The Industrial Internet of Things (IIoT) enhances production efficiency through inter-factory resource sharing and intelligent human-machine interaction (HMI) in flexible manufacturing. This study addresses large-scale multiobjective resource scheduling optimization in the complex IIoT environments to improve production efficiency and resource scheduling under growing customization and order demands. We develop a multiobjective IIoT scheduling model under assumptions of task priority and resource constraints, optimizing makespan, logistics time, energy consumption, tardiness time, production cost, and carbon emission. To improve resource scheduling performance, a fuzzy decision-enhanced dual directed sampling-assisted large-scale multiobjective optimization algorithm (LMOEA-FDDS) is proposed. The algorithm employs a dual directed sampling method, uses two different types of search directions to guide the population evolution, and combines a complementary environmental selection strategy based on angle penalty distance (APD), effectively improving the algorithms search eiciency and performance. Experimental results show that LMOEA-FDDS achieves 30%-70% higher HV values than state-of-the-art algorithms, demonstrating its effectiveness in solving complex IIoT scheduling problems.

Neural Architecture Search (NAS) requires global topological exploration and is hence time consuming. To address this challenge, we propose the comprehensive-forecast multiobjective genetic programming for NAS, or CFMOGP-NAS for short. By integrating the strengths of various regression models and synthesizing the forecast of multiple candidates, the accuracy and robustness of architecture predictions are enhanced. The resultant algorithm this way incorporates a strategy of a mixture of complete and partial training, which balances cost and accuracy of evaluation. To also balance the population diversity, we develop a regularized tournament scheme for genetic programming. Experimental studies show that CFMOGP-NAS achieves a 50% reduction in search time without sacrificing accuracy, and verify that it substantially improves efficacy and efficiency compared with the state-of-the-art NAS methods.

This article proposes a cloud-edge–terminal collaborative resource allocation architecture that efficiently allocates resources. Traditional resource allocation often focuses solely on optimizing delay and service cost, making it less suitable for intensive real-world scenarios. In response, a comprehensive multiobjective resource allocation model is developed, encompassing delay, service cost, load balancing, and resource utilization. This article proposes a diversity-filling large-scale multiobjective evolutionary algorithm based on generative adversarial networks (DFGAN-LSMOEA). The Otsu-based grouping method in DFGAN-LSMOEA is employed to group decision variables and improve optimization performance. Compared with state-of-the-art algorithms, the proposed method validates its effectiveness and advantages in the applications, particularly when handling high-dimensional decision variables and dynamic demands.

Deep learning has made remarkable achievements in many fields. However, although fuzzy neural networks with natural interpretability are widely used in prediction and control scenarios, there are very few studies on the deepening of fuzzy systems. By integrating rough set theory, fuzzy rough neural network has unique advantages benefiting from the complementarity of the fuzzy set theory and the rough set theory as well as the powerful learning ability of neural networks. Similarly, research on deep fuzzy rough neural networks is even rarer. In this article, in order to improve the performance of the fuzzy rough neural network and expand its application range, the deep fuzzy rough neural network model is constructed and optimized by stacking blocks of fuzzy rough neural network to imitate the deepening deep neural network based on multiobjective evolution. Each fuzzy rough neural network block is interpretable, and its stacked architecture also has high interpretability. To automatically generate deep fuzzy rough neural network models with high efficiency, a distributed parallel multiobjective neuroevolution framework is developed, thus blocks can be stacked flexibly and deep architecture can be optimized considering multiple optimization objectives of accuracy, interpretability, and generalization simultaneously. In addition, multiobjective evolution is combined with Wang–Mendel method, pseudoinverse, and backpropagation to effectively learn specific parameters. Finally, based on the time series prediction problems, the superiority of the multiobjective deep fuzzy rough neural network evolutionary framework is verified.

The rapid expansion of intelligent vehicles in 6G networks has intensified the demand for real-time task processing. However, traditional cloud-edge collaboration models for large-scale vehicle task offloading are increasingly inadequate to address the growing complexity and demands. To address this challenge, we propose a unified cloud-edge-end collaborative vehicle task offloading multiobjective optimization model for large-scale vehicle task offloading, which simultaneously considers four optimization objectives: latency, energy consumption, load balancing and quality of service (QoS). To solve the large-scale multiobjective optimization problem, we propose a large-scale multiobjective evolutionary algorithm based on problem transformation and bidirectional vectors (LSMOEA-PTBV). Experiments in a simulated 6G vehicular network demonstrate that LSMOEA-PTBV outperforms state-of-the-art methods. Our work enhances the end-user experience, meets the increasingly complex demands of modern applications, and advances the development of integrated sensing and computing systems and intelligent transportation systems in the 6G era.

