objective optimization problems (MOPs). Previous studies have proposed several multi-objective evolutionary algorithms (MOEAs) to deal with the problem characterized by HDBs. Nevertheless, these methods lack consideration of the evolutionary status, potentially resulting in low efficiency when addressing problems that entail a confluence of HDB and other intricate characteristics. This paper proposes an MOEA with evolutionary-status-driven environmental selection (MOEA-ESD) to address such an issue. Specifically, in each generation, the current and historical information are used to evaluate the evolutionary status. Based on the estimated evolutionary status, the proposed MOEA-ESD algorithm adaptively uses three types of environmental selection: the traditional environmental selection (TES) based on Pareto-dominance and crowding distance, a convergence-first environmental selection (CFES) based on Gaussian mixture model clustering, and a diversity-first environmental selection (DFES) based on outlier detection and extreme solutions. In this way, inferior solutions situated on the HDB can be effectively eliminated, thereby facilitating the convergence of the population while concurrently preserving a commendable degree of diversity. Moreover, a set of new benchmark problems with different objective magnitudes and complicated Pareto sets is developed to enrich the features of HDB-MOPs and to verify the algorithm's performance. Our experimental results on 22 HDB-MOPs show the promising performance of the proposed algorithm. The source code of MOEA-ESD is available at https://github.com/CIAM-Group/EvolutionaryAlgorithm_Codes/tree/main/MOEA-ESD. [ABSTRACT FROM AUTHOR]

• A novel evolutionary multiobjective multi-tasking algorithm MS-MOMFEA is proposed. • Cross-dimensional search is introduced to accelerate the convergence. • Prediction-based search is proposed to facilitate knowledge transfer. • MS-MOMFEA is efficient at solving various multi-factorial optimization problems. Transfer learning is an important research topic in machine learning and recently has been introduced into evolutionary computation to form evolutionary multi-task optimization (EMTO). EMTO focuses on tackling multiple optimization tasks simultaneously based on knowledge transfer and reuse. Many EMTO algorithms have been proposed mainly for single-objective optimization problems and achieved success in various fields, yet multi-objective EMTO remains a big challenge. The existing multi-objective EMTO algorithms tend to suffer from issues like slow convergence and degraded performance on less correlated tasks. To alleviate these issues, this paper proposes a new multi-objective EMTO algorithm by introducing cross-dimensional variable search and prediction-based individual search for efficient knowledge transfer. The cross-dimensional variable search optimizes a decision variable using information collected from other variables. The prediction-based individual search performs individual mapping where the offspring solutions and the corresponding parent solutions are symmetrized about the predicted population center to maintain the population diversity. The proposed algorithm is tested on benchmark problems and the experimental results demonstrate the effectiveness and efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

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

Dynamic multi-objective optimization problems (DMOPs), in which the environments change over time, have attracted many researchers' attention in recent years. Since the Pareto set (PS) or the Pareto front (PF) can change over time, how to track the movement of the PS or PF is a challenging problem in DMOPs. Over the past few years, lots of methods have been proposed, and the prediction based strategy has been considered the most effective way to track the new PS. However, the performance of most existing prediction strategies depends greatly on the quantity and quality of the historical information and will deteriorate due to non-linear changes, leading to poor results. In this paper, we propose a new prediction method, named MOEA/D-GMM, which incorporates the Gaussian Mixture Model (GMM) into the MOEA/D framework for the prediction of the new PS when changes occur. Since GMM is a powerful non-linear model to accurately fit various data distributions, it can effectively generate solutions with better quality according to the distributions. In the proposed algorithm, a change type detection strategy is first designed to estimate an approximate PS according to different change types. Then, GMM is employed to make a more accurate prediction by training it with the approximate PS. To overcome the shortcoming of a lack of training solutions for GMM, the Empirical Cumulative Distribution Function (ECDF) method is used to resample more training solutions before GMM training. Experimental results on various benchmark test problems and a classical real-world problem show that, compared with some state-of-the-art dynamic optimization algorithms, MOEA/D-GMM outperforms others in most cases. [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]

