Copy number variation (CNV) is a remarkable manifestation of genomic structural variations that affect human health. However, CNV detection in low coverage and low purity data is one of the challenging issues. To fill this gap, a hybrid algorithm combining an improved whale optimization algorithm (IWOA) and backpropagation (BP) neural networks (hereafter called IWOABP) is developed for CNV detection. First, to enhance the precision of detection, the detectable categories for the gain and loss are respectively expanded to two types, where gain is divided into tand_gain and inte_gain, and loss is divided into hemi_loss and homo_loss. Then, IWOA is introduced to tune the weights and bias values of BP neural network, which can improve the BP neural network abilities to jump out of the local optimums. Next, to ensure the population diversity and the uniform distribution of solutions, a pooling mechanism and a migration search strategy are designed. In addition, to balance the exploitation and exploration abilities, three position update strategies based on an adaptive inertia-weight are used. Finally, to evaluate the detection performance of IWOABP, seven state-of-the-art detection methods are chosen to make detailed comparisons with the proposed algorithm. The results show that IWOABP has outstanding performance in sensitivity, precision, and Fl-score using both simulated and real data.

Big data applications often use workflows shown as Directed Acyclic Graphs (DAGs). These DAGs link jobs and stages with order rules. Regular Spark-based workflow scheduling assumes all executors are identical and expects jobs to run one after another. This approach fails in mixed cloud setups, where machines vary in speed and computing capabilities. Efficient workflow scheduling in heterogeneous Spark nodes is crucial for reducing makespan and achieving load balancing. However, many existing methods overlook the challenge created by DAG-constrained jobs, stage-level dependencies, and varied node performance. This paper addresses efficient workflow scheduling on a mixed Spark cluster. We seek to minimize workflow completion time while keeping node loads balanced. We propose a modified Spark framework. It includes both a job scheduler and a stage scheduler tailored for mixed setups. Our method introduces multi-level node classification based on load status, a Speculative Stage Execution strategy for dynamic scheduling, and a Node Awareness Strategy for real-time task assignment. Compared to Rainbow, SAF, and DSWTS algorithms, SWTS reduces makespan by up to 40%, improves load balancing by 55%, and increases resource utilization by 20%. This demonstrates superior efficiency across all workflows.

Federated learning enables collaborative intrusion detection without centralizing sensitive network data, but existing approaches optimize solely for detection accuracy while neglecting critical performance and privacy constraints. This paper presents MOFL-CyberNet, a novel multi-objective federated learning framework that simultaneously optimizes three competing objectives: detection accuracy, network efficiency, and privacy preservation. The framework integrates three key innovations: (1) a lightweight Cross-Attention Transformer architecture (5.0 M parameters) specifically designed for distributed intrusion detection, capturing complex attack patterns with minimal computational overhead; (2) an adaptive Pareto-optimal aggregation mechanism using NSGA-II that dynamically balances objectives based on real-time network conditions; and (3) comprehensive privacy-preserving mechanisms including differential privacy and secure aggregation. Through rigorous evaluation on four major data sets totaling over 27 million samples (NSL-KDD, EDGE-IIoTset, CICIDS-2018, and CIC-IoT-2023), MOFL-CyberNet demonstrates exceptional performance: 97.86% detection accuracy coupled with 47% latency reduction and 36% energy savings compared to state-of-the-art baselines. These results demonstrate that multi-objective optimization can achieve favorable performance across all evaluated metrics concurrently making federated intrusion detection practical for resource-constrained IoT deployments.

Production scheduling that involves distributed factories, machine maintenance, and resource constraints plays a crucial role in manufacturing. However, these realistic constraints have rarely been considered simultaneously in the hybrid flow shop (HFS). To address this issue, a distributed resource-constrained hybrid flow shop scheduling problem with machine breakdowns (DRCHFSP-MB) is studied. There are two optimization objectives, i.e., makespan and total energy consumption (TEC). To solve the strongly NP-hard problem, a mathematical model is established and a block–neighborhood-based multi-objective evolutionary algorithm (BNMOEA) is developed. In the proposed algorithm, an efficient hybrid initialization method is adopted to obtain high-quality individuals to participate in the evolutionary process of the population. Next, to enhance the search capability of the BNMOEA, three well-designed crossover operators are used in the global search. Then, the convergence of the proposed algorithm is improved by utilizing eight critical factory-based local search operators combined with block–neighborhood. Finally, the BNMOEA is compared with several of the most advanced multi-objective algorithms; the results indicate that the BNMOEA has an outstanding performance in solving DRCHFSP-MB.

