With the continuous development of industrial manufacturing, rationally scheduling multiple-source flexible orders is crucial for achieving sustainable production. However, most existing methods adopt a single-task optimization paradigm with independent modeling, overlooking the similarities among multi-source orders and the correlations between scheduling optimizations. This leads to additional waste of computational resources and the loss of prior experience. To address this issue, we propose a many-objective multi-task optimization paradigm that takes into account the correlations among multi-source flexible orders. Specifically, through the multi-task optimization paradigm, multiple flexible orders with different variable dimensions are uniformly modeled by sharing a set of objective functions, thereby enabling the joint optimization of related scheduling tasks. Secondly, to investigate the impact of tool wear on scheduling performance, an exponential function-based tool wear coefficient is introduced, and a many-objective optimization model is constructed that considers indicators such as processing time, energy consumption, load balancing, and tool wear amount. Next, considering the discrete problem properties, a many-objective multi-task evolutionary algorithm based on load balancing (MTMOEA-LB) is designed to avoid premature convergence of the multi-task optimization algorithm due to task differences. Finally, the actual production order data set of a flange enterprise is used for experimental comparison. Experimental results indicate that the proposed algorithm can output high-quality scheduling schemes quickly and effectively compared with other advanced optimization algorithms.

Multi-modal classification (MMC) leverages effective fusion of information from diverse modalities to achieve superior classification performance. Existing fusion methods, however, rely on expert-designed architectures that demand substantial domain expertise and computational resources, with fixed topologies that offer limited structural flexibility across tasks and datasets. Although neural architecture search (NAS)-based fusion methods have been proposed to automatically discover high-performing architectures, these approaches are computationally expensive and predominantly rely on pairwise modality combinations, which fail to capture complex multi-variable correlations, limiting the architectures' expressiveness and flexibility. Consequently, there remains a lack of multi-modal fusion frameworks that can simultaneously achieve high efficiency and high accuracy. To break through these bottlenecks, we propose a multi-branch tree-based fusion neural architecture search framework (MBTF-NAS). For performance enhancement, MBTF-NAS employs a multi-branch tree-structured encoding strategy that enables dynamic and computationally efficient exploration of fusion topologies and substantially strengthens cross-modal interaction. A learnable model-level attention weighting mechanism further emphasizes informative modalities, improving the overall quality of multi-modal feature fusion. For efficiency improvement, MBTF-NAS leverages zero-cost proxy metrics for architecture evaluation, enabling rapid identification of high-potential candidates while dramatically reducing computational overhead. We conducted a comprehensive evaluation of MBTF-NAS on seven representative multi-modal benchmarks. The experimental results demonstrate that MBTF-NAS consistently outperforms state-of-the-art approaches, highlighting its effectiveness and generalizability.

Neural architecture search-based multi-modal classification (NAS-MMC) aims to automatically find optimal network structures for improving the multi-modal classification performance. However, most current NAS-MMC methods are quite time-consuming during the training process. In this paper, we propose a knowledge sharing-based neural architecture search (KS-NAS) method for multi-modal classification. The KS-NAS optimizes the search process by introducing a dynamically updated knowledge base to reduce the consumption of computational resource. Specifically, during the deep evolutionary search, individuals in the initial population acquire initial parameters from a knowledge base, and then undergo training and optimization until convergence is reached, avoiding the need for training from scratch. The knowledge base is dynamically updated by aggregating the parameters of high-quality individuals trained within the population, thus progressively improving the quality of the knowledge base. As the population evolves, the knowledge base continues to optimize, ensuring that subsequent individuals can obtain higher-quality initialization parameters, which significantly accelerates the training speed of the population. Experimental results show that the KS-NAS method achieves state-of-the-art results in terms of classification performance and training efficiency across multiple popular multi-modal tasks.

ABSTRACT In practical engineering problems, uncertainties due to prediction errors and fluctuations in equipment efficiency often lead to constrained many‐objective optimization problem with interval parameters (ICMaOPs). These problems pose significant challenges for evolutionary algorithms, particularly in balancing solution convergence, diversity, feasibility, and uncertainty. To address these challenges, a personalized indicator‐based evolutionary algorithm (PI‐ICMaOEA) specifically designed for ICMaOPs is proposed. The PI‐ICMaOEA integrates a comprehensive quality indicator that encapsulates convergence, diversity, uncertainty, and feasibility factors, converting multiple objectives in high‐dimensional search spaces into a single evaluative metric. Each factor's weight is personalized assigned based on individual performance, objective dimension, and the evolving conditions of the population. By prioritizing individuals with excellent indicator values for mating and environmental selection, PI‐ICMaOEA effectively enhances selection pressure in high‐dimensional spaces. Comparative simulations demonstrate that PI‐ICMaOEA is highly competitive, offering a robust solution for balancing convergence, diversity, uncertainty, and feasibility in ICMaOPs.

