This paper tackles denial-of-service (DoS) attacks and output constraints in secondary voltage control of islanded microgrids. While existing literature predominantly addresses communication security, it largely overlooks the operational boundaries of power converters. This oversight may result in control saturation, device failure and ultimately, compromised system stability. Furthermore, traditional consensus-based voltage regulation fails to facilitate necessary power interchange among sub-microgrids, limiting its practical applicability. To overcome these limitations, a novel distributed voltage control scheme based on the inclusion principle is proposed. Firstly, a distributed control system model incorporating output constraints is established. The nonlinearities of the system are effectively handled via a barrier Lyapunov function approach, ensuring strict adherence to the output voltage amplitude limits. Secondly, an adaptive state estimator with a switching mechanism is developed to mitigate intermittent communication failures induced by DoS attacks. The controller parameters are then obtained by solving a set of linear matrix inequalities, guaranteeing the semi-global uniform ultimate boundedness (SGUUB) of all closed-loop signals and the ultimate convergence of errors to a neighborhood of the origin. Simulation results verify that the proposed strategy effectively ensures voltage stability while simultaneously satisfying both output constraints and cybersecurity requirements.

Large-scale multimodal multiobjective optimization problems with sparse Pareto optimal solutions pose a significant challenge in the field of optimization, primarily stemming from the multimodality characteristic, the curse of dimensionality, and the uncertainty of sparse solutions. In this work, we propose a sparse large-scale multimodal multiobjective evolutionary algorithm (MVDE-MMEA) to solve such complex tasks. In MVDE-MMEA, a multiview diversity enhancement mechanism is designed to improve the exploration ability of the algorithm across the entire decision space. The diversity mechanism seamlessly transits from a global perspective to a local one as the population evolves, which contributes to an effective convergence towards multiple Pareto optimal sets in large-scale decision space. Furthermore, a clustering method is proposed to divide the population into several niches, guided by the shared characteristics among candidates. In this way, the algorithm shifts its focus from exploration in the whole search space to exploitation in local regions. Experimental studies are conducted on eight benchmark test problems and 12 feature selection problems. The comparative results with the state-of-the-art algorithms demonstrate the superiority of MVDE-MMEA.

With the rapid development of industrial Internet of Things (IIoT), the edge-cloud collaboration architecture combining the powerful computing ability of cloud computing with the low latency of edge computing plays an increasingly important role in providing the computing resources and reducing the latency for IIoT. However, under this architecture, existing methods in scheduling the resources for IIoT often focus on latency and energy consumption but ignore some other important factors especially the reliable factor, thereby making it difficult for them to adapt to real-world IIoT scenarios. To this end, we propose a reliable resource scheduling method with knowledge transfer for edge-cloud collaboration-enabled IIoT. Specifically, we first model the resource scheduling as a many-objective optimization problem, considering these optimized objectives: latency, energy consumption, load balance, resource utilization, and trust measure between tasks and servers. Then, we develop a knowledge transfer accelerated clustering evolutionary algorithm (KTCEA) for many-objective optimization to solve the model, where the knowledge transfer aims at accelerating the evolution and the clustering makes the population converge from various directions. Under the collaboration of knowledge transfer and clustering, KTCEA can utilize the small population size to effectively search the objective space, and thus have the high real-time performance. Extensive experiment results on a benchmark test suite and the constructed model demonstrate that KTCEA is highly competitive compared with some advanced methods and our method can efficiently achieve the resource scheduling for edge-cloud collaboration-enabled IIoT, respectively.