Multimodal multi-objective optimization problems (MMOPs) involve locating equivalent Pareto optimal solutions in decision space with the same objective values. The key to handling MMOPs is finding all equivalent Pareto optimal solutions and maintaining a promising balance between the convergence and diversity of solutions in both decision space and objective space. To tackle this issue, a self-organizing quantum-inspired particle swarm optimization algorithm (MMO_SO_QPSO) is proposed in this paper for handling MMOPs. In the proposed MMO_SO_QPSO, a self-organizing map is used to find the best neighbor leader of particles. With the aid of neighbor leader particles, a special zone searching method is adopted to update the position of particles and locate equivalent Pareto optimal solutions in decision space. To maintain diversity and convergence of Pareto optimal solutions, a special archive mechanism that relies on the maximum-minimum distance among solutions is introduced into MMO_SO_QPSO. And some outstanding Pareto optimal solutions are maintained in the special archive. In addition, a new performance indicator is developed to estimate properly the similarity between obtained Pareto optimal solutions and true Pareto optimal solutions. The performance of the proposed MMO_SO_QPSO is compared with six state-of-the-art multimodal multi-objective evolutionary algorithms on two well-known benchmark problems. Experimental results demonstrate the superior performance of MMO_SO_QPSO for solving MMOPs. The effectiveness of several strategies is also discussed. [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]

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

• The 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]

Prototype-based approaches generally provide better explainability and are widely used for classification. However, the majority of them suffer from system obesity and lack transparency on complex problems. In this paper, a novel classification approach with a multi-layered system structure self-organized from data is proposed. This approach is able to identify local peaks of multi-modal density derived from static data and filter out more representative ones at multiple levels of granularity acting as prototypes. These prototypes are then optimized to their locally optimal positions in the data space and arranged in layers with meaningful dense links in-between to form pyramidal hierarchies based on the respective levels of granularity accordingly. After being primed offline, the constructed classification model is capable of self-developing continuously from streaming data to self-expend its knowledge base. The proposed approach offers higher transparency and is convenient for visualization thanks to the hierarchical nested architecture. Its system identification process is objective, data-driven and free from prior assumptions on data generation model with user- and problem- specific parameters. Its decision-making process follows the "nearest prototype" principle, and is highly explainable and traceable. Numerical examples on a wide range of benchmark problems demonstrate its high performance. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a human behavior learning approach for nonlinear systems control. We use several cognitive models and human skills to model and accelerate the learning process. A neural reinforcement learning algorithm is applied as main cognitive model. A persistent exciting signal and experience replay methods are proposed to improve learning accuracy and overcome the sensitivity problem of the human actions. The stability and convergence of the neural network based reinforcement learning is discussed. Simulations results verify the approach with two benchmark control problems. [ABSTRACT FROM AUTHOR]

In the past decades, automated theorem proving (ATP) for first-order logic has made good progress, in which binary resolution inference rule plays a crucial role. However, as shown in the latest benchmark library of the ATP system, there are still many practical problems that have not been resolved or cannot be effectively resolved. Recently, in order to overcome the limitations of ATP based on binary resolution inference rules, a novel multi-clause dynamic standard contradiction separation (S-CS) inference rule and its automated deduction theory have been proposed. Based on this theory, this paper first clarifies the generality of this S-CS rule by comparing it with some well-known variants of the binary resolution rule, and then focuses on how to design a specific and effective algorithm along with search strategies to realize the S-CS based deductive theory with its implementation. Specifically, the present work proposes a novel S-CS dynamic deduction algorithm (in short SDDA) based on different strategies and summarizes its implementation procedures. In addition, we focus on evaluating whether SDDA, as a novel perspective multi-clause dynamic automatic deduction algorithm, can be applied on top of the current leading ATP system architectures to further improve their performances. Therefore, SDDA is applied to the current leading first-order ATP systems, i.e., Vampire and E, respectively forming two integrated APT systems, denoted as SDDA_V and SDDA_E. Then the capabilities of SDDA_V and SDDA_E are evaluated on the latest benchmark database TPTP, such as the CASC-J9 problems (FOF division) as well as the hard problems with a rating of 1 in the TPTP benchmark database. The experimental results show the effectiveness of SDDA: SDDA_V outperforms Vampire itself, and SDDA_E, outperforms E itself, and the two improved ATP systems have solved a number of hard problems with the rating of 1 in TPTP, that is, some problems in the latest benchmark database TPTP which have not yet been solved by other current first-order ATP systems. [ABSTRACT FROM AUTHOR]

