TheComputing Power Network(CPN) is a distributed system that integrates computing resources to optimize utilization, but ensuringQuality of Service(QoS) is challenging due to high demand and complex heterogeneous connections. Accurate workload prediction is essential for maintaining QoS, yet the diverse and complex user requirements in CPN make prediction difficult. To address this challenge, we propose an ensemble workload prediction model with fluctuation division control for workload prediction in CPN, comprising three key components. First, we use theThree-Way Decision(3WD) approach to partition workload fluctuations, controlling granularity thickness and applying clustering to capture dynamic workload characteristics. Second, we develop tailored prediction methods for each of the three partitioned regions and ensembles them to enhance overall prediction performance. Third, the ensemble prediction method is applied to each region to obtain the final predicted values. The proposed method introduces an innovative fluctuation division control strategy for characteristic mining to capture dynamic workload fluctuation patterns and designs the effective ensemble workload prediction model deal with the problem of non-stationary workload prediction in CPN. Experimental results on trace datasets from Alibaba and Dinda demonstrate that the proposed model improves the higher average prediction accuracy by up to 26.06%$\sim$66.4% than the comparison methods.

Minimizing the classification error rate and the number of selected features are the two major objectives of feature selection, and they are often in conflict with each other, which is a multiobjective problem. Evolutionary algorithms have been widely used for multiobjective feature selection problems. Preselection in evolutionary algorithms is used to improve the sampling quality by selecting only potentially promising candidate solutions for fitness evaluations. However, traditional preselection methods struggle to effectively handle feature selection due to its large-scale combinatorial nature and intricate feature interactions. To alleviate this issue, this paper proposes a filter-based performance predictor to preselect feature subsets for subsequent classification fitness evaluations. It uses multiple filter measures to estimate the classification performance of a feature subset, which can explore complex feature interactions and is also insensitive to the dimensionality. Additionally, a correlation coefficient is used to measure the compatibility between the learned performance predictor and the classification performance. Based on the degree of compatibility, a preselection method that considers both the predicted classification performance and the feature subset diversity is proposed, which can preselect promising solutions from multiple candidate solutions and thus improve the feature subset search efficiency. The proposed method is verified experimentally on a total of 18 classification datasets spanning various domains, and the results reveal that it can find feature subsets with better classification performance and converge faster to competitive results compared to state-of-the-art methods.

In the big data era, the large volume and high dimensionality of data challenge many data mining algorithms. Since many classification algorithms are sensitive to data distribution, removing redundant or noisy features and instances can greatly improve their performance. Feature selection and instance selection are two major data reduction techniques that are inherently interconnected. This article proposes an auxiliary-optimization-assisted constrained multiobjective optimization method that concurrently tackles feature and instance selection, with two key constraints: forcing the obtained subsets to have better classification performance than that of using all features and instances under the given classification algorithm, and bounding the worst-class error. A simple but effective initialization method is designed to sample initial solutions relatively uniformly across different regions of the objective space, to provide a diverse and high-quality set of initial feature and instance subsets. An auxiliary-optimization-based search approach is proposed to fully utilize useful infeasible solutions, which can further reduce the number of selected features and instances without compromising classification performance. The proposed method is compared with a number of promising methods on 20 real-world classification datasets, and the experimental results show that it is generally better than those methods. Additionally, the proposed method offers a significant advantage whereby the majority of its solutions exhibit superior or comparable classification performance compared to using all original features and instances, while selecting no more than 30% of the features and 50% of the training instances across most datasets.

Biomedical image segmentation plays a critical role in clinical applications such as disease diagnosis and surgical planning. While deep learning, especially U-Net and its variants, have achieved impressive performance in this domain, their success heavily relies on manual architectural design, which limits scalability and generalizability. Neural architecture search (NAS) offers a promising solution by automating model design, but existing NAS-based methods still suffer from high computational costs and limited architectural diversity. In this work, we propose a novel NAS framework, termed ranking-aware predictorassisted architecture design (RPA2D), for efficient and accurate biomedical image segmentation. RPA2D introduces a lightweight and expressive search space comprising diverse convolution and pooling operations tailored for medical images. Furthermore, we design a contrastive learning-based ranking-aware performance predictor that enables accurate architecture ranking under limited supervision. Extensive experiments on public biomedical datasets demonstrate that RPA2D consistently outperforms both handcrafted and NAS-based baselines in segmentation accuracy while significantly reducing search overhead.

The computing power network links distributed and heterogeneous computing resources via the network, to enable efficient configuration and utilization of computing power. However, scheduling computing resources within this network presents several challenges, such as resource heterogeneity, vast search spaces, uncertainty, high constraints, and real-time requirements. To simulate the real-world computing power network scheduling problem, this paper integrates cloud servers, fog servers, and edge servers into a unified computing power network, considering their respective GPU, CPU, and bandwidth resources. We introduce a Dual-Tree Genetic Programming (DTGP) approach that simultaneously optimizes two critical decisions—routing and sequencing—to automatically evolve computing power network scheduling heuristics for real-time decision-making. Additionally, to improve the performance of DTGP, we propose new terminal sets tailored to fit within these two GP trees. Experimental results demonstrate that the proposed method significantly outperforms existing state-of-the-art methods in six test scenarios, achieving up to 40% reduction in completion time.