ABSTRACT In the cloud computing environment, workflow scheduling presents a significant challenge due to the unpredictable and dynamic nature of user demands and cloud resources. To address the complexities of workflow scheduling, this paper introduces a dynamic multi‐objective workflow scheduling model that comprehensively considers task completion time, load balancing, as well as dynamic changes in power consumption and cost in real‐world scenarios. To effectively solve this model and better adapt to dynamic multi‐objective optimization problems, we propose a dynamic reference vector guided evolutionary algorithm (DRVEA). The proposed algorithm incorporates an adaptive random mutation strategy, which dynamically adjusts the evolutionary process based on changing optimization goals, thereby enhancing convergence and solution diversity. Experimental results, obtained from both workflow scheduling simulations and standard multi‐objective test environments, demonstrate that the proposed algorithm outperforms existing methods, achieving superior results in both solution quality and adaptability.

In FL-assisted Internet of Vehicles (IoV) system, joint vehicle scheduling and resource management have become an effective approach to improving Federated Learning (FL) communication efficiency. However, heterogeneity in data, varying computational capabilities, and limited resources among different vehicle devices lead to significant disparities in how frequently devices participate in FL and in their training performance. This generates unfairness during device selection, which in turn constrains overall system performance and the model’s generalization ability. To address these challenges, we propose a fairness-aware interval constrained many-objective optimization method for joint vehicle scheduling and bandwidth allocation. The proposed method considers factors such as device accuracy, latency, server utilization, and fairness in vehicle participation while satisfying energy consumption constraints. During FL parameter aggregation, a fairness-driven aggregation strategy is designed, which adjusts aggregation weights based on a fairness indicator. Additionally, we develop an indicator-driven multi-level interval constrained many-objective evolutionary algorithm (IM-ICMaOEA) to efficiently identify the Pareto Front that satisfies the constraints. Extensive simulation results demonstrate the effectiveness of the proposed method in terms of accuracy, device delay, energy consumption, and fairness in vehicle participation, significantly enhancing training efficiency in wireless channel environments. It provides significant scientific value and application potential in the field of the IoV.

In multi-modal classification tasks, a good fusion algorithm can effectively integrate and process multi-modal data, thereby significantly improving its performance. Researchers often focus on the design of complex fusion operators and have proposed numerous fusion operators, while paying less attention to the design of feature fusion usage, specifically how features should be fused to better facilitate multi-modal classification tasks. In this article, we propose a progressive skip reasoning fusion network (PSRFN) to make some attempts to address this issue. Firstly, unlike most existing multi-modal fusion methods that only use one fusion operator in a single stage to fuse all view features, PSRFN utilizes the progressive skip reasoning (PSR) block to fuse all views with a fusion operator at each layer. Specifically, each PSR block utilizes all view features and the fused features from the previous layer to jointly obtain the fused features for the current layer. Secondly, each PSR block utilizes a dual-weighted fusion strategy with learnable parameters to adaptively allocate weights during the fusion process. The first level of weighting assigns weights to each view feature, while the second level assigns weights to the fused features from the previous layer and the fused features obtained from the first level of weighting in the current layer. This strategy ensures that the PSR block can dynamically adjust the weights based on the actual contribution of features. Finally, to enable the model to fully utilize feature information from different levels for feature fusion, the skip connections are adopted between PSR blocks. Extensive experiment results on six real multi-modal datasets show that a better usage for fusion operator is indeed able to improve performance.

Summary With the rising adoption of the Internet of Things (IoT) across a variety of industries, malware is increasingly targeting the large number of IoT devices that lack adequate protection. Malware hunting is challenging in the IoT due to the variety of instruction set architectures of devices, as shown by the differences in the relevant characteristics of malware on different platforms. There are also serious concerns about resource utilization and privacy leaks in the development of conventional detection models. This study suggests a novel federated malware detection framework based on many‐objective optimization (FMDMO) for the IoT to overcome the problems. First, the framework provides a cross‐platform compatible basis with the federated mechanism as the backbone, while avoiding raw data sharing to improve privacy protection. Second, an intelligent optimization‐based client selection method is designed for four objectives: learning performance, architectural selection deviation, time consumption, and training stability, which leads malware detection to retain a high degree of cross‐architectural generalization while enhancing training efficiency. Based on a large IoT malware dataset we constructed, containing 62,515 malware samples across seven typical architectures, the FMDMO is evaluated comprehensively in three scenarios. The experimental results demonstrate the FMDMO substantially enhances the model's cross‐platform detection performance while preserving effective training and flexibility.

Summary Charging path planning in wireless sensor networks (WSNs) refers to designing an efficient charging path for sensor nodes in the network. However, most charging schemes mainly consider the planning of charging paths and pay little attention to the impact of uncertainties, such as road conditions and environment on the planning of charging paths, as well as ignoring the charging problem of new nodes in need of charging. Road conditions and the environment directly affect the energy consumption of wireless charging vehicles (WCVs) during traveling. To address the aforementioned challenges, this article proposes an interval many‐objective charging path scheme model, the WCV consumption is an uncertain value, it will change according to the environment, and road conditions, so we represent it as an interval parameter with upper and lower bounds. An interval high‐dimensional multi‐objective model with target energy consumption, path distance, number of dead nodes, and communication delay is constructed. Second, to implement this model, an interval SPEA2 algorithm (I‐SPEA2) that introduces an environmental response mechanism is proposed. I‐SPEA2 treats individual target interval values as ranges of values on a two‐dimensional coordinate axis, forming a quadrilateral, calculates individual size probabilities based on the area to determine the dominant relationship, and combines fixed distance and interval overlap to eliminate redundant individuals. The simulation results show that the interval dynamic model is effective in prolonging the lifecycle of WSN as well as the proposed algorithm reduces the mortality rate of the nodes by 15%, 28%, 13%, 16%, and 21% compared with other algorithms.