This paper presents sufficient stability conditions for distributed prediction-based control of interconnected systems subject to network-induced time-varying delay. Due to the flexibility of the proposed criteria, continuous-time, sampled-data control and output-feedback problems can be handled by the same framework. A detuning procedure is combined with a distributed LQR design in order to ensure the closed-loop stability for a given network-induced delay bound. If compared with related works, the proposed framework can be applied to obtain the time-varying delay bound derived from distinct combinations of distributed dead-time compensation strategies with stabilizing control laws. Two simulation case studies based on a benchmark problem and the level control of a irrigation canal are presented to illustrate the usefulness of the proposed framework. [ABSTRACT FROM AUTHOR]

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

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

• Multiple features are strategically implemented in MOCI to enhance its capability. • Dual stopping criteria implemented to assess performance of all the algorithms in stringent manner. • Performance is assessed over 8 algorithms, 5 benchmark test suite, 7 real problems with 3 metrics. • Framework for exploratory analysis of performance metrics is proposed. • MOCI performance is statistically validated and verified. In the recent days, several novel and specialized algorithms are coming up for solving particular class of problems. However, their performance on new benchmark or real-world problem remains unsure. This paper proposes a novel Multiobjective Cohort Intelligence (MOCI) algorithm. It is based on Pareto dominance and coevolutionary design principles to achieve efficient, effective, productive and robust performance. The capability of MOCI algorithm is enhanced through use of multiple features for balance of exploration versus exploitation, search towards promising region and avoidance of search stagnation. The performance of MOCI is assessed against the state-of-the-art algorithms, such as: ARMOEA, CMOPSO, hpaEA, LMOCSO, LSMOF, NMPSO and WOFSMPSO across multiple test suites including Classical, ZDT, DTLZ, WFG and UF. The performance assessment is conducted with truly uncorrelated performance metrics. In this regard, an exploratory approach of multiple correlation analysis is proposed. Performance of MOCI algorithm is statistically verified and validated using PROMETHEE-II and nonparametric statistical tests. MOCI is capable of achieving well converged and diversified solutions on most of the test as well as real world problems. The success of MOCI is attributed to multiple features incorporated in the algorithm. In the future, MOCI could be applied to challenging problems in engineering and management. [ABSTRACT FROM AUTHOR]

Artificial bee colony (ABC) and its most modifications use a probability method to select good food sources (called solutions) in the onlooker bee search phase. However, the probability selection does not work with increasing of iterations, because the fitness values cannot be used to distinguish two different solutions. In order to tackle this problem, this paper proposes a new ABC (called NSABC), in which a new selection method based on neighborhood radius is used. Unlike the probability selection in the original ABC, NSABC chooses the best solution in the neighborhood radius to generate offspring. Based on the neighborhood radius, two new solution search strategies are modified. The scout bee search phase is improved by using opposition-based learning and the neighborhood radius. To evaluate the search ability of NSABC, there are 22 benchmark problems used in the experiments. Performance comparison shows NSABC achieves better results than five other ABC algorithms. [ABSTRACT FROM AUTHOR]