The sensing-computing integrated chips and systems can be used for intelligent transportation to process and acquire traffic data. Traffic data can be used to effectively forecast real-time traffic flow at a specific future time, which is crucial for promoting efficient transportation systems and supporting economic development in the era of 6G. However, traditional real-time traffic flow prediction models exhibit poor performance when dealing with noise, uncertainty, and nonlinear data. To address this issue, this paper constructs a deep fuzzy rough neural network model based on large-scale multiobjective optimization algorithm(LMO-DFRNN) for real-time traffic flow prediction. By simultaneously optimizing multiple objectives, the model achieves an optimal balance between performance and simplicity in traffic flow tasks. To improve the model’s accuracy and adaptability in real-time traffic flow forecasting, this study presents a large-scale multiobjective optimization method that uses a state-information-based dynamic balancing evaluation strategy. The evaluation method comprises diversity and convergence, each corresponding to a specific factor. By dynamically adjusting the weights of two factors based on the individual performance on diversity and convergence, a balance between these two indicators is achieved. The experiments were conducted by using real-world traffic flow datasets, and the findings reveal that, in comparison with five advanced models, the proposed model achieved reductions in the evaluation metrics MAE, RMSE and MAPE by 43.73%, 46.22%, and 34.87% respectively.

In vehicular edge computing (VEC), vehicle users (VUs) can offload their computation-intensive tasks to edge server (ES) that provides additional computation resources. Due to the edge server being closer to VUs, the propagation delay between the ESs and the VUs is lower compared to cloud computing. Applying digital twin to VEC allows for low-cost trial in task offloading. In real-word, the mobility of VUs cannot be ignored and the downlink delay in receiving process results from ES is related to the mobility of VUs. Therefore, a five-objective optimization model including downlink delay, computation delay, energy consumption, load balancing, and user satisfaction of the VUs is constructed. To solve the above model, an improved CMA-ES algorithm based on the guiding point (GP-CMA-ES) is proposed. When the number of VUs increases, the dimension of variables also increases. Therefore, a convergence-related variable grouping strategy based on the relationship detection between variables and objectives is proposed. The performance of algorithm GP-CMA-ES is compared with five algorithms in the digital twin environment.

The wide area measurement system (WAMS) based on synchronous phasor measurement technology plays an increasingly important role in dynamic monitoring and wide area protection of modern power systems. If the phasor measurement unit (PMU) is placed on all buses of the power system, the voltage and branch current of all buses can be directly observed. However, due to the high placement cost of PMU and its ability to measure the voltage phasor of the installed bus and the current of the associated branch, it is unrealistic and unnecessary to install PMU on all buses of the system. This article discusses the incomplete observability under single PMU loss (N-1) contingencies and its effect on PMUs placement. An improved two-archive algorithm is proposed to solve the five-objective placement optimization model. In addition, a fuzzy decision-making method combining subjective and objective is proposed to help power grid enterprises select the most appropriate solution. The proposed method is tested on several IEEE bus systems and Polish 2383-bus system, and the test results verify its effectiveness.

The space–air–ground-integrated network (SAGIN) can enhance the performance of the Internet of Vehicles (IoV). However, the basic hardware differences among communication systems are large, which leads to communication difficulties between different communication systems. To effectively manage multiple communication networks (satellite networks, air networks, and terrestrial networks) and computing resources in IoV, this article proposes a SAGIN-IoV edge–cloud architecture based on software-defined networking (SDN) and network function virtualization (NFV). In addition, we construct an optimization model based on SAGIN-IoV’s service requirements, and propose an improved algorithm. Experimental results show that the improved algorithm can effectively optimize the resource scheduling problem of SAGIN-IoV.

Recommender systems are of great significance for mining the data generated by the Internet of Things (IoT) and are important for the intelligent IoT systems. The traditional recommendation algorithms only consider the accuracy as the optimization objective. In this article, a many-objective optimization model consisting of the F1 measure, recommendation novelty, recommendation coverage, customer satisfaction, landmark similarity, and overfitting is constructed for recommendation. Then, to improve the recommendation performance, we propose to use a large-scale many-objective optimization algorithm based on problem transformation (LSMaOA) to optimize the matrix factorization model for the recommender system in the intelligent IoT systems. The experimental results show that LSMaOA is robust and can effectively optimize the model’s six objectives. Compared with the knee point-driven evolutionary algorithm (KnEA), the grid-based evolutionary algorithm (GrEA), the large-scale multiobjective optimization framework (LSMOF), and the reference vector guided evolutionary algorithm (RVEA), the proposed algorithm can promote the F1 measure by 7.78%, 13.63%, 21.85%, and 28.63%, respectively.