Stable operation of IoT systems in extreme environments is critical for infrastructures, including energy, aerospace, and healthcare. But resource-constrained devices are vulnerable to malware exploiting known weaknesses due to complex operating conditions and low-frequency device maintenance, and systems are at serious risk of failure or information leakage. However, automated security defense based on machine learning faces the challenges of low cross-architectural generalization and multidimensional data imbalance. We propose a many-objective-optimization-driven data balancing strategy for cross-architectural malware classification (MODSC) to address the above issues. MODSC constructs the optimization problem model for data balancing strategy search based on data set information, which focuses on rebalancing the data space in different dimensions, including category distribution and architectural distribution. The many-objective evolutionary algorithm (MaOEA-PBF), guided by the performance balance function, is then designed to solve the above model. The MODSC framework was tested on a group of IoT malware data sets with stepped imbalance rates containing six common architectures. The experimental results show that MODSC can both steadily and effectively improve cross-architectural generalization while maintaining a high level of confidence compared to popular data processing methods.

Epilepsy, one of the world's most common neurological diseases, impacts over 1% of the global population. Accurate early prediction of epileptic seizure has a great influence on epileptic patients' lives and attracted extensive attention. However, existing methods do not fully consider the complexity of multi-channel electroencephalogram (EEG) signal, which is the most common measurement for epileptic seizures. In this letter, we propose a Dynamic Functional Connectivity neural Network (DynFCNet) for epileptic seizure prediction. The proposed DynFCNet can discover dynamic brain functional connections and generate dynamic functional connectivity graphs, as well as extract non-Euclidean features from multi-channel EEG signals by Graph Convolutional Network (GCN). To take Euclidean features into consideration, Convolutional Neural Network (CNN) as one of the branches is also employed. Further, we incorporated both intra-group loss and inter-group loss to enhance our DynFCNet. Extensive experiments were implemented on a public multi-channel EEG dataset (CHB-MIT). The results confirm that our proposal outperforms the other competitors

Summary With the rapid development of big data, the explosive growth of data promotes the progress of the Internet of Things (IoT). Because it is hard for traditional cloud computing to meet vast computing tasks, scholars propose mobile edge computing (MEC) for the IoT. However, the mobility of users results in the instability of MEC performance. Besides, the conflict of interest between users and service providers needs to be balanced. To solve these problems, this paper constructs a virtual machine migration model based on many‐objective optimization (MaOVMMM). In MaOVMMM, four objectives are considered simultaneously: communication expense, computing expense, delay, and energy consumption. A many‐objective evolutionary algorithm with double population confrontation (MaOEA‐DPC) is suggested to support the MaOVMMM that is proposed. First, the population confrontation strategy is designed to better simulate the relationship between users and service providers. Second, the dynamic probability integration selection strategy is used to ensure the evolution ability of the algorithm. Simulation results demonstrate the effectiveness and superiority of MaOEA‐DPC when compared with other algorithms. This proposed approach can provide a superior virtual machine migration scheme for decision‐makers.

Summary With the number of services expanding in the Internet of Things (IoT), the limited resources of user terminals are insufficient to satisfy the computation needs of all running services. Therefore, we design a collaborative computation‐offloading model (CCOM) composed of multiple servers and task offloading modes to solve the problem by offloading tasks from resource‐constrained terminals to other computing entities, which achieves the following four objectives: model execution time minimization, task execution time minimization, energy consumption minimization, and most efficient device workload. And the global evaluation strategy based on angle and distance is proposed to address the individual selection problems caused by the overly localized Pareto dominance relationship and objective conflicts in the many‐objective evolutionary algorithms. In simulations, the strategy achieves the best Inverted Generation Distance (IGD) performance on 22 benchmark test problems based on Wilcoxon's rank sum statistical test and improves performance in the four objectives above by 18%, 31%, 20%, and 42%, respectively. Finally, we think that the strategy can provide adequate offloading performance for decision‐makers.

Summary Data imbalance and parameter selection have always been two important factors affecting the accuracy of software defect prediction. However, the existing methods have been poor in balancing these two factors. To address this challenge, a multi‐objective software defect prediction model is employed to describe the under sampled software defect prediction problem. And in this model, defect detection rate and defect false alarm rate are deemed as two objectives which should be optimized. Simultaneously, we design a novel multi‐objective immune optimization algorithm based on the comprehensive fitness of evaluation mechanism to effectively address the employed model. In the algorithm, the original mechanism based on neighborhood individual selection is replaced based on comprehensive fitness evaluation,which have better selection ability to attaining the predicted effect of software to improving in the process of selection solution of population evolution and further effectively help decision makers choose better scheme that meets requirements. In addition, in order to verify the effectiveness of the designed algorithm, the proposed algorithm is compared on eight different public data sets. Simulation results show that the proposed algorithm has better performance in handling with the multi‐objective under sampling software defect prediction problem.

