Evolutionary algorithms have been proven effective in solving complex optimization problems. This paper proposes a production shape optimization framework, and a data-driven and decomposition-based multiobjective multitask evolutionary algorithm with multiple neighbor structures and knowledge types, called MTEA/D-MNK, for complex shape optimization problems. Initially, a 3D point cloud autoencoder is trained via unsupervised learning to extract key design variables across tasks. Subsequently, each task is decomposed into a series of single-objective subproblems using weight vectors. We constructed diverse neighbors and knowledge types for each subproblem to fully exploit beneficial information in both the objective and decision spaces, accelerating the optimization process. Additionally, we proposed an adaptive parameter adjustment strategy to dynamically manage the type and amount of transferred knowledge during different evolutionary stages. The proposed MTEA/D-MNK effectively addresses the critical issues in knowledge transfer: which knowledge to transfer, how to transfer it, and how much to transfer. Finally, we comprehensively test MTEA/D-MNK on nineteen multiobjective multitask optimization (MO-MTO) benchmark instances and apply it to a practical automotive topology shape design problem, using computer simulations to optimize wind resistance coefficients and volumes of both sedan and SUV simultaneously. Experimental results demonstrate that the proposed algorithm significantly outperforms the other five state-of-the-art algorithms, chieving the best performance metrics on 18 of 20 CEC2017 benchmark instances, all 20 CEC2019 instances, and one case study of automotive shape design, as well as the highest rank in the Friedman rank test.

In recent years, utilizing data from the evolutionary process of multiobjective evolutionary algorithms (MOEAs) to learn knowledge and guide evolutionary search has become a popular research topic. However, existing knowledge learning (KL) frameworks often suffer from the low quality of collected datasets and the inefficiency of model construction, which significantly limits their effectiveness. To address this issue, this paper proposes a novel evolutionary direction learning (EDL) framework, which aims to learn the evolutionary direction (ED) knowledge for each objective to enhance the population generation of MOEAs. The proposed EDL incorporates an effective data collection method based on objective improvement to generate high-quality datasets, based on which a multivariate Gaussian probabilistic model is employed to learn ED knowledge for each objective through a data fusion modeling approach. Besides, a knowledge assignment method is designed to select the most suitable ED knowledge to guide the evolution of solutions. Experimental results on both synthetic and real-world problems demonstrate that the proposed EDL framework can accelerate the convergence of MOEAs and significantly improve their performance. A comparison of the proposed EDL with three state-of-the-art KL frameworks indicates that EDL is a highly competitive learning framework, achieving superior performance with larger datasets and impressive efficiency.

Evolutionary multitasking optimization achieves efficient solutions to multi-task optimization problems through the transfer and reuse of genetic information across tasks. However, in scenarios with limited computational resources, how to allocate resources among tasks effectively remains a challenge. This paper addresses the multi-objective multi-task optimization problem and proposes a computational resource allocation strategy based on the analytics of evolutionary changes in the objective space and the unified search space. The algorithm decomposes each multi-objective task into single-objective optimization subproblems using a decomposition strategy, and constructs a dual-utility function based on the scalarizing function of the subproblems and the diversity changes in the unified search space to determine the optimization priorities of the subproblems. The experimental results demonstrate that our proposed algorithm can effectively allocate computational resources dynamically and significantly outperforms many comparison algorithms in terms of inverted generational distance related metrics.

Evolutionary multi-task optimization is an emerging research topic in the field of evolutionary computation. It aims to achieve simultaneous optimization of different tasks by dynamically leveraging the synergies that exist between them. As the number of tasks being optimized simultaneously increases, the differences between the tasks can vary significantly, and their iterative trends may also diverge. These factors contribute to a higher likelihood of negative transfer during the knowledge transfer process. To address these challenges, this paper proposes a matrix-driven adaptive dual-space evolutionary optimization algorithm, referred to as MaKAM. The MaKAM algorithm aims to compute the similarity between tasks using dual measurement criteria from both the objective space and decision space, effectively avoiding negative transfer between tasks. For many-task single-objective optimization problems, comparative algorithms are evaluated using the CEC19MaTSO and WCCI20MaTSO test suites. For many-task multi-objective optimization problems, comparisons are made using the CEC19MaTMO and WCCI20MaTMO test suites. The results indicate that the overall performance of the proposed MaKAM algorithm significantly surpasses that of the compared algorithms in the literature.