Most of the current research on dynamic multiobjective optimization problems (DMOPs) assumes that environmental changes can be detectable. However, undetectable changes are frequently encountered in real-world applications, which pose a serious challenge for the existing methods. Because undetectable changes can lead to the failure of change detection techniques, thereby making it difficult to adapt to environmental changes for most algorithms. Therefore, to effectively deal with DMOPs with undetectable changes, this work proposes a dual mutation-based dynamic multiobjective evolutionary algorithm (DM-DMOEA). The proposed DM-DMOEA incorporates the following two main components. First, based on the exploration level of the population, an adaptive selection strategy is proposed, which enables the adaptive identification of individuals for mutation. Second, a dual mutation scheme is developed, utilizing both the polynomial mutation and the Gaussian mutation. These mutation operations are applied on the selected individuals to generate the mutated individuals, allowing for diverse exploration in the search space. After conducting the above two strategies, the population will evolve by the evolutionary criterion of multiobjective optimization. As a result, the algorithm can effectively adapt to undetectable changes in the environment. Comprehensive empirical studies are conducted on different benchmark functions and a real-world application to evaluate the performance of DM-DMOEA. Experimental results have demonstrated that DM-DMOEA is competitive in tracking the Pareto front over time when facing undetectable changes.

Constrained multimodal multiobjective optimization problems (CMMOPs) are challenging in the field of optimization, requiring to consider the balance between the constraints and objectives, the balance between exploration and exploitation in the decision space and the objective space, and the balance of diversity between the decision space and the objective space. In this work, we propose a multitask-assisted evolutionary algorithm (CMMO-MTA) to achieve these balances. In CMMO-MTA, a tri-task multitasking framework is proposed, which contains one main task and two assisting tasks. The main task aims to solve the original CMMOP, and two assisting tasks are designed to transfer desired knowledge to the main task to achieve the first two balances. Furthermore, a space balance-based selection mechanism is proposed to ensure a balanced representation of solutions in both the decision space and the objective space, thereby striking the third balance. Experimental studies are conducted on 31 test problems and a real-world application to compare the proposed algorithm with seven state-of-the-art algorithms. The results demonstrate the superiority of CMMO-MTA in solving CMMOPs.

With the rapid development of 5G, numerous data is generated in the blockchain-enabled industrial Internet of Things (IIoT). Although these peers in the blockchain system have the storage ability, they are far from meeting the storage requirements of the generated data. In addition, all data is stored in the blockchain network, which is unfriendly to applications that require real-time information. To address the above storage problems, this article proposes a block storage optimization method for blockchain-enabled IIoT, whose core idea is to conditionally select some blocks to store in the cloud. This method firstly models the selection conditions of blocks as a many-objective optimization problem, where the selection conditions include using probability, storage cost, space occupation, and transmission cost. Then, a cascading selection-based evolutionary algorithm (CSEA) for many-objective optimization is developed to solve the model and thereby obtain the optimal blocks stored in the cloud, where CSEA adopts the diversity-first principle. Finally, CSEA is first compared with seven state-of-the-art methods on two benchmark test suites for validating its ability to obtain reliable experimental results, and then is used to solve the proposed model. The corresponding results demonstrate that CSEA has high competitiveness, and our method can effectively address the storage problems above. In summary, this article provides a novel method for addressing the storage problem in the blockchain-enabled IIoT.

Medium-scale expensive multiobjective optimization problems (EMOPs) present a significant challenge to most existing surrogate-assisted evolutionary algorithms (SAEAs). Because the algorithms must balance convergence and diversity with a limited number of fitness evaluations (FEs), while managing the uncertainty in surrogate predictions within the medium-scale decision space. Therefore, this work proposes a surrogate-assisted multiobjective evolutionary algorithm based on two-level model management (SAMOEA-TL2M) to effectively address medium-scale EMOPs. In SAMOEA-TL2M, infill solutions are selected using the proposed two-level model management strategy. In the first level, the estimated non-dominated solutions with good shift-based density estimation (SDE) values are selected for the balance of convergence and diversity. In the second level, the estimated non-dominated solutions and high uncertainty solutions are considered. To quantify uncertainty, an inverse distance weighting (IDW) is introduced. Moreover, an accuracy rate indicator (ARI) is proposed for the optimization state assessment, providing guidance for adaptively executing the two model management levels. Extensive experiments on three widely used instances and time-varying ratio error estimation (TREE) problems with up to 120 dimensions demonstrate the superiority of SAMOEA-TL2M over five state-of-the-art SAEAs in solving medium-scale EMOPs.