Summary In many‐objective optimization algorithms, it is very important to maintain significant convergence and diversity of the population. And with the increasing demand in various fields, the optimization problem also becomes gradually complicated. Some existing many‐objective optimization algorithms are faced with challenges such as domination resistance and dimensional crisis. To solve these challenges, a many‐objective optimization algorithm based on dual criteria and mixed distribution correction strategy (MaOEA‐CSMDC) is proposed in this paper. To be specific, a matching selection strategy based on dual criteria combined by pareto domination strategy and achievement scalar function, which alleviates the domination resistance phenomenon and enhances the selection pressure of the algorithm. After that, an environment selection strategy based on equal probability mixed distribution correction is designed to better balance convergence and diversity. In this strategy, normal distribution, exponential distribution, and Cauchy distribution are introduced to adjust the weight of convergence and diversity in evolution by means of equal probability, so as to alleviate the problem that the conflict between them is intensified in the later stage of the algorithm. The experimental results show that, MaOEA‐CSMDC not only has advantages in convergence and diversity indicators, but also is more competitive in solving many‐objective optimization problems.

Summary With the rapid growth of malicious codes, personal privacy, and Internet security are seriously threatened. Existing transfer learning‐based malicious code detection improves detection accuracy by transferring pre‐trained neural networks. However, it cannot efficiently tune the structure and parameters of the neural networks. Here, we first propose a novel many‐objective transfer model. It mainly focuses on the detection accuracy and the total number of parameters of the neural network model. The optimal structure and parameters are captured from the pre‐trained neural network by many‐objective optimization algorithm. Second, the partitioned crossover‐mutation vector angle‐based evolutionary algorithm for unconstrained many‐objective optimization is proposed to solve the model. The algorithm performs crossover mutation operations in different ways on different regions of the candidate solution to improve population diversity. The simulation results show that the model can reduce the pre‐trained neural network structure by 49% while maintaining the accuracy in malicious code detection.

This article establishes an edge computing architecture based on blockchain sharding to apply blockchain technology at the edge layer. The tasks offloaded to the edge layer are performed by a set of edge server nodes for consensus operations, which improves the security of offloading. At the same time, the nodes and offloaded tasks are divided into multiple shards, and the typical practical Byzantine fault tolerance (PBFT) consensus is performed in each shard to improve scalability. In order to avoid the impact of malicious nodes in an unreasonable sharding scheme on network security and performance, we model the many-objective optimization sharding problems, which includes reducing consensus latency, energy consumption, sharding failure probability, and improving sharding throughput. Moreover, we design a many-objective evolutionary algorithm based on information entropy (MaOEA-IE) to solve the model. In the process of population environment selection, the distribution information of individuals is mapped to a Gaussian function, and we aggregate the distribution functions of all individuals and calculate the information entropy to measure the distribution of the population. The simulation results of benchmark test problems and model solving problems show that the solution set of MaOEA-IE has the best convergence, diversity, and comprehensive performance. This article provides an idea for the formulation of blockchain sharding scheme.

Cloud platforms scheduling resources based on the demand of the tasks submitted by the users, is critical to the cloud provider's interest and customer satisfaction. In this paper, we propose a multi-objective cloud task scheduling algorithm based on an evolutionary multi-factorial optimization algorithm. First, we choose execution time, execution cost, and virtual machines load balancing as the objective functions to construct a multi-objective cloud task scheduling model. Second, the multi-factor optimization (MFO) technique is applied to the task scheduling problem, and the task scheduling characteristics are combined with the multi-objective multi-factor optimization (MO-MFO) algorithm to construct an assisted optimization task. Finally, a dynamic adaptive transfer strategy is designed to determine the similarity between tasks according to the degree of overlap of the MFO problem and to control the intensity of knowledge transfer. The results of simulation experiments on the cloud task test dataset show that our method significantly improves scheduling efficiency, compared with other evolutionary algorithms (EAs), the scheduling method simplifies the decomposition of complex problems by a multi-factor approach, while using knowledge transfer to share the convergence direction among sub-populations, which can find the optimal solution interval more quickly and achieve the best results among all objective functions.

As an application area of social computing, social recommendation aims to exploit the richness of social relationships to improve recommendation accuracy. Current research mainly considers social information that can be directly observed, with little attention to indirect social relationships between users or the explainability of social recommendation results. To address this challenge, this article proposes a knowledge graph-based many-objective model for explainable social recommendation (KGMESR) by considering the explainability, accuracy, novelty, and content quality of social recommendation results. The model takes advantage of social behavior information to calculate user similarity and quantifies the explainability of social recommendation results using entity vectors and embedding vectors. To ensure model efficiency, a many-objective recommendation algorithm based on the partition deletion strategy is designed. It employs the association of individuals with the nearest reference vector to render the diversity of the population and then obtains the final solution by deleting poorly converged individuals in each partition. Experimental results show that many-objective optimization recommendation algorithm based on partition deletion strategy (MaOEA-PDS) allows for preferable recommendation results for users in real datasets. The explainability of the proposed model is demonstrated by two case studies.