In recent years, the application of learning-based methods in flow shop scheduling problem has gained considerable attention. However, there are gaps in the quality of their solution due to the difficulty of fully exploring the huge search space faced by learning-based methods and the difficulty of reward function design. In this paper, a hybrid approach of meta-heuristic algorithm and imitation learning (IL) is proposed to solve the permutation flow shop scheduling problem with sequence-dependent setup times (PFSP-SDST). Firstly, jobs are treated as nodes, and the processing time and setup times of PFSP-SDST are considered as features of the nodes, respectively. Secondly, a graph neural network based on an attention feature fusion (AFF) mechanism is designed as an encoder to embed the feature information of the problem. Finally, an iterative greedy algorithm based on critical path is proposed to provide high-quality expert solutions for the IL algorithm. The running results on randomly generated datasets and benchmark datasets demonstrate the effectiveness of the proposed method.

In practical industrial production, workers are often critical resources in manufacturing systems. However, few studies have considered the level of worker fatigue when assigning resources and arranging tasks, which has a negative impact on productivity. To fill this gap, the distributed hybrid flow shop scheduling problem with dual-resource constraints considering worker fatigue (DHFSPW) is introduced in this study. Due to the complexity and diversity of distributed manufacturing and multi-objective, a Q-learning driven multi-objective evolutionary algorithm (QMOEA) is proposed to optimize both the makespan and total energy consumption of the DHFSPW at the same time. In QMOEA, solutions are represented by a four-dimensional vector, and a decoding heuristic that accounts for real-time worker productivity is proposed. Additionally, three problem-specific initialization heuristics are developed to enhance convergence and diversity capabilities. Moreover, encoding-based crossover, mirror crossover and balanced mutation methods are presented to improve the algorithm’s exploitation capabilities. Furthermore, a Q-learning based local search is employed to explore promising nondominated solutions across different dimensions. Finally, the QMOEA is assessed using a set of randomly generated instances, and a detailed comparison with state-of-the-art algorithms is performed to demonstrate its efficiency and robustness

In this study, a realistic flexible or hybrid flowshop scheduling problem (HFS) is investigated, in which the following constraints are embedded, i.e., resource-dependent processing, robotic arm loading, and transportation. To solve the considered problem, a multi-dimensional co-evolutionary algorithm (MDCEA) is proposed to minimize makespan and total energy consumption (TEC) simultaneously. First, in the MDCEA, solutions are encoded by a three-dimensional vector with a two-phase decoding heuristic. Then, the initialized population is divided into three subsets to focus on different search tasks. To improve the efficiency of the global search task, a dual-population-based variable dimension cooperative search method is developed. In addition, to explore the promising non-dominated solutions in different dimensions, a Q-learning-based dimension detection search method is designed for the local search task. Finally, to keep the diversity in the evolutionary process, a knowledge-based individual transfer strategy is conducted for populations. The proposed algorithm was tested on 25 randomly generated instances, and detailed comparisons verified the efficiency and robustness compared to six state-of-the-art algorithms was achieved.

The distributed flexible job shop scheduling problem (DFJSP) has gained increasing attention in recent years. Meanwhile, the family setup time constraint exists in many realistic manufacturing systems, e.g., prefabricated components system. In this study, first, a mixed integer programming (MIP) model is formulated for the DFJSP with family setup time. To minimize the makespan, a hybrid heterogeneous graph neural network with a principal component analysis (PCA)-based transform mechanism (HGNP) is proposed. In the proposed algorithm, a novel state representation is designed, which combines the features of operation, machine and factory assignment. Then, a multilayer perceptron (MLP) mechanism is used for the operation embedding, and graph attention networks (GATs) are embedded for the machine and factory embeddings. Next, a PCA-based transform mechanism is developed to further fuse all the three embeddings. To improve the solution performance, a simple enhanced local search method is developed. Three different scale of instances are generated to test the performance of HGNP, including small instances to test the effectiveness of the mathematical model, medium and large instances to test the efficiency, and extended public instances to test the generalization abilities. Experimental results and comparisons with different types of state-of-the-art algorithms show the competitiveness and efficiency of the proposed algorithm, both in performance and generalization capabilities.