Meta-heuristic algorithms play an important role in the optimization field thanks to their robustness and programming simplicity. Many meta-heuristic methods have been devised in recent years. Inspired by nature, they usually simulate natural or human-specific phenomena in a better way. A large amount of them are based on complicated behaviors requiring several implementation steps and algorithm-specific control parameters, which impedes users and limits solutions to different types of optimization problems. Hence, designing effective simple and parameter-free optimization methods attracts much attention. In this paper, we propose a novel population-based optimization algorithm based on balancing composite motions (BCMO). The core idea is balancing composite motion properties of individuals in solution space. Equalizing global and local searches via a probabilistic selection model creates a movement mechanism of each individual. Four test suites selected in the literature, which vary from numerical benchmarks to practical problems, to demonstrate the performance of BCMO include: (1) 23 classical benchmark functions, (2) CEC 2005 benchmark functions, (3) CEC 2014 benchmark functions, and (4) 3 real engineering design problems. The statistical results reveal the promising performance and application of BCMO in a variety of optimization and practical problems with constrained and unknown search spaces. [ABSTRACT FROM AUTHOR]

Surrogate models have been widely used for solving computationally expensive multi-objective optimization problems (MOPs). The efficient global optimization (EGO) algorithm, a Bayesian approach to surrogate-assisted optimization, has become very popular in surrogate-assisted evolutionary optimization. In this paper, we propose an adaptive Bayesian approach to surrogate-assisted evolutionary algorithm to solve expensive MOPs. The main idea is to tune the hyperparameter in the acquisition function according to the search dynamics to determine which candidate solutions are to be evaluated using the expensive real objective functions. In addition, the sampling selection criterion switches between an angle based distance and an angle-penalized distance over the course of optimization to achieve a better balance between exploration and exploitation. The performance of the proposed algorithm is examined on a set of benchmark problems and an airfoil design optimization problem using a maximum of 300 real fitness evaluations. Our experimental results show that the proposed algorithm is competitive compared to four popular multi-objective evolutionary algorithms. [ABSTRACT FROM AUTHOR]

Although many variable decomposition methods for cooperative co-evolution (CC) have been proposed, researches on scalable and efficient decomposition have rarely been done, particularly, for the large-scale global optimization (LSGO) problems. In this paper, we propose an efficient variable interdependency identification and decomposition method, called EVIID. Different from existing studies focusing on only limited scale efficient or accurate variable decomposition, our purpose is to develop a scalable variable decomposition method with high efficiency and accuracy even on very high-dimensional problems. EVIID utilizes three core strategies: a binary variable space search, a dynamic perturbation caching, and a pre-variable sorting. Their synergy effect enables scalable and efficient variable decomposition without sacrificing decomposition accuracy by pruning many redundant computations required to identify interdependencies among decision variables. In comprehensive experiments, EVIID showed highly scalable decomposition ability on 1000 to 10,000 dimensional benchmark problems compared against the state-of-the-art variable decomposition methods. Moreover, when EVIID was embedded into practical CC frameworks, it showed good optimization performance and also fast convergence. [ABSTRACT FROM AUTHOR]

Multifactorial Optimization (MFO) has attracted considerable attention in the community of evolutionary computation, which aims to deal with multiple optimization tasks simultaneously by information transfer. Unfortunately, information transfer may cause both positive and negative effects. To address this issue, this paper exploits an explicit multipopulation evolutionary framework (MPEF) to intelligently take advantage of positive information transfer and effectively reduce negative information transfer. In MPEF, each task possesses an independent population and has its random mating probability for exploiting the information of other tasks. Moreover, the random mating probability of each task is adjusted adaptively. The benefits of using MPEF are twofold. 1) Various well-developed search engines can be easily embedded into MPEF for solving the single task of multifactorial optimization problems. 2) The positive information transfer can be exploited. Meanwhile, negative information transfer can be prevented. A multifactorial evolutionary algorithm (named MFMP) is realized as an instance by embedding a well-designed search engine into MPEF. The experimental results on some MFO benchmark problems demonstrate the advantage of MFMP over some state-of-the-art algorithms. Moreover, MFMP is also successfully employed to solve the spread spectrum radar polyphase code design (SSRPCD) problem. [ABSTRACT FROM AUTHOR]