The rapid progress of artificial intelligence expands its wide applicability in Internet of Things (IoT). Meanwhile, data insufficient and data source privacy are key supply chain challenges facing IoT especially in the healthcare industry. To address this problem in healthcare IoT, in this article, we propose a skin cancer detection model based on federated learning integrated with deep generation model. First, we employ dual generative adversarial networks to address the problem of insufficient data. In addition, to improve the quality of generated images, we synchronously optimize the sharpness of images, Frechet inception distance, image diversity, and loss using knee point-driven evolutionary algorithm (KnEA). Then, we protect patient information privacy by training federated skin cancer framework. Finally, we employ the ISIC 2018 dataset to test the performance of the proposed training model under different situations, including using identically distributed data, nonidentically distributed data, a sparse convolutional neural network, and a fully connected convolutional neural network. The experiment results demonstrate that the accuracy and area under the curve reach 91% and 88%, respectively. This model can help resolve problems of insufficient data in smart medicine of IoT and protect the privacy of user data while also providing an excellent detection rate.

Abstract Malicious code, which is used to threaten network security, has been improved by many methods and strategies. However, the use of unreasonable deep learning models and single‐objective algorithms often affects the accuracy of data classification. Moreover, as an optimization problem, the existence of low‐quality datasets (imbalanced datasets) constrains the training effect of neural network models. Therefore, it is a big challenge to effectively design data processing methods and suitable training models. To enhance the robustness of the model and obtain better data classification results, it is essential to develop an efficient training model and strategy. To resolve this problem, a novel multi‐objective convolution restricted Boltzmann machine (CRBM) model based on the spatial pyramid pooling strategy is proposed to identify images and classify data in this study. Moreover, a fast nondominated sorting genetic algorithm based on the constraint‐dividing crossover strategy (CDCS‐NSGA‐II) is designed to optimize the imbalance datasets of the malware families. Extensive experimental results show that the multi‐objective CRBM model designed in this study combined with the CDCS‐NSGA‐II algorithm can effectively enhance the learning ability of the dataset, increase the effect of data classification and improve the robustness of the model.

Summary The problem of convergence and diversity in the course of population evolution is difficult to be balanced for solving the many‐objective optimization problem (MaOP). To track with the problem, a many‐objective optimization algorithm is designed. In the algorithm, a hybrid selection mechanism under the concurrent integration strategy is built to improve algorithm performance by employing the different selection operators. The concurrent integration strategy can select the suitable operator to balance the convergence and diversity of the solution in the course of the population evolutionary. To verify the effectiveness of the algorithm, the designed algorithm is compared with other five excellent many‐objective algorithms on DTLZ and WFG test problem. What is more, the designed algorithm is applied to solve the coal green production optimization problem. The simulation results show that the performance of designed algorithm is superior to whether the DTLZ and WFG test problem or the application problem.

Summary Privacy data security has become an important bottleneck for the overall development of artificial intelligence and a key challenge that needs to be broken in the Internet era. The current research mainly considers differential privacy to effectively protect the private information in the data. However, as the noise increases, the precision of the training model will decrease. In order to solve above problem, an adaptive differential privacy (ADP) method is constructed and applied to deep neural networks. ADP adds noise adaptively in the training process according to the importance of features. We also build the differential privacy multi‐objective optimization model (DPMOM). DPMOM adopts multi‐objective optimization characteristics, takes accuracy and privacy protection as the optimization objectives. It optimizes the super parameters of deep neural networks and the noise of differential privacy. In addition, to better solve the ADP model, with the NSGA‐II algorithm as the basic framework, a multi‐objective optimization algorithm based on differential privacy protection (DPPMOA) is designed. Simulation experiments show that compared with other machine learning methods and differentially private stochastic gradient descent, the accuracy of ADP is higher under the same amount of noise. Through comparison with NSGA‐II, IBEA, PESA‐II, and AGE‐II, DPPMOA is proved that the solution set of this algorithm is better.

The Internet-of-Things (IoT) technology is widely used in various fields. In the Earth observation system, hyperspectral images (HSIs) are acquired by hyperspectral sensors and always transmitted to the cloud for analysis. In order to reduce cost and reply promptly, we deploy artificial intelligence (AI) models for data analysis on edge servers. Subspace clustering, the core of the AI model, is employed to analyze high-dimensional image data such as HSIs. However, most traditional subspace clustering algorithms construct a single model, which can be affected by noise more easily. It hardly balances the sparsity and connectivity of the representation coefficient matrix. Therefore, we proposed a postprocess strategy of subspace clustering for taking account of sparsity and connectivity. First, we define close neighbors as having more common neighbors and higher coefficients neighbors, where the close neighbors are selected according to the nondominated sorting algorithm. Second, the coefficients between the sample and close neighbors are reserved, incorrect, or useless connections are pruned. Then, the postprocess strategy can reserve the intrasubspace connection and prune the intersubspace connection. In experiments, we verified the universality and effectiveness of postprocessing strategies in the traditional image recognition field and IoT field, respectively. The experiment results demonstrate that the proposed strategy can process noise data in the IoT to improve clustering accuracy.