Minimizing the number of selected features and maximizing the classification performance are two main objectives in feature selection, which can be formulated as a bi-objective optimization problem. Due to the complex interactions between features, a solution (i.e., feature subset) with poor objective values does not mean that all the features it selects are useless, as some of them combined with other complementary features can greatly improve the classification performance. Thus, it is necessary to consider not only the performance of feature subsets in the objective space, but also their differences in the search space, to explore more promising feature combinations. To this end, this paper proposes a tri-objective method for bi-objective feature selection in classification, which solves a bi-objective feature selection problem as a tri-objective problem by considering the diversity (differences) between feature subsets in the search space as the third objective. The selection based on the converted tri-objective method can maintain a balance between minimizing the number of selected features, maximizing the classification performance, and exploring more promising feature subsets. Furthermore, a novel initialization strategy and an offspring reproduction operator are proposed to promote the diversity of feature subsets in the objective space and improve the search ability, respectively. The proposed algorithm is compared with five multiobjective-based feature selection methods, six typical feature selection methods, and two peer methods with diversity as a helper objective. Experimental results on 20 real-world classification datasets suggest that the proposed method outperforms the compared methods in most scenarios.

Maximizing the classification accuracy and minimizing the number of selected features are two primary objectives in feature selection, which is inherently a multiobjective task. Multiobjective feature selection enables us to gain various insights from complex data in addition to dimensionality reduction and improved accuracy, which has attracted increasing attention from researchers and practitioners. Over the past two decades, significant advancements in multiobjective feature selection in classification have been achieved in both the methodologies and applications, but have not been well summarized and discussed. To fill this gap, this paper presents a broad survey on existing research on multiobjective feature selection in classification, focusing on up-to-date approaches, applications, current challenges, and future directions. To be specific, we categorize multiobjective feature selection in classification on the basis of different criteria, and provide detailed descriptions of representative methods in each category. Additionally, we summarize a list of successful real-world applications of multiobjective feature selection from different domains, to exemplify their significant practical value and demonstrate their abilities in providing a set of trade-off feature subsets to meet different requirements of decision makers. We also discuss key challenges and shed lights on emerging directions for future developments of multiobjective feature selection.

Reducing the number of selected features and improving the classification performance are two major objectives in feature selection, which can be viewed as a multi-objective optimization problem. Multi-objective feature selection in classification has its unique characteristics, such as it has a strong preference for the classification performance over the number of selected features. Besides, solution duplication often appears in both the search and the objective spaces, which degenerates the diversity and results in the premature convergence of the population. To deal with the above issues, in this paper, during the evolutionary training process, a multi-objective feature selection problem is reformulated and solved as a constrained multi-objective optimization problem, which adds a constraint on the classification performance for each solution (e.g., feature subset) according to the distribution of nondominated solutions, with the aim of selecting promising feature subsets that contain more informative and strongly relevant features, which are beneficial to improve the classification performance. Furthermore, based on the distribution of feature subsets in the objective space and their similarity in the search space, a duplication analysis and handling method is proposed to enhance the diversity of the population. Experimental results demonstrate that the proposed method outperforms six state-of-the-art algorithms and is computationally efficient on 18 classification datasets.

Constrained multiobjective optimization problems (CMOPs) pose great difficulties to the existing multiobjective evolutionary algorithms (MOEAs), in terms of constraint handling and the tradeoffs between diversity and convergence. The constraints divide the search space into feasible and infeasible regions. A key to solving CMOPs is how to effectively utilize the information of both feasible and infeasible solutions during the optimization process. In this article, we propose a multiform optimization framework to solve a CMOP task together with an auxiliary CMOP task in a multitask setting. The proposed framework is designed to conduct a search in different sizes of feasible space that is derived from the original CMOP task. The derived feasible space is easier to search and can provide a useful inductive bias to the search process of the original CMOP task, by leveraging the transferable knowledge shared between them, thereby helping the search to toward the Pareto optimal solutions from both the infeasible and feasible regions of the search space. The proposed framework is instantiated in three kinds of MOEAs: 1) dominance-based; 2) decomposition-based; and 3) indicator-based algorithms. Experiments on four sets of benchmark test problems demonstrate the superiority of the proposed method over four representative constraint-handling techniques. In addition, the comparison against five state-of-the-art-constrained MOEAs demonstrates that the proposed approach outperforms these contender algorithms. Finally, the proposed method is successfully applied to solve a real-world antenna array synthesis problem.

