In the real world, there exists a special category of multi-objective optimization problems with more than 1000 decision variables. However, only a few decision variables play a crucial role in optimizing the objective functions. Such problems are defined as sparse large-scale multi-objective optimization problems (SLSMOPs). Due to the difficulty in effectively identifying the non-zero positions of decision variables, traditional evolutionary optimization algorithms suffer from slow convergence speed and poor convergence effect, which means it is unable to efficiently obtain the Pareto optimal solution set. To address this challenge, the Impact Factor Assisted Algorithm (IFA) is proposed, which adopts a novel initial population strategy to generate sparse populations. Meanwhile, the impact factor of each decision variable is calculated, serving as a key basis for measuring the importance of each decision variable. During the algorithm’s operation, the impact factors are iteratively updated to rationally group decision variables and guide population evolution. This approach can accurately identify the positions of non-zero decision variables. The experimental results on eight benchmark and real-world problems indicate that the algorithm outperforms several existing sparse large-scale multi-objective optimization algorithms (SLSMOEAs).

This study developed a multi-stage decision model to optimize detection and disassembly strategies for minimizing costs and maximizing profits in the production of a popular electronic product. The product, assembled from two key components, is deemed defective if either component is faulty, though other factors may also cause defects. For defective products, the company can choose to either scrap them directly or disassemble them to recover parts, which incurs additional costs. Using sampling inspection methods, the study estimated the defect rate in production and optimized inspection plans for components and finished products. The model simulated various strategy combinations, calculating and comparing the total cost and profit of each to identify the optimal solution. Additionally, the study examined the impact of sampling errors on defect rate estimation and made dynamic adjustments to detection and disassembly strategies to enhance production efficiency and quality management. The findings provide important theoretical and practical guidance for quality control in enterprise production decision-making.

Manufacturing shops have common dynamic factors that often disrupt pre-established schedules. In production, a buffer time is typically set to account for such dynamic disturbances. However, which increases scheduling complexity and expands the Flexible Job Scheduling Problem (FJSP) into the Flexible Job Shop Rescheduling Problem (FJSRP). Consequently, an efficient method is urgently needed. In this context, the insertion of a new order alters the scheduling state. This study aims to address the objectives of minimizing the earliest completion time of orders and maximizing the utilization of machine resources. For the FJSRP, it is essential to establish both the independent insertion time and pre-processing buffer time while also devising a rescheduling method that balances the number of jobs across orders. To tackle these challenges, the Proximal Policy Optimization for Hybrid Feature Extraction Network (PPO-HFEN) strategy was developed. Innovations in this strategy include an attention mechanism that integrates a Multi-layer Hybrid Feature Extraction Network (HFEN) for feature extraction and job prioritization. Furthermore, a Mixed Reward Function (MRF) is introduced to resolve convergence issues during the training process. Experimental evaluations demonstrated that PPO-HFEN outperformed four state-of-the-art algorithms, yielding superior solutions in 21 out of 40 instances, thereby underscoring the effectiveness of the HFEN and MRF components. Moreover, the validity of the proposed rescheduling strategy is further validated on a real production foundry instance. The primary objective is to analyze the impact of varying order sizes, insertion times, and pre-processing times on the test results of diverse sampling methods.