The traditional coal energy system cannot meet the requirements of modern industrial production for sustainable development because extensive economic growth has caused significant coal consumption. Therefore, it is particularly important to formulate an effective coal production decision-making scheme to support complex coal production systems for sustainable development. To address this challenge, an improved many-objective fuzzy decision-making model with human participation for coal production prediction is established in this article. The model includes five objective functions: economic, energetic, environmental, coal gangue, and safety profits. Moreover, a novel multistage many-objective optimization algorithm is designed to adjust relevant model parameters and make the obtained model solution more accurate when compared with involved algorithms. In the algorithm, there are three stages of optimization. In stage one, the model with the relatively good convergence solution is chosen. In stage two, the diversity of the model solution needs to be retained by employing a diversity maintenance mechanism. In stage three, a comprehensive measurement approach is designed to ensure the balance of convergence and diversity during population evolution. To verify the validity of the model and the superiority of the optimization algorithm, five other advanced many-objective algorithms are used for comparison. The results from simulations on a benchmark function show that the proposed optimization algorithm has better performance than involved algorithms. Model solutions obtained on different metrics have better convergence and diversity for the coal fuzzy decision-making problem.

While the industrial Internet of Things (IIoT) can support efficient control of the physical world through large amounts of industrial data, data security has been a challenge due to various interconnections and accesses. Blockchain technology can support security and privacy preservation in IIoT data with its trusted and reliable security mechanism. Sharding technology can help improve the overall throughput and scalability of blockchain networks. However, the effectiveness of sharding is still challenging due to the uneven distribution of malicious nodes. By aiming to improve the performance of blockchain networks and reduce the possibility of malicious node aggregation, in this article, we propose a many-objective optimization algorithm based on the dynamic reward and penalty mechanism (MaOEA-DRP) to optimize the shard validation validity model. Then, an optimal blockchain sharding scheme is obtained. Compared with other state-of-the-art many-objective optimization algorithms, MaOEA-DRP performs better on the DTLZ test suite. The simulation results demonstrate that our proposed algorithm can significantly improve the throughput and validity of sharding for better security in the blockchain-enabled IIoT.

Summary Both the problem of class imbalance in datasets and parameter selection of Support Vector Machine (SVM) are crucial to predict software defects. However, there is no one working to solve these problems synchronously at present. To tackle this problem, a hybrid multi‐objective cuckoo search under‐sampled software defect prediction model based on SVM (HMOCS‐US‐SVM) is proposed to solve synchronously above two problems. Firstly, a hybrid multi‐objective cuckoo search with dynamical local search (HMOCS) is utilized to select synchronously the non‐defective sampling and optimize the parameters of SVM. Then, three under‐sampled methods for decision region range are proposed to select the non‐defective modules. In the simulation, the three indicators, including the false positive rate (pf), the probability of detection (pd), and G‐mean, are employed to measure the performance of the proposed algorithm. In addition, eight datasets from Promise database are selected to verify the proposed software defect predication model. Comparing with the result of eight prediction models, the proposed method comes into effect on solving software defect prediction problem.

Abstract Currently the generative adversarial networks (GANs) have rapidly become a popular research hotspot that people concerned and have been applied to various fields. Lots of meaningful work have been proposed and various variants of GANs sprung up in last few years. The scholars usually design GAN structure like the layers and hyperparameters setting according to the experience and constantly attempts. For the propose of finding the appropriate structure more conveniently and efficiently. A method with multiobjective algorithm is proposed to obtain the optimal structure for the GANs. In the proposed method, the nondominated sorting genetic algorithm II (NSGA‐II) is utilized to optimize the hyperparameters and structure of deep convolutional generative adversarial network (DCGAN). The experiments are conducted on MNIST and Malware datasets demonstrate the efficiency and high performance of proposed method.

Summary Distance vector‐hop (DVHop), as a range‐independent positioning algorithm, is a significant positioning method in wireless sensor networks (WSNs). It is composed of three parts, including connectivity detection, distance estimation, and position estimation. However, this simple positioning method results in a larger positioning error. Therefore, to enhance the positioning precision, this paper investigates the characteristic of error distribution between the estimated and real distance in the DVHop algorithm and reveals that the error is subjecting to the Gaussian distribution, N∼(0,1/3CR). Furthermore, to improve positioning accuracy, we propose a Gaussian error correction multi‐objective positioning model with non‐dominated sorting (NSGA‐II), which named GGAII‐DVHop. Finally, this model is tested on three complex network topologies, and the results demonstrate that it is significantly superior to other four algorithms in both positioning precision and robustness.