Evolutionary multiobjective feature selection (FS) has gained increasing attention in recent years. However, it still faces some challenges, for example, the frequently appeared duplicated solutions in either the search space or the objective space lead to the diversity loss of the population, and the huge search space results in the low search efficiency of the algorithm. Minimizing the number of selected features and maximizing the classification performance are two major objectives in FS. Usually, the fitness function of a single-objective FS problem linearly aggregates these two objectives through a weighted sum method. Given a predefined direction (weight) vector, the single-objective FS task can explore the specified direction or area extensively. Different direction vectors result in different search directions in the objective space. Motivated by this, this article proposes a multiform framework, which solves a multiobjective FS task combined with its auxiliary single-objective FS tasks in a multitask environment. By setting different direction vectors, promising feature subsets from single-objective FS tasks can be utilized, to boost the evolutionary search of the multiobjective FS task. By comparing with five classical and state-of-the-art multiobjective evolutionary algorithms, as well as four well-performing FS algorithms, the effectiveness and efficiency of the proposed method are verified via extensive experiments on 18 classification datasets. Furthermore, the effectiveness of the proposed method is also investigated in a noisy environment.

Expensive constrained optimization refers to problems where the calculation of the objective and/or constraint functions are computationally intensive due to the involvement of complex physical experiments or numerical simulations. Such expensive problems can be addressed by Gaussian process-assisted evolutionary algorithms. In many problems, the (single) objective and constraints are correlated to some extent. Unfortunately, existing works based on the Gaussian process for expensive constrained optimization treat the objective and multiple constraints as being statistically independent, typically for the ease of computation. To fill this gap, this article investigates the correlation among the objective and constraints. To be specific, we model the correlation amongst the objective and constraint functions using a multitask Gaussian process prior, and then mathematically derive a constrained expected improvement acquisition function that allows the correlation among the objective and constraints. The correlation between the objective and constraints can be captured and leveraged during the optimization process. The performance of the proposed method is examined on a set of benchmark problems and a real-world antenna design problem. On problems with high correlation amongst the objective and constraints, the experimental results show that leveraging the correlation yields improvements in both the optimization speed and the constraint-handling ability compared with the method that assumes the objective and constraints are statistically independent.

Objectives optimization and constraints satisfaction are two equally important goals to solve constrained many-objective optimization problems (CMaOPs). However, most existing studies for CMaOPs can be classified as feasibility-driven-constrained many-objective evolutionary algorithms (CMaOEAs), and they always give priority to satisfy constraints, while ignoring the maintenance of the population diversity for dealing with conflicting objectives. Consequently, the population may be pushed toward some locally feasible optimal or locally infeasible areas in the high-dimensional objective space. To alleviate this issue, this article presents a problem transformation technique, which transforms a CMaOP into a dynamic CMaOP (DCMaOP) for handling constraints and optimizing objectives simultaneously, to help the population cross the large and discrete infeasible regions. The well-known reference-point-based NSGA-III is tailored under the problem transformation model to solve CMaOPs, namely, DCNSGA-III. In this article, ε -feasible solutions play an important role in the proposed algorithm. To this end, in DCNSGA-III, a mating selection mechanism and an environmental selection operator are designed to generate and choose high-quality ε -feasible offspring solutions, respectively. The proposed algorithm is evaluated on a series of benchmark CMaOPs with three, five, eight, ten, and 15 objectives and compared against six state-of-the-art CMaOEAs. The experimental results indicate that the proposed algorithm is highly competitive for solving CMaOPs.

The following topics are dealt with: evolutionary computation; genetic algorithms; search problems; optimisation; learning (artificial intelligence); particle swarm optimisation; Pareto optimisation; pattern classification; pattern clustering; computational complexity.

For computationally expensive constrained optimization problems, one crucial issue is that the existing expected improvement (EI) criteria are no longer applicable when a feasible point is not initially provided. To address this challenge, this paper uses the expected improvement of constraint violation to reach feasible region. A new constrained expected improvement criterion is proposed to select sample solutions for the update of Gaussian process (GP) surrogate models. The validity of the proposed constrained expected improvement criterion is proved theoretically. It is also verified by experimental studies and results show that it performs better than or competitive to compared criteria.

A novel multiobjective technique is proposed for solving constrained optimization problems (COPs) in this paper. The method highlights three different perspectives: 1) a COP is converted into an equivalent dynamic constrained multiobjective optimization problem (DCMOP) with three objectives: a) the original objective; b) a constraint-violation objective; and c) a niche-count objective; 2) a method of gradually reducing the constraint boundary aims to handle the constraint difficulty; and 3) a method of gradually reducing the niche size aims to handle the multimodal difficulty. A general framework of the design of dynamic constrained multiobjective evolutionary algorithms is proposed for solving DCMOPs. Three popular types of multiobjective evolutionary algorithms, i.e., Pareto ranking-based, decomposition-based, and hype-volume indicator-based, are employed to instantiate the framework. The three instantiations are tested on two benchmark suites. Experimental results show that they perform better than or competitive to a set of state-of-the-art constraint optimizers, especially on problems with a large number of dimensions.