The complex coupling between transportation and production poses significant challenges for scheduling algorithms, particularly in dynamic environments where contingencies are frequent. The traditional Flexible Job Shop Scheduling Problem (FJSP) does not fully account for these factors. Therefore, a two-stage knowledge-driven inverse diffusion prediction algorithm (TKIDP) is proposed for FJSP with transportation resources and multiple breakdowns (MBFJSPT). In the first phase, TKIDP operates in a static environment and aims to minimize the makespan and load imbalance, thereby reducing the risk of machine breakdowns. When a machine breakdown occurs, TKIDP enters a rescheduling phase and minimizes total energy consumption as an additional objective. An inverse diffusion prediction strategy is proposed to address the occurrence of multiple machine breakdowns. By learning from optimization processes of historical breakdowns, the proposed strategy identifies potential evolutionary patterns and predicts the evolutionary trends of future breakdowns. A similarity measure based on mutual entropy is introduced to select the most relevant historical breakdowns for learning. This method enhances prediction accuracy. To further improve exploration and exploitation capabilities, an adaptive competitive reconfiguration strategy is proposed. This strategy incorporates multiple deletion and reconstruction operators to guide the algorithm toward the optimal solution. To verify the effectiveness of MBFJSPT, a dedicated MB test set is constructed. On the MB1-18 test, TKIDP is compared with five other algorithms. Based on the Inverted generational distance (IGD), hypervolume (HV), and relative deviation (RD) metrics, TKIDP achieves the best results on 15, 18, and 18 out of the 18 test instances, respectively.

In non-cyclic dynamic multi-objective optimization problems, the non-cyclic nature of environmental changes may cause the Pareto optimal front (PF) to be different from historical times. In addition, changes may also occur on the Pareto optimal solutions set (PS). However, predictions based solely on a single space show lower accuracy due to insufficient information. Therefore, solving non-cyclic dynamic multi-objective optimization problems via gate recurrent unit (GRU) prediction and multi-information hybrid exploration (GPMHE) is designed to overcome the above challenges. In the objective space, the GRU-based prediction strategy (GP) captures patterns of population change, predicts its distribution in new environments, and subsequently maps the results to the decision space; The multi-information hybrid exploration strategy (MHE) takes the feature individual as the representative individual, adaptively guides the population evolution direction in the decision space, thereby enhancing the algorithm’s adaptability. Compared with five advanced algorithms on the non-cyclic dynamic benchmark test set (NCD), the proposed algorithm GPMHE has shown robust adaptation to dynamic environmental changes.

Current theoretical studies on dynamic multiobjective optimization problems (DMOPs) are based on periodic problems, while most DMOPs in real life have non-cyclic variations. To better reflect real-life problems, a non-cyclic benchmark test suite was designed to better test the performance of algorithms. The proposed test suite contains 15 problems that introduce difficult and complex geometric features. These features will become increasingly complex over time. Thus, a dual strategy of adaptive knee-point guidance and niche sampling (AKGNS) is proposed. For non-cyclic problems with complex geometric features, knee points are used as feature points to represent the variation of the Pareto front (PF). When faced with increasingly complex PFs, the number of subregions is adaptively adjusted according to the predicted PF complexity such that almost all knee points are identified. To maintain population diversity, new individuals are obtained by sampling around the knee point. The competitiveness of AKGNS was proven by comparing it with four advanced algorithms. AKGNS performed best on 26, 24, and 24 of the 45 test problems in terms of Schott’s Spacing Metric (SP), Hypervolume Difference (HVD), and Inverted Generational Distance (IGD) metrics, respectively.

In real life, many dynamic multiobjective optimization problems (DMOPs) have both time-varying and non-cyclic properties. Their non-cyclic nature differentiates the dynamics of the problem from all previous moments, and the changes become increasingly complex over time. Therefore, geometric changes in the Pareto-optimal front (PF) are more difficult to track. A novel knee-guided algorithm based on frequency analysis (NKGFA) is designed to solve non-cyclic DMOPs. To identify sufficient feature points to describe the change in PF, a knee-guided prediction strategy based on frequency analysis is proposed. From the perspective of frequency-domain analysis, almost all concave and convex knee points that contain critical feature information on the PF are identified. By predicting the frequency-domain information of the knees, the population's evolutionary trend is obtained in the frequency-domain space. An interpolation strategy based on approximate frontier manifold construction is proposed to ensure that the population is uniformly distributed on the PF. This strategy established an approximate PF between concave and convex knee points. Moreover, it adaptively interpolated the new individuals in the approximate PF. A non-cyclic dynamic (NCD) benchmark test suite is designed, including PFs with increasingly complex geometric features. The effectiveness of the NKGFA is verified by comparing it with four algorithms in the NCD test suite. The NKGFA performed best on 26, 23, and 29 of the 39 test problems on Inverted Generational Distance (IGD), Schott's Spacing Metric (SP), and Hypervolume Difference (HVD), respectively.