The incipient fault detection of a complex industrial process is a challenging problem for traditional dynamic detection methods. Traditional dynamic detection methods usually decouple the correlations among the variables and dynamic correlations simultaneously, which makes the two types of correlations mixed and may lead to performance deterioration in long-sequence dynamic detection. Some incipient faults may not change the amplitudes of process variables but change the long-sequence dynamic features. Based on the$T^{2}$statistic and matrix multiplication transformation ($T^{2}$S-MMT), traditional dynamic detection methods can detect many faults effectively. However, the$T^{2}$S-MMT can not effectively detect some incipient faults due to the above two types of correlations mixed. In order to overcome the shortcomings of$T^{2}$S-MMT and improve the detection ability of some incipient faults, this paper proposes a fault detection method based on the dynamic k-nearest neighbor model and Dual Control Chart (DKNN-DCC), which can improve the incipient fault detection performance by using long-sequence dynamic detection. The proposed method is verified by the Tennessee Eastman (TE) process and the continuously stirred tank reactor (CSTR) process. The experimental results show the effectiveness of the proposed method in incipient fault detection compared with traditional dynamic detection methods.Note to Practitioners—This paper presents a novel incipient fault detection method, which directly mines the long-sequence dynamic abnormal information from the process variable and overcomes the problem of some abnormal information being submerged in the$T^{2}$statistic calculated based on the matrix multiplication transformation. The proposed method can detect incipient faults that are not easily detected by some traditional methods and can help operators find the abnormal and avoid more serious losses. The structure of the proposed method jumps out of the frameworks of traditional dynamic detection methods, which is feasible to apply to different stable industrial processes.

Modern industrial processes are characterized by numerous measurement points and wide operating ranges, resulting in extremely complex correlations among variables. Therefore, an effective monitoring system should balance diverse process characteristics such as nonlinearity, non-Gaussianity, and multiscale simultaneously. Moreover, it should have the ability to detect and diagnose faults in the incipient stage, thus avoiding accident escalation. With these goals in mind, this paper proposes an integrated monitoring solution based on multiscale kernel entropy component analysis (MSKECA). Specifically, process variables are first decomposed into approximations and details at different scales in real-time using the moving window-based wavelet, and contributions from each scale are collected in separate matrices. Then, KECA-based local-scale models are built to sift out important detail scales for reconstruction along with the approximate scale. Lastly, a KECA-based global-scale model is developed to monitor the reconstructed data. To improve the fault detection performance, a novel monitoring index based on the angle metric called angle variance index (AVI) is designed. In addition, to achieve effective diagnosis, MSKECA-based contribution plots are constructed, which depict the contributions of variables to faults at each scale, thus comprehensively revealing the root causes. Finally, the effectiveness and superiority of the proposed solution are validated by comparisons with other advanced counterparts in two industrial scenarios.Note to Practitioners—This paper proposes an integrated monitoring solution for complex industrial processes, i.e., MSKECA-based fault detection and diagnosis. The solution takes into account the diversity of process characteristics, the effectiveness of incipient fault detection, and the richness of diagnostic information. Specifically, 1) MSKECA can simultaneously handle the nonlinear, non-Gaussian, and multiscale characteristics that are prevalent in real process data. It enables on-line detection of significant events occurring at different scales and extraction of fault-sensitive features for monitoring; 2) based on the angular structure of KECA, the AVI statistic is designed, which exhibits low autocorrelation and is sensitive to faults. Leveraging the statistic, MSKECA allows reliable and prompt responses to faults; 3) MSKECA-based contribution plots not only convey diverse diagnostic information including fault variable, type, and grade but also are not susceptible to the smearing effect, which is helpful for practitioners to achieve fault repair. The solution has proven useful for a real hot rolling process. It can also be extended to other industrial processes.