With the development of economic globalization, group scheduling with outsourcing option has attracted much attention. This study considers a hybrid flow shop with group and outsourcing constraints, named HFGSP_OO. To solve this problem, adaptive reference-points learning and cooperation driven multi-objective algorithm (ARPCMOA) is proposed to optimize makespan, total energy consumption (TEC) and outsourcing cost, simultaneously. First, according to the characteristics of the problem, a strategy for determining the group to be outsourced is considered to generate the promising initial solutions. Second, a two-stage co-evolutionary method is used to explore the solution space in depth. In the first stage, a hybrid local search (HLS) is proposed to obtain more extreme solutions. In the second stage, the reference points adaptation mechanism is employed to enhance the global search capability of the algorithm, which can select high-quality solutions. These two stages are working cooperatively during the iterative process so that the population evolves towards the true Pareto front. In addition, an energy saving strategy based on idle time is proposed to better optimize TEC. Finally, a large number of statistical analysis experiments (KW) show that ARPCMOA outperforms existing multi-objective algorithms.

Precast scheduling is a special case of optimization problem, in which the curing stage requires parallel processing of a batch of jobs. In this study, distributed flexible job shop scheduling with crane transportation, fuzzy processing, and curing constraints is modeled for precast scheduling. Three objectives are considered simultaneously, namely, fuzzy makespan, energy consumption, and economic cost. To solve this complex problem, a bi-level collaborative multi-objective optimization evolution algorithm (BCMOEA) is developed. First, a double-Q network is designed considering different groups of features to generate valuable solutions for the second-level components. Then, a dynamic-adjusted reference point set is embedded to divide the current population into three sub-populations. Furthermore, a collaboration mechanism is developed to learn different knowledge from these sub-populations to balance the convergence and diversity abilities. Moreover, a knowledge driven curing batching heuristic is designed to improve the fuzzy makespan. Finally, a set of instances generated based on the realistic precast process is tested, and detailed comparisons with the state-of-the-art algorithms show the competitive performances of the proposed algorithm.

The performance of evolutionary algorithms using reference vectors to guide the evolution process mainly depends on the adaptive reference vector update strategy. In order to solve the challenging many-objective optimization problems with irregular Pareto fronts, this paper proposes an adaptive reference vector update strategy based on the Pareto front density estimation, which estimates the true Pareto front by finding sparse regions while ensuring the uniform distribution of reference vectors. In addition, an improved environmental selection strategy using the angle-based neighborhood density estimation has been proposed for estimating the neighborhood density to effectively guide the population evolution. On this basis, this paper proposes an adaptive reference vector guided many-objective optimization algorithm based on Pareto front density estimation (MaOEA-PDE). Experimental results on a large number of benchmark problems show MaOEA-PDE achieves better performance compared with some state-of-the-art algorithms in the literature.

Inspired by the production model of pressure vessels for spacecraft, i.e., tanks and cylinders, this study addresses the sequence-dependent group flow shop scheduling problem with consistent sublots (SDGFSP_CS) to minimize makespan and total energy consumption. In the problem under consideration, there are several coupling subproblems, namely, the group sequencing, job sequencing, lot assignment, and machine speed assignment. To solve these problems, a multi-population cooperative multi-objective evolutionary algorithm (MPCMOEA) is proposed. In the MPCMOEA, a hybrid initial method that combines two problem-specific heuristics is designed to generate high-quality initial solutions. Then, considering the problem features, a cooperative mechanism considering the co-evolution of multi-population and the archive set is designed to accelerate the optimization process. In the co-evolutionary stage, to deepen the exploitation ability of local search, an enhanced search with multiple problem-specific operators is implemented. Furthermore, a re-initialization method is developed to improve the global search abilities. Finally, 27 different scale instances are generated for a series of numerical experiments. For the hypervolume and inverse generational distance metrics, MPCMOEA gets 20/27 and 21/27 optimal values, respectively. It verifies that the MPCMOEA outperforms efficient algorithms in terms of the diversity and convergence performance.