To perform fast and accurate classification of pumpkin seeds, three batches of pumpkin seed images were taken. A self-iterative learning large kernel attention-Squeeze and Excitation-Residual Network34 (LKA-SE-ResNet34) model was proposed by adding dual attention mechanism fusion of large kernal attention (LKA) mechanism and Squeeze and Excitation (SE) attention mechanism to each residual module of ResNet34 for recognizing pumpkin seeds. ResNet34 network model was chosen as the basic framework by comparing GoogleNet, AlexNet, EfficientNet, MobileNet, DenseNet, ResNet34 and Residual Network50 (ResNet50) deep learning network models. The comparation result showed that the top two models with the highest accuracy (Acc) are ResNet50 network model and ResNet34 network model among the compared models. The experimental results showed that the self-iterative learning LKA-SE-ResNet34 model outperformed the above-mentioned other network models in pumpkin seed recognition with an accuracy of 91.8%. To further validate the effectiveness of the proposed model for small sample size of data, two-sided images and deformed images of pumpkin seeds were collected and used, and the experimental results still proved that the proposed model had good generalization ability and accuracy, with the accuracies of 93.63% and 94.15% for two sides of pumpkin seeds as well as an accuracy of 99.03% for deformed pumpkin seeds. A set of seed sorting machine and an application (APP) for non-destructive testing of seeds were initially developed.

Establishing a closed-loop system that could facilitate the reusing, renovation, and recycling of the various garbage products generated by this business could prove significant value to the particular business chains involved. A system of shipping that is mindful of the surroundings and takes accountability regarding all the relevant money, sustainable, and societal concerns. The sustainability Closed-Loop Supply-Chain Networks (CLSCN) architecture and the marketplace are brought together in the present article, which serves as the study’s primary part in the body of knowledge. As a result, an optimization with multiple objectives paradigm has been offered to arrive at their choices regarding position, allocations, and stock in relation to the challenge under consideration. The goals of the optimized model, derived from the triple bottom line strategy, are aimed at lowering overall expenditure and emissions of CO2 as much as possible while increasing the number of employment possibilities. In this study, we have proposed Hybrid electromagnetism with a genetic algorithm (HEGA) and compare our proposal with the existing methods. The obtained results show that the proposed model integrated with HEGA gives significant improvements with significant outcomes in terms of sensitivity (97%), specificity (95%), transportation cost (30%), and computational time (5.3s). This knowledge serves as a driving force behind the development of CLSN in the sector to establish a viable and affordable approach.

Dynamic multiobjective optimization problems (DMOPs) are constantly changing over time, which re-quires algorithms to keep track of the location of the Pareto optimal front (POF) at different moments in time. In this work, a decision variable classification strategy based on the degree of environmental change (DVCEC) is proposed. To accurately capture the occurrence of environmental changes, DVCEC designs an adaptive change detection method based on multiple regions. Since environmental changes affect each decision variable to different degrees, DVCEC classifies decision variables into several types and applies an appropriate prediction method to each type. In addition, an adjustment strategy is developed to minimize the impact of inaccurate predictions. The proposed DVCEC is evaluated on 22 benchmark problems and compared with four algorithms. Statistical results show that DVCEC can quickly approach POF and uniformly distribute it in most problems.(c) 2023 Elsevier B.V. All rights reserved.