In evolutionary dynamic optimization (EDO), most of the existing studies have assumed that dynamic optimization problems are black boxes. However, for many real-world problems, the dynamic parameters that cause the problems to change are observable. However, determining the utility of these parameters in improving optimization performance has not yet been well studied. In this paper, we propose and compare three strategies for this task: rote learning, fitting data with a feedforward neural network and an ensemble strategy. The main idea of these strategies is to learn the relation between the observable parameters and the optimal solutions and then predict new optima once the environment changes. We also propose a set of test cases representing different kinds of characteristics of real-world problems. In the experiments, the proposed strategies are compared with existing methods that do not use observable parameters, and the results validate our proposed strategies. [ABSTRACT FROM AUTHOR]

As one of the most popular evolutionary algorithms for solving complex optimization problems, genetic algorithm has been extensively studied in the last three decades. Since genetic algorithm is a stochastic algorithm that may revisit duplicated solutions, it could suffer from low convergence speed on some real-world problems making algorithms likely to get trapped into local optimums. To address this issue, this paper proposes a non-revisiting genetic algorithm with a novel binary space partition (BSP) tree. The proposed BSP tree records all the generated solutions, which enables the algorithm to quickly determine whether a newly generated solution is duplicated or not. Moreover, the proposed algorithm fine-tunes the solutions according to the topology of the BSP tree in each generation, and thus can improve the population diversity and convergence speed. In comparison to six representative evolutionary algorithms, the proposed non-revisiting genetic algorithm exhibits better overall performance on eight benchmark problems, the power system fault diagnosis problem, and the molecular signatures selection problem. [ABSTRACT FROM AUTHOR]

• A decomposition strategy that converts the MO-MFO problem into a number of single-objective optimization subproblems is proposed. • A dynamic resource allocation strategy with multifactorial environment is proposed. • The proposed algorithm performs superior on a variety of benchmark MO-MFO problems. • The proposed algorithm is used to solve a practical problem. Multiobjective multifactorial optimization (MO-MFO), i.e. , multiple multiobjective tasks are simultaneously optimized by a single population, has received considerable attention in recent years. Traditional algorithms for the MO-MFO usually allocate equal computing resources to each task, however, this may not be reasonable due to the fact that different tasks usually have different degrees of difficulty. Motivated by the idea that the limited computing resources should be adaptively allocated to different tasks according to their difficulties, this paper proposes an algorithm for the MO-MFO based on decomposition and dynamic resource allocation strategy (denoted as MFEA/D-DRA). In the MFEA/D-DRA, each multiobjective optimization task is firstly decomposed into a series of single-objective subproblems. Thereafter, a single population is used to evolve all the single-objective subproblems. In the process of evolution, subproblems with fast evolution rate will have the opportunity to get more rewards, i.e. , computing resources. The evolution rate is measured by a utility function and updated periodically. Moreover, different multiobjective optimization tasks can communicate with each other according to a random mating probability. Finally, a set of evenly distributed approximate Pareto optimal solutions is obtained for each multiobjective optimization task. The statistical analysis of experimental results illustrates the superiority of the proposed MFEA/D-DRA algorithm on a variety of benchmark MO-MFO problems. [ABSTRACT FROM AUTHOR]

In many comparison papers Evolutionary Algorithms are stopped after a pre-defined number of function calls, which is a code-independent measure of computational time. This number of function calls is either defined by the inventors of particular benchmark problems, or set subjectively by the user for the specific problem. The question how much improvement could be achieved by Evolutionary Algorithms if they were given much more time is surprisingly rarely asked. In the present study we analyze improvements obtained by thirty Evolutionary Algorithms on four different benchmark sets, including one composed of 22 real-world problems, when the allowed number of function calls is extended ten times with respect to the values defined in the comparison criteria for the specific benchmark sets. We analyze how the prolonged search would affect the ranking of algorithms, how much improvement could be obtained by Evolutionary Algorithms in general, on what kind of problems the improvement will be achieved, and which type of algorithms would benefit most from such an extended search. We show that the improvements obtained in prolonged search are higher for real-world problems than for mathematical functions, and such improvements are mainly achieved by similar kinds of adaptive algorithms proposed relatively recently. Many metaheuristics fail to benefit from the extended search on most benchmark problems, or benefit only marginally. [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]