In some real-world applications, the optimization problems may involve multiple design stages. At each design stage, the objective is incrementally modified by incorporating more decision variables and optimized. In addition, the fitness evaluations (FEs) are often highly costly. Such optimization problems can be called expensive incremental optimization problems (EIOPs). Despite their importance, EIOPs have not attracted much attention over the past few years. Since the objectives of different design stages are different but related, reusing the search experience from the past design stages is beneficial to the evolutionary search of the current design stage. Therefore, a surrogate-assisted differential evolution with knowledge transfer (SADE-KT) is proposed in this work, which aims to fill the current gap in solving EIOPs. The major merit of the proposed SADE-KT is its ability to seamlessly integrate knowledge transfer and the surrogate-assisted evolutionary search. In SADE-KT, a surrogate based hybrid knowledge transfer strategy is first proposed. This strategy makes it possible to reuse the knowledge captured from the past design stages by leveraging different knowledge transfer techniques. As a result, the convergence for the current design stage can be speeded up. Then, a two-level surrogate-assisted evolutionary search is developed to search for the optimum. Comprehensive empirical studies have demonstrated that the proposed algorithm works efficiently on EIOPs.

The evolution of multi-constellation Global Navigation Satellite Systems (GNSS) has presented an opportunity to enhance user positioning accuracy. However, practical constraints, such as limited receiver channels and power consumption, necessitate judicious satellite selection. Geometric Dilution of Precision (GDOP) serves as a critical indicator for optimizing positioning performance, but determining the subset with the optimal GDOP value involves solving an impractical combinatorial optimization problem. A compromise solution seeks to balance computational complexity while sacrificing some optimality. Consequently, finding an optimal combination of satellites with a low computational burden yet quasi-optimal GDOP value remains a challenge. In response to this challenge, we introduce a pioneering approach in this paper: a super-fast satellite selection algorithm based on power series expansion (SF-PSE). This paper derives a “Xiao-Liang formula” based on power series expansion and the Sherman-Morrison formula. Using this formula, we propose two low-computational-cost rapid iterative algorithms (F-PSE and SF-PSE). Among these algorithms, SF-PSE notably reduces the computational burden through an approximate iterative inverse matrix-guided search method. Experimental results demonstrate that satellite combinations identified by F-PSE and SF-PSE yield nearly the same accuracy while reducing computation time by 70% and 87%, respectively, compared to the SMALLER method.

Traditional projection dynamic monitoring methods focus on simultaneously decoupling the correlations among the process variables and the autocorrelations of the variables, which leads to a mixing problem of the two correlations. The mixing problem decreases the ability to model the dynamic correlations, thus decreasing the detection rates (DRs) of some faults. Considering that the projection matrix may cause the mixing of the two correlations, this article proposes a dynamic monitoring method based on directly monitoring original variables. This article first adopts the kernel least-mean-squares (KLMS) method to establish a univariate dynamic model, then adopts the univariate dynamic model and the dual control chart (DCC) to build the multivariate direct monitoring method, which is named the KL2C method (KL represents KLMS and 2 C represents DCC). Then, the dynamic nearest neighbor kernel space (DNNKS) is proposed to overcome the redundant dimensions problem of the KL2C method, which is named the DKL2C method (D represents DNNKS). Furthermore, based on the joint control chart, this article puts forward a dynamic monitoring method of two sequences, which both considers the advantages of the projection dynamic monitoring method and the direct dynamic monitoring method together. Finally, this article utilizes the Tennessee Eastman process and the continuously stirred tank reactor process to verify the effectiveness of the proposed methods.

Surrogate-assisted evolutionary algorithms (SAEAs) are well suited for computationally expensive optimization. However, most existing SAEAs only focus on low- or medium-dimensional expensive optimization. Thus, a novel SAEA for high-dimensional expensive optimization, denoted as surrogate-assisted multipopulation particle swarm optimizer (SA-MPSO), is proposed and fully investigated in this work. The proposed algorithm employs a parameter-free clustering technique, denoted as affinity propagation clustering, to generate several subswarms. A surrogate-assisted learning strategy-based particle swarm optimizer is proposed for guiding the search of each subswarm. Furthermore, a model management strategy is adapted to choose the promising particles for real fitness evaluations. Finally, a subswarm diversity maintenance scheme and a surrogate-based trust region local search technique are introduced to enhance both exploration and exploitation. The experimental results on commonly used benchmark test problems with dimensions varying from 30 to 100 and airfoil design problem have shown that SA-MPSO outperforms some state-of-the-art methods.