As manufacturing shifts towards large-scale production, the size of the workshop increases, and its search space exponentially expands. It is difficult for existing algorithms to obtain an ideal scheduling solution in an acceptable time. For the large-scale flexible job shop scheduling problem (LSFJSP), a multi-guided population co-evolutionary algorithm based on multiple similarity decomposition (MPCSD) is designed. Faced with the problem of high dimensionality and complex solution space, a multiple similarity decomposition strategy is proposed. It proceeds to group based on similarity information at the dimension and population level. To obtain convergence-preferred and diversity-preferred dimension groupings, a training-set solution selection method is proposed. Inspired by the idea of divide-and-conquer, a multi-guided co-evolutionary strategy is proposed. It improves the exploration efficiency of the algorithm in the search space. To test effectiveness on more complex LSFJSP, a set of large-scale test problems including LS1-12 are designed. On LS1-12, MPCSD is compared with seven other algorithms to demonstrate its superiority. MPCSD performed best on 11, 7, and 10 of the 12 test problems on Inverted Generational Distance (IGD), Hypervolume (HV) and Schott’s Spacing Metric (SP), respectively. Meanwhile, the Relative Deviation (RD) results showed that MPCSD obtained the best fitness performance.

Multi-objective mixed-variable optimization problems (MO-MVOPs) are common and complex practical design optimization problems. MO-MVOPs often include multiple complex functions, constraints and mixed types of decision variables. Compared with single objective mixed-variable optimization problems (MVOPs), the decision space of MO-MVOPs presents more complex spatial distribution features. These features of MO-MVOPs make solving such problems face a big challenge. In this paper, fundamental advancements are made to MCDEmv which is previously proposed for single objective MVOPs. This improved version can solve MO-MVOPs, which can be named as MO-MCDEmv. In MO-MCDEmv, the best solution in the population is no longer the solution with the best fitness value, but a random solution in the first rank after executing the fast non-dominated sorting approach in NSGA-II. The generation of offsprings is generated by using the selection operator in NSGA-II. In addition, the local search in MCDEmv is utilized to improve the parents. The quality of the newly generated individual depends on the dominance relationship between itself and its parent. The experimental results of two actual MO-MVOPs are obtained by using two advanced multi-objective algorithms, i.e., CMOEA/D and NSGA-II, and the proposed MO-MCDEmv. The experimental results show that the MO-MCDEmv has better performance than the two advanced multi-objective algorithms.

Multi-objective evolutionary algorithm (MOEA) has become a common and effective method to solve real-world multi-objective optimization problems. However, in some practical problems, such as the microgrid energy optimization problem (MEOP), the algorithm needs to run on the micro controller to control each distributed power supply in real time. Due limitation of hardware resources on the micro controller, the MOEAs are not suitable. The emerging micro population MOEAs are suitable for this scenario. But the micro population MOEA is vulnerable to lost diversity, resulting in its performance decline. Therefore, this paper proposes a new micro multi-strategy multi-objective ABC algorithm to solve MEOP, called μMMABC. Multi-strategy ABC optimizer is used to divide the population into multiple subgroups and produce offspring in parallel to balance the exploration and exploitation. In addition, an adaptive updating mechanism is proposed to renew the population adaptively. The mechanism can adaptively select more convergent and diverse solutions at different stages to balance the exploration and exploitation of the algorithm. Furthermore, in order to improve the performance of μMMABC on problems with irregular Pareto fronts, the reference point reconstruction with intermediate strategy is also proposed. Some benchmark test suites are used to test the performance of μMMABC. Finally, it is used to solve the MEOP. The experimental results show that the proposed algorithm is more competitive and effective than the traditional MOEAs and other micro population MOEAs in solving the MEOP.

One of the main characteristics of dynamic multiobjective optimization problems is that the optimization objectives will change over time, so tracking the changing Pareto optimal front becomes a challenge. To this end, a knowledge learning prediction strategy based on a factorization machine is proposed (FMP). In the strategy proposed in this article, it reacts to changes by learning from the historical evolutionary process. Specifically, the factorization machine is introduced as a model to extract knowledge from the evolutionary experience of known historical time steps, and the knowledge is applied to the current time step to predict the population at the next time step. The performance of the proposed FMP is evaluated by comparing with two advanced prediction algorithms on 11 benchmark problems. Experimental results show that FMP can obtain a competitive population with good convergence and distribution in a dynamic environment.