Recommendation technology is an important part of the Internet of Things (IoT) services, which can provide better service for users and help users get information anytime, anywhere. However, the traditional recommendation algorithms cannot meet user's fast and accurate recommended requirements in the IoT environment. In the face of a large-volume data, the method of finding neighborhood by comparing whole user information will result in a low recommendation efficiency. In addition, the traditional recommendation system ignores the inherent connection between user's preference and time. In reality, the interest of the user varies over time. Recommendation system should provide users accurate and fast with the change of time. To address this, we propose a novel recommendation model based on time correlation coefficient and an improved K-means with cuckoo search (CSK-means), called TCCF. The clustering method can cluster similar users together for further quick and accurate recommendation. Moreover, an effective and personalized recommendation model based on preference pattern (PTCCF) is designed to improve the quality of TCCF. It can provide a higher quality recommendation by analyzing the user's behaviors. The extensive experiments are conducted on two real datasets of MovieLens and Douban, and the precision of our model have improved about 5.2 percent compared with the MCoC model. Systematic experimental results have demonstrated our models TCCF and PTCCF are effective for IoT scenarios.

Internet of Things (IoT) equipment is usually in a harsh environment, and its security has always been a widely concerned issue. Node identity authentication is an important means to ensure its security. Traditional IoT identity authentication protocols usually rely on trusted third parties. However, many IoT environments do not allow such conditions, and are prone to single point failure. Blockchain technology with decentralization features provides a new solution for distributed IoT system. In this paper, a blockchain based multi-WSN authentication scheme for IoT is proposed. The nodes of IoT are divided into base stations, cluster head nodes and ordinary nodes according to their capability differences, which are formed to a hierarchical network. A blockchain network is constructed among different types of nodes to form a hybrid blockchain model, including local chain and public chain. In this hybrid model, nodes identity mutual authentication in various communication scenarios is realized, ordinary node identity authentication operation is accomplished by local blockchain, and cluster head node identity authentication are realized in public blockchain. The analysis of security and performance shows that the scheme has comprehensive security and better performance.

Ensemble learning is a popular machine learning technique, which employs multiple learning methods to obtain better performance than any single constituent method. Recently, ensemble learning was successfully used in several bio-inspired optimization algorithms to achieve good performance. Artificial bee colony (ABC) is an efficient optimization technique inspired by the social behavior of bees. To enhance the optimization ability of ABC, this paper proposes a new ABC variant based on ensemble learning. The proposed approach is called multi-strategy and dimension perturbation ensemble of ABC (MPEABC), in which multiple distinct solution search strategies are used to balance the exploration and exploitation. To accelerate the search, each solution search strategy is assigned an independent probability to control the frequency of dimension perturbation. To avoid manually setting the probability, an adaptive method is used to dynamically adjust its value. Experimental verifications are conducted on a set of well-known benchmark functions. Results show that MPEABC achieves better solutions than the standard ABC, multi-strategy ensemble ABC (MEABC) and several improved ABC variants.

Summary It is difficult to protect users' privacy and to process private information due to the complexity and uncertainty of such information. To protect private information quickly and accurately, a many‐objective optimization algorithm framework based on the hybrid elite selection strategy is proposed in this paper. First, a mating selection mechanism combined with the achievement scale function and angle information index is used to generate elite offspring of the internal population. Then, the balanceable fitness estimation method is employed to select and update the external archive. To test performance, the proposed algorithm is tested on many‐objective optimization problems (MaOPs) and compared with five state‐of‐the‐art algorithms. Experimental simulation results show that the proposed algorithm is more effective in solving MaOPs and can inspire development of a better privacy protection strategy.

With the development of the Internet, malicious code attacks have increased exponentially, with malicious code variants ranking as a key threat to Internet security. The ability to detect variants of malicious code is critical for protection against security breaches, data theft, and other dangers. Current methods for recognizing malicious code have demonstrated poor detection accuracy and low detection speeds. This paper proposed a novel method that used deep learning to improve the detection of malware variants. In prior research, deep learning demonstrated excellent performance in image recognition. To implement our proposed detection method, we converted the malicious code into grayscale images. Then, the images were identified and classified using a convolutional neural network (CNN) that could extract the features of the malware images automatically. In addition, we utilized a bat algorithm to address the data imbalance among different malware families. To test our approach, we conducted a series of experiments on malware image data from Vision Research Lab. The experimental results demonstrated that our model achieved good accuracy and speed as compared with other malware detection models.

Recently, inspired by the human brainstorming process, a new kind of metaheuristic algorithm, called brain storm optimization (BSO) algorithm was proposed for global optimization. Experimental results have shown its excellent performance when solving optimization problems. In order to further improve the search ability of the BSO, this paper proposes an improved BSO (IBSO) algorithm by introducing graph theory into it. In IBSO, new individuals will be generated to replace some old individuals when the BSO algorithm is in a poor status. Whether a BSO algorithm is in a poor status is determined by the length of Hamiltonian cycle, which can be obtained by transferring all the individuals into an undirected weight graph. A Hamiltonian cycle and its length will be computed according to a modified cycle algorithm. The proposed IBSO algorithm is tested on twelve benchmarks, and the experimental results illustrate its effectiveness.