Dominance robustness (DR) has been proposed for assessing the ability of the Pareto-optimal solutions to remain to be nondominated when the decision variables are subject to noise. There are two main challenges in search for dominance robust optimal solutions in dominance robust multiobjective optimization (MOP), namely, accurate estimation of the DR measure and a good balance between convergence and DR in the presence of uncertainty. In this article, a novel robust MOP evolutionary algorithm based on decision variable assortment (DVA) is proposed to tackle these challenges. To be specific, an indicator, termed as dominance robust indicator, is proposed to measure the DR based on the dominance level and dominance relationship of the sampled points. Then, the decision variables are divided into low DR-related variables and high DR-related variables based on the DVA strategy. Finally, low and high DR related variables are optimized separately to obtain the dominance robust optimal solutions. In addition, performance indicators to quantify the performance of dominance robust optimal solution set obtained by robust MOP algorithm are proposed. Experimental results have demonstrated that the proposed algorithm is competitive in search for dominance robust optimal solutions.

In recent years, surrogate-assisted evolutionary algorithms have been developed for expensive optimization. However, a majority of applications are dynamic optimization problems in the real-world. In this paper, therefore, a surrogate-assisted clustering particle swarm optimizer is proposed for expensive dynamic optimization. In the proposed method, several clusters are first created by affinity propagation clustering, and then local radial basis function (RBF) surrogates are built based on the neighbor evaluated points for each cluster. Finally, in each cluster, the local RBF assists particle swarm optimizer to search the most promising point, which is evaluated by real objective function. To track dynamic environment, the points with best exact fitness in each cluster are added into new cradle swarm, if environmental change has occurred. A variety of experiments have been conducted on the moving peaks benchmark (MPB) with 500 change frequency in each environment. The experimental results have demonstrated that the proposed approach has a good performance.

Haze removal is important to improve performance of outdoor vision systems. However, it is challenging to remove haze from a single nighttime haze image. In this paper, a novel superpixel-based single image haze removal algorithm is proposed for nighttime haze images. The input nighttime image is first decomposed into a glow image and a glow-free nighttime haze image using their relative smoothness. A superpixel-based method is then introduced to compute the value of the atmospheric light and dark channel for each pixel in the glow-free haze image. The transmission map is decomposed from the dark channel of the glow-free haze image by the weighted guided image filter. Since superpixels usually adhere to the boundaries of objects well, a smaller local window size can be selected. As such, details in areas of fine structures are preserved better. In addition, to avoid noticeable noise in the sky area, an adaptive threshold is added to the transmission map when the nighttime haze image is restored. Experiments show that our method produces better results than the existing haze removal algorithms for nighttime haze images.

This paper proposes a general multi-objective particle swarm optimizer based on R2-indicator and decomposition (called R2-MOPSO) to deal with multi-objective optimization problems and then to solve many-objective optimization problems. R2-MOPSO makes use of the R2 contribution of the archived solutions to select global best leaders and update the swarm. R2-MOPSO uses decomposition method for selecting the personal best leaders and updates them for each particle in the population. In order to enhance the diversity of the particles, elitist-learning strategy and gaussian learning strategy are used. Our proposed algorithm is evaluated adopting benchmark test problems and indicators reported in the specialized literature, comparing is results with respect to those obtained by the state-of-the-art multi-objective evolutionary algorithms. Our preliminary results indicate that our proposal is competitive with respect to state-of-the-art multi-objective evolutionary algorithms, being particularly suitable for solving multi-objective and many-objective optimization problems.

The aim of this paper is to develop a nonlinear orthogonal signal correction (OSC) algorithm using kernel-based technique, termed as kernel OSC (KOSC), and investigate its effects on multivariate calibration. As a nonlinear data pretreatment, the proposed KOSC method can better analyze the nonlinear relationships between descriptor and response variables and remove from process measurement those undesirable variations not correlated with process property from a nonlinear point of view, which well prepares the corrected process trajectory for the subsequent calibration modeling. Two data sets are employed in illustration experiment. It is found that nonlinear OSC plus nonlinear calibration algorithm seems to have the superiority over other methods to improve the interpretation ability of regression model when process data nonlinearly vary with quality.