The fuzzy logic-based neural network usually forms fuzzy rules via multiplying the input membership degrees, which lacks expressiveness and flexibility. In this article, a novel neural network model is designed by integrating the gene expression programming into the interval type-2 fuzzy rough neural network, aiming to generate fuzzy rules with more expressiveness utilizing various logical operators. The network training is regarded as a multiobjective optimization problem through simultaneously considering network precision, explainability, and generalization. Specifically, the network complexity can be minimized to generate concise and few fuzzy rules for improving the network explainability. Inspired by the extreme learning machine and the broad learning system, an enhanced distributed parallel multiobjective evolutionary algorithm is proposed. This evolutionary algorithm can flexibly explore the forms of fuzzy rules, and the weight refinement of the final layer can significantly improve precision and convergence by solving the pseudoinverse. Experimental results show that the proposed multiobjective evolutionary network framework is superior in both effectiveness and explainability.

The sensor nodes in wireless sensor networks have the deficiency of limited energy, and the multihop transmission of information will lead to a premature paralysis of nodes near the sink. The use of the mobile sink can balance the energy consumption and greatly prolong the lifetime. Therefore, this article studies the scheduling strategy of multiple mobile sinks and proposes a heuristic strategy based on interval type-2 fuzzy rough neural network. The energy and lifetime of sensor nodes, as well as location information of the mobile sink and special nodes are taken as input features. Through neural network learning, the outputs determine whether to move, moving direction, moving distance, and residence time, which can complete the scheduling task. The scheduling problem is regarded as a multiobjective optimization problem, and the network lifetime, the moving path length, and the network interpretability are optimized at the same time, so as to obtain a lightweight network with good interpretability and performance. Based on the parallel multiobjective evolutionary algorithm, a multiobjective neural evolutionary framework is constructed. This framework can balance multiple objectives and complete complex scheduling tasks. Compared with static sinks, random-moving sinks, sinks with manually designed strategy, gene expression programming-based sinks, as well as the other state-of-the-art multiobjective evolutionary algorithms, the proposed framework can achieve superior results.

Medical data widely exist in the hospital and personal life, usually across institutions and regions. They have essential diagnostic value and therapeutic significance. The disclosure of patient information causes people’s panic, therefore, medical data security solution is very crucial for intelligent health care. The emergence of federated learning (FL) provides an effective solution, which only transmits model parameters, breaking through the bottleneck of medical data sharing, protecting data security, and avoiding economic losses. Meanwhile, the neural architecture search (NAS) has become a popular method to automatically search the optimal neural architecture for solving complex practical problems. However, few papers have combined the FL and NAS for simultaneous privacy protection and model architecture selection. Convolutional neural network (CNN) has outstanding performance in the image recognition field. Combining CNN and fuzzy rough sets can effectively improve the interpretability of deep neural networks. This article aims to develop a multiobjective convolutional interval type-2 fuzzy rough FL model based on NAS (CIT2FR-FL-NAS) for medical data security with an improved multiobjective evolutionary algorithm. We test the proposed framework on the LC25000 lung and colon histopathological image dataset. Experimental verification demonstrates that the designed multiobjective CIT2FR-FL-NAS framework can achieve high accuracy superior to state-of-the-art models and reduce network complexity under the condition of protecting medical data security.

The traditional deployment research on wireless sensor networks (WSNs) has mainly focused on 2D plane and 3D full space; also, the sensors considered are almost always omni-directional sensors and are usually homogeneous. However, this type of research cannot fulfill the diverse requirements required for practical 3D environment. We study the deployment problem of heterogeneous directional sensor networks (HDSNs) on 3D terrain, which is more suitable for practical security monitoring requirements and has more practical significance. In this paper, we propose a novel uncertain comprehensive coverage model: a modified 3D directional sensing model is presented, and a non-probabilistic measure based fusion operator is utilized. We transform the deployment problem into a multiobjective optimization problem by comprehensively considering Coverage, Connectivity Uniformity and Deployment Cost, and we use various state-of-the-art multiobjective optimization algorithm based deployment approaches to address it. We conduct deployment experiments on three types of real-world 3D terrain data (plain, hill and mountain). Through the analysis of the deployment results, we obtain a deeper understanding and insight into the multiobjective deployment problem of HDSN. Meanwhile, we more clearly recognize the characteristics of the deployment approaches.