This special issue of Fundamenta Informaticae focuses on the foundations and applications of Cognitive Informatics and Computational Intelligence (briefly, CI2).CI2 focuses on studies of human information processing as well as the byproducts of perception and cognition.Cognitive Informatics (CI) is a multidisciplinary study of cognition, computing and information sciences which investigates the information processing mechanisms and processes of the brain and natural intelligence, as well as their engineering applications in cognitive computing.Specifically, CI2 provides a coherent set of fundamental theories and contemporary mathematics that form the foundation for most science and engineering disciplines such as applied mathematics (e.g., perceptual forms of fuzzy sets, near sets and rough sets), computer science, cognitive science, computer engineering (e.g., computer vision), cybernetics (e.g., machine behavior), neuropsychology and pure mathematics (e.g., proximity spaces, topological spaces via near and far).This special issue presents some of the latest advances in cognitive informatics and cognitive computing.A total of 11 papers were accepted for publication.Each accepted paper has undergone a thorough review (at least two reviewers for each paper) and a second round of review and revision cycle.The paper by M.H-Herrero, P. Rabanal, I. Rodríguez, and F. Rubio on Comparing Problem Solving Strategies for NP-hard Optimization Problems, present analysis of performance of humans when solving NP-complete problems.These analyses are supported by experiments which include the human capability to compute good suboptimal solutions to these problems, and the authors try to identify the kind of problem instances which make humans compute the best and worst solutions (including the dependance of their performance on the size of problem instances).Finally, their performance with computational heuristics typically used to approximately solve these problems are compared, and participants in these experiments are also interviewed in order to infer the most typical strategies used by them, as well as how these strategies depend on the form and size of problem instances.The paper by G. Virginia and H.S. Nguyen on Lexicon-based Document Representation, is based on tolerance rough sets model(TRSM) to model document-term relations in text mining.Specifically, this representation maps the terms occurring in TRSM-representation to terms in the lexicon, hence the final representation of a document is a weight vector consisting only of terms that occurred in the lexicon (lexicon-representation).The lexicon-representation can be viewed as a compact form of TRSM-v-viii v

Integral-controlled particle swarm optimization (ICPSO) is an effective variant of particle swarm optimization (PSO) aiming to increase the population diversity. Due to the additional accelerator items, the behavior of ICPSO is more complex, and provides more chances to escaping from a local optimum than the standard version of PSO. However, many experimental results show the performance of ICPSO is not always well because of the particles' un-controlled movements. Therefore, a new variant, integral particle swarm optimization with dispersed accelerator information (IPSO-DAI) is designed to improve the computational efficiency. In IPSO-DAI, a predefined predicted velocity index is introduced to guide the moving direction. If the average velocity of one particle is superior to the index value, it will choice a convergent manner, otherwise, a divergent manner is employed. Furthermore, the choice of convergent manner or divergent manner for each particle is associated with its performance to fit different living experiences. Simulation results show the proposed variant is more effective than other three variants of particle swarm optimization especially for multi-modal numerical problems. The IPSO-DAI algorithm is also applied to directing the orbits of discrete chaotic dynamical systems by adding small bounded perturbations, and achieves the best performance among four different variants of PSO.

In standard particle swarm optimization (PSO), the velocity only provides a position displacement contrast with the longer computational time. To avoid premature convergence, a new modified PSO is proposed in which the velocity considered as a predictor, while the position considered as a corrector. The algorithm gives some balance between global and local search capability, and results the high computational efficiency. The optimization computing of some examples is made to show the new algorithm has better global search capacity and rapid convergence rate.

Particle swarm optimizer is a novel algorithm where a population of candidate problem solution vectors evolves "social" norms by being influenced by their topological neighbors. The standard particle swarm optimizer (PSO) may prematurely converge on suboptimal solutions that are not even guaranteed to be local extrema. A new particle swarm optimizer, called stochastic PSO (SPSO), which combined with tabu technique is presented based on the analysis of the standard PSO. And because of its local search capability, the SPSO is more efficient. And the global convergence analysis is made using the F. Solis and R. Wets' research results. Finally, several examples are simulated to show that SPSO is more efficient than the standard PSO.

Particle swarm optimizer (PSO) is a new evolutionary computation method, which has been successfully applied to many fields. Through mechanism analysis of the standard particle swarm optimizer, a linear equivalent representation of the velocity update equation is given. Thus a new particle swarm optimizer-nonlinear particle swarm optimizer (NPSO) is described in this paper. It can dynamically adjust the limit position that distribute within the ellipse located by the best positions of the population and itself, and drop out of the local minimum point. The simulation results show the correctness and efficiency of the presented methods.

Through mechanism analysis of genetic algorithm (GAs), every genetic operator of SGA and their combination action can be considered as linear transformations to the corresponding individuals. By modifying the traditional genetic operators, the nonlinear genetic algorithm (NGA) is introduced. In this paper, abstract model of NGA based on function group is discussed in which every function is selected with some probability, and if the function group is correctly selected, then the algorithm can be convergent to global optimal within every given generation number. With this technique the premature convergence and calculation efficiency may be solved.

Through mechanism analysis of simple genetic algorithm (SGA) every genetic operator can be considered as a linear transform. So some disadvantages of SGA may be solved if genetic operators are modified to nonlinear transforms. According to the above method, nonlinear genetic algorithm is introduced, and different nonlinear genetic operators with some probability are designed and applied to numerical optimization problems. The optimization computing of some examples is made to show that the new genetic algorithm is useful and simple.