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]

Over the last two decades numerous metaheuristics have been proposed and it seems today that nobody is able to understand, evaluate, or compare them all. In principle, optimization methods, including the recently popular Evolutionary Computation or Swarm Intelligence-based ones, should be developed in order to solve real-world problems. Yet the vast majority of metaheuristics are tested in the source papers on artificial benchmarks only, so their usefulness for various practical applications remains unverified. As a result, choosing the proper method for a particular real-world problem is a difficult task. This paper shows that such a choice is even more complicated if one wishes, with good reason, to use metaheuristics twice, once to find the best and then to find the worst solutions for the specific numerical real-world problem. It often occurs that for either case different optimizers are to be recommended. The above finding is based on testing 30 metaheuristics on numerical real-world problems from CEC2011. First we solve 22 minimization problems as defined for CEC2011. Then we reverse the objective function for each problem and search for its maximizing solution. We also observe that algorithms that are highly ranked on average may not perform best for any given specific problem. Rather, the highest average ranking may be achieved by methods that are never among the poorest ones. In other words, occasional winners may get less attention than rare losers. [ABSTRACT FROM AUTHOR]

Multi-mode resource and precedence-constrained project scheduling is a well-known challenging real-world optimisation problem. An important variant of the problem requires scheduling of activities for multiple projects considering availability of local and global resources while respecting a range of constraints. A critical aspect of the benchmarks addressed in this paper is that the primary objective is to minimise the sum of the project completion times, with the usual makespan minimisation as a secondary objective. We observe that this leads to an expected different overall structure of good solutions and discuss the effects this has on the algorithm design. This paper presents a carefully-designed hybrid of Monte-Carlo tree search, novel neighbourhood moves, memetic algorithms, and hyper-heuristic methods. The implementation is also engineered to increase the speed with which iterations are performed, and to exploit the computing power of multicore machines. Empirical evaluation shows that the resulting information-sharing multi-component algorithm significantly outperforms other solvers on a set of “hidden” instances, i.e. instances not available at the algorithm design phase. [ABSTRACT FROM AUTHOR]

Abstract Randomized algorithms have been successfully applied in modeling dynamic system. How do random weights affect system identification and why do they sometimes work well? In this paper, we use the convolutional neural network (CNN) as an identification model to answer these questions. Since the convolution operation is an important property of the dynamic system and in the frequency domain it becomes the product, the CNN model is analyzed in the frequency domain. We first modify the CNN model, so that it can model both the input and the output series. Then we analyze the impact of the random weights of CNN in the frequency domain. We prove the existence of optimal weights and analyze the modeling accuracy under optimal weights and random weights. Through theoretical analysis, we propose a two-step training method and compare it with the random weight algorithm. The proposed CNN model with random weights is validated with three benchmark problems. [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]

Non-dominated sorting has widely been adopted and shown to be very effective in dominance based evolutionary multi-objective optimization where the number of objectives is two or three. In dealing with many-objective optimization problems, where the number of objectives is more than three, however, the effectiveness of dominance based evolutionary algorithms will seriously degrade and the computational complexity of non-dominated sorting will considerably increase. In this paper, we propose an approximate non-dominated sorting algorithm for many-objective optimization, where the dominance relationship between two solutions is determined by a maximum of three objective comparisons on top of a sorted population according to one of the objectives. The time complexity of the proposed approximate sorting is independent of the number of objectives, which significantly enhances the time efficiency, in particular when the number of objectives is large. To examine the influence of inaccurate sorting on the search performance, the proposed approximate sorting method is embedded in three popular dominance based evolutionary many-objective optimization algorithms. Our experimental results on 16 widely used many-objective optimization benchmark problems suggest that the approximate non-dominated sorting method is not only computationally much more efficient than the state-of-the-art accurate non-dominated sorting methods, but also leads to better search performance on most test problems used in this study. [ABSTRACT FROM AUTHOR]