The power transmission network is easily to be destroyed when natural or man-made disasters occur. Restoration of power supply under disaster environments faces difficulties since a large-scale network typically contains many uninspected faulty nodes. Utilizing unmanned aerial vehicles (UAVs) to inspect these unknown faulty nodes can significantly improve the efficiency for subsequent restoration work performed by human-teams. Nevertheless, efficient cooperation of UAV and human-team is a complicated work due to the complexity of network structure and correlation between UAV scheduling and human-team scheduling. In this paper, a mathematical model is established to describe the considered problem aiming at maximizing the restored power supply in a limited response time. Then a Q-learning based iterated local search (Q ILS) algorithm is proposed to formulate the collaborative scheduling problem. Firstly, an initialization method is designed to assign UAVs for inspecting unknown faulty nodes and human-teams for repairing faulty nodes, which ensures each unknown faulty node is inspected before maintenance. Secondly, searching operators including perturbation and local search procedures are designed to ensure exploration and exploitation capability. Thirdly, Q-learning method is utilized as a learning engine to guide the direction of solution evolution. Moreover, the parameters of Q ILS are calibrated by multi-factor analysis of variance method to determine proper values. The computational simulations and comparison experiments validate the superiority of proposed algorithm.

In this study, a multi-objective blocking group flow shop scheduling problem with outsourcing option (BGFSP_OO) is addressed, where three objectives, including makespan, total energy consumption (TEC) and outsourcing cost, are considered simultaneously. To solve the BGFSP_OO, a bi-evolutionary cooperative multi-objective algorithm (BECMOA) is proposed. First, a machine switching strategy based on machine idle and blocking time is used in the decoding part to optimize the objective value TEC. Then, an effective heuristic for classifying outsourcing groups is proposed. To balance convergence and diversity abilities, a bi-evolutionary mechanism is proposed. The particle swarm optimization algorithm based on the gravity factor (IPSO) is employed which exploiting individual performance, can enhance the convergence ability. Cross evolutionary search (CES) strategy is developed which can improve search ability, aiming to ensure diversity of solutions and access to more non-dominated solutions. Finally, the experimental results show that BECMOA is effective in solving BGFSP_OO compared to the state-of-the-art methods.

Time-dependent vehicle routing problem with time windows (TDVRPTW) is a pivotal problem in logistics domain. In this study, a special case of TDVRPTW with temporal-spatial distance (TDVRPTW-TSD) is investigated, which objectives are to minimize the total travel time and maximize customer satisfaction while satisfying the vehicle capacity. To address it, an improved multiobjective evolutionary algorithm (IMOEA) is developed. In the proposed algorithm, a hybrid initialization strategy with two efficient heuristics considering temporal-spatial distance is designed to generate high-quality and diverse initial solutions. Then, two crossover operators are devised to broaden the exploration space. Moreover, an efficient local search heuristic combing the adaptive large neighborhood search (ALNS) and the variable neighborhood descent (VND) is developed to improve the exploration capability. Finally, detailed comparisons with several state-of-the-art algorithms are tested on a set of instances, which verify the efficiency and effectiveness of the proposed IMOEA.

Confronted with complex industrial environments, dynamic disruptions like new job arrival and machine breakdown bring significant challenges to the robustness and stability of the manufacturing process, making the static production depart from the original scheduling scheme. To address this problem, a flexible job shop scheduling problem with fuzzy processing time, dynamic disruptions, and variable processing speeds is considered simultaneously. As well as three objectives of maximum completion time, total energy consumption, and average agreement index are demonstrated in this study. Then, a predictive-reactive dynamic/static rescheduling model is developed, where the off-line based mixed integer linear programming model and the on- line based rescheduling heuristics are proposed. Next, a multi-objective immune algorithm combined with a Q learning algorithm (Q-MOIA) is developed. In the proposed algorithm, an active decoding heuristic based on the interval insertion mechanism is used to optimize the initial solutions. After that, the clonal selection-based immune algorithm and the Q-learning algorithm are adopted to improve the exploration and exploitation ca- pabilities, respectively, where four objective-thiten Tierghborifood structures are designet: Everftually, extensive computational experiments were conducted on 27 instances under static and dynamic scenarios to demonstrate the superiority and stability of the proposed predictive-reactive dynamic static rescheduling model and the Q- MOIA. Comparative analysis with four state-of-the-art approaches revealed that proposed Q-MOIA outperformed in approximately 51.9, 66.7, and 83.3 % of the instances for the three multi-objective metrics.