The development of smart cities and the emergence of three-dimensional (3-D) urban terrain data have introduced new requirements and issues to the research on the 3-D deployment of wireless sensor networks. We study the deployment issue of heterogeneous wireless directional sensor networks in 3-D smart cities. Traditionally, studies on the deployment problem of WSNs focus on omnidirectional sensors on a 2-D plane or in full 3-D space. Based on 3-D urban terrain data, we transform the deployment problem into a multiobjective optimization problem, in which objectives of Coverage, Connectivity Quality, and Lifetime, as well as the Connectivity and Reliability constraints, are simultaneously considered. A graph-based 3-D signal propagation model employing the line-of-sight concept is used to calculate the signal path loss. Novel distributed parallel multiobjective evolutionary algorithms (MOEAs) are also proposed. For verification, real-world and artificial urban terrains are utilized. In comparison with other state-of-the-art MOEAs, the novel algorithms could more effectively and more efficiently address the deployment problem in terms of optimization performance and operation time.

Wireless sensor networks (WSNs) are applied more and more widely in real life. In actual scenarios, 3-D directional wireless sensor nodes are constantly employed, thus, research on the real-time deployment optimization issue of 3-D directional WSNs based on terrain big data has more practical significance. Based on this, we study the deployment optimization issue of directional WSNs in the 3-D terrain through comprehensive consideration of coverage, lifetime, connectivity of sensor nodes, connectivity of cluster headers, and reliability of directional WSNs. We present a modified differential evolution algorithm by adopting crossover rate sort and polynomial-based mutation on the basis of the cooperative coevolutionary framework, and apply it to address the deployment problem of 3-D directional WSNs. In addition, to reduce computation time, we realize implementation of message passing interface parallelism. As is revealed by the experimentation results, the modified algorithm proposed in this paper achieves better performance with respect to either optimization results or operation time.

Effectively monitoring maritime environments has become a vital problem in maritime applications. Traditional methods are not only expensive and time consuming but also restricted in both time and space. More recently, the concept of an industrial wireless sensor network (IWSN) has become a promising alternative for monitoring next-generation intelligent maritime grids, because IWSNs are cost-effective and easy to deploy. This paper focuses on solving the issue of 3-D IWSN deployment in a 3-D engine room space of a very large crude-oil carrier and also considers numerous power facilities. To address this 3-D IWSN deployment problem for maritime applications, a 3-D uncertain coverage model is proposed that uses a modified 3-D sensing model and an uncertain fusion operator. The deployment problem is converted into a multiobjective optimization problem that simultaneously addresses three objectives: coverage, lifetime, and reliability. Our goal is to achieve extensive coverage, long network lifetime, and high reliability. We also propose a distributed parallel cooperative coevolutionary multiobjective large-scale evolutionary algorithm for maritime applications. We verify the effectiveness of this algorithm through experiments by comparing it with five state-of-the-art algorithms. Numerical results demonstrate that the proposed method performs most effectively both in optimization performance and in minimizing the computation time.

A considerable amount of research has been devoted to multiobjective optimization problems. However, few studies have aimed at multiobjective large-scale optimization problems (MOLSOPs). To address MOLSOPs, which may involve big data, this paper proposes a message passing interface MPI -based distributed parallel cooperative coevolutionary multiobjective evolutionary algorithm (DPCCMOEA). DPCCMOEA tackles MOLSOPs based on decomposition. First, based on a modified variable analysis method, we separate decision variables into several groups, each of which is optimized by a subpopulation (species). Then, the individuals in each subpopulation are further separated to several sets. DPCCMOEA is implemented with MPI distributed parallelism and a two-layer parallel structure is constructed. We examine the proposed algorithm using the multiobjective test suites Deb-Thiele-Laumanns-Zitzler and Walking-Fish-Group. In comparison with cooperative coevolutionary generalized differential evolution 3 and multiobjective evolutionary algorithm based on decision variable analyses, which are state-of-the-art cooperative coevolutionary multiobjective evolutionary algorithms, experimental results show that the novel algorithm has better performance in both optimization results and time consumption.