For multi-objective optimization problems with irregular Pareto Fronts, most widely used decomposition methods in MOEA/D (multi-objective evolutionary algorithms based on decomposition) have shown to be lack of the ability to balance the diversity and the convergence to track the true Pareto Fronts during the search. This research investigates the recently proposed grid-based decomposition methods, which reflect the inherent characteristics of the neighborhood structure in the solution to address the issues of diversity and convergence. The performance of the grid-based decomposition method, however, depends on the size of its grid segmentation, and its time complexity increases with the number of grids. In order to improve the computational efficiency, we propose a new concept of Pareto Front grid to guide the search in MOEA. In order to reduce the computing time, a new nadir point estimation strategy based on statistical analysis has been proposed to estimate the whole population. In addition, based on the idea of knee point, a novel grid-based knee point selection method is proposed in the environmental selection of the next generation. Finally, a grid-based decomposition multi-objective evolutionary algorithm with Pareto Front Grid (PFG-MOEA) is proposed. Extensive experimental analysis demonstrates the effectiveness of the proposed PFG-MOEA against state-of-the-art multi-objective evolution algorithms. As the extension of the CDG-MOEA (Constrained Decomposition approach with Grids MOEA) algorithm in the literature, PFG-MOEA can obtain better performance by consuming much less computing time.

Most existing multiobjective evolutionary algorithms treat all decision variables as a whole to perform genetic operations and optimize all objectives with one population at the same time. Considering different control attributes, different decision variables have different optimization effects on each objective, so decision variables can be divided into convergence- or diversity-related variables. In this article, we propose a new metric called the optimization degree of the convergence-related decision variable to each objective to calculate the contribution objective of each decision variable. All decision variables are grouped according to their contribution objectives. Then, a multiobjective evolutionary algorithm, namely, decision variable contributing to objectives evolutionary algorithm (DVCOEA), has been proposed. In order to balance the convergence and diversity of the population, the DVCOEA algorithm combines the multipopulation multiobjective framework, where two different optimization strategies are designed to optimize the subpopulation and individuals in the external archive, respectively. Finally, DVCOEA is compared with several state-of-the-art algorithms on a number of benchmark functions. Experimental results show that DVCOEA is a competitive approach for solving large-scale multi/many-objective problems.

Efficient allocating and scheduling emergency rescue tasks are a primary issue for emergency management. This paper considers emergency scheduling of rescue tasks under stochastic deterioration of the injured. First, a mathematical model is established to minimize the average mathematical expectation of all tasks' completion time and casualty loss. Second, an improved multi-objective estimation of distribution algorithm (IMEDA) is proposed to solve this problem. In the IMDEA, an effective initialization strategy is designed for obtaining a superior population. Then, three statistical models are constructed, which include two tasks existing in the same rescue team, the probability of first task being processed by a rescue team, and the adjacency between two tasks. Afterward, an improved sampling method based on referenced sequence is employed to efficiently generate offspring population. Three multi-objective local search methods are presented to improve the exploitation in promising areas around elite individuals. Furthermore, the parameter calibration and effectiveness of components of IMEDA are tested through experiments. Finally, the comprehensive comparison with state-of-the-art multi-objective algorithms demonstrates that IMEDA is a high-performing approach for the considered problem.

In the production and processing of precision shaft-hole class parts, the wear of cutting tools, machine chatter, and insufficient lubrication can lead to changes in their roundness, which in turn affects the overall performance of the relevant products. To improve the accuracy of roundness error assessments, Bat algorithm (BA) is applied to roundness error assessments. An improved bat algorithm (IBA) is proposed to counteract the original lack of variational mechanisms, which can easily lead BA to fall into local extremes and induce premature convergence. First, logistic chaos initialisation is applied to the initial solution generation to enhance the variation mechanism of the population and improve the solution quality; second, a sinusoidal control factor is added to BA to control the nonlinear inertia weights during the iterative process, and the balance between the global search and local search of the algorithm is dynamically adjusted to improve the optimization-seeking accuracy and stability of the algorithm. Finally, the sparrow search algorithm (SSA) is integrated into BA, exploiting the ability of explorer bats to perform a large range search, so that the algorithm can jump out of local extremes and the convergence speed of the algorithm can be improved. The performance of IBA was tested against the classical metaheuristic algorithm on eight benchmark functions, and the results showed that IBA significantly outperformed the other algorithms in terms of solution accuracy, convergence speed, and stability. Simulation and example verification show that IBA can quickly find the centre of a minimum inclusion region when there are many or few sampling points, and the obtained roundness error value is more accurate than that of other algorithms, which verifies the feasibility and effectiveness of IBA in evaluating roundness errors.