High-quality predictions of key indicators are essential to maintain stable production in the iron and steel industry. However, most existing prediction methods rely on manually designed supervised learning models. These methods do not consider the effective utilization of unlabeled data, which is prevalent in practical production environments, to improve the model performance. As a result, the accuracy and generalization of these methods tend to perform poorly in real-world applications. To tackle this issue, this paper develops a multiobjective semi-supervised ensemble learning method with evolutionary neural architecture search (MOSSEL-ENAS), in which a one-dimensional convolutional neural network (OD-CNN) is employed as the base learner. MOSSEL-ENAS takes the input feature permutation and neural architecture of each OD-CNN as the decision variables, and an improved non-dominated sorting genetic algorithm is developed to simultaneously optimize two objectives, i.e., accuracy and complexity of each base learner. Moreover, an adaptive evaluation pattern adjustment strategy is proposed to adaptively adjust the learning paradigm (i.e., semi-supervised learning and supervised learning) of OD-CNNs by incorporating unlabeled data into the training process, further improving the learning performance of the algorithm. After evolution, a set of elite base learners with high-accuracy and low-complexity are selected and combined using a LightGBM-based stacking ensemble method to construct the final ensemble model. Experimental results on two key indicator prediction tasks in the iron and steel industry demonstrate that MOSSEL-ENAS achieves competitive or even better accuracy compared to other powerful learning methods, and also outperforms the existing task-specific learning methods. Furthermore, the competitiveness of a modified version of MOSSEL-ENAS on a classification task highlights the scalability of our proposal.

When solving dynamic multiobjective optimization problems, most evolutionary algorithms attempt to predict the initial population in a new environment by mining the relationships between solutions during historical environment changes. However, the complex relationships between solutions and the limited amount of available data often make it difficult to extract useful information efficiently, which may deteriorate the prediction accuracy. To address this problem, this paper proposes a spatial-temporal topological tensor-based prediction method to generate the initial population in a new environment under the decomposition framework of MOEA/D. The method relies on the idea that the population distribution in each environment has topological similarity along the time dimension in the objective space, which makes it efficient to represent the population distribution in terms of a tensor and predict new solutions along each decomposition axis in a new environment by an improved tensor-based multi-short time series prediction method. Experimental results on various benchmark problems and a real-world problem show that the proposed method is competitive or even superior to state-of-the-art dynamic multiobjective evolutionary algorithms based on prediction strategies.

Amid the global push for sustainable development, rising market demands have necessitated a multiregional, multiobjective, and flexible production model. Against this backdrop, this article investigates the multiobjective distributed flow shop group scheduling problem by formulating a mathematical model and introducing an advanced memetic algorithm integrated with reinforcement learning (RLMA). The RLMA involves a novel cooperative crossover operation in conjunction with the nature of the coupled problems to extensively explore the solution space. Additionally, the Sarsa algorithm enhanced with eligibility traces guides the selection of optimal schemes during the local enhancement phase. To ensure a balance between convergence and diversity, a solution selection strategy based on penalty-based boundary intersection decomposition is utilized. Furthermore, the increasing-efficiency and reducing-consumption strategies integrating a rapid evaluation mechanism are designed by dynamically changing the machine speed to balance economic and sustainability metrics. Comprehensive numerical experiments and comparative analyses demonstrate that the proposed RLMA surpasses existing state-of-the-art algorithms in addressing this complex problem.

The stochastic resource allocation (SRA) problem is widely encountered in complex systems, where the resource may probabilistically fail to complete its assigned task. In practical scenarios, the assignment of resources to tasks should be handled within specified time windows, and the success probability of each assignment changes over time. Such a problem can be represented as the SRA problem with time window (SRA-TW). Both the discrete assignment relationship and the corresponding continuous-valued assignment time are indispensable in the decision scheme of SRA-TW. This mixed-variable nature poses a great challenge for optimization. Based on these requirements, SRA-TW is formulated as a mixed-variable optimization problem (MVOP) with temporal constraints. To solve this problem, an adaptive hybrid algorithm with clustering-based diversity preservation (AHACDP) is proposed. Firstly, a variable-length hybrid encoding method with constructive decoding is proposed for incremental constraint handling. Secondly, a hybrid search mechanism incorporating a matching-similarity-guided adaptive selection method is proposed to balance the search in discrete and continuous subspaces. Then, a clustering-based diversity preservation strategy is developed, facilitating a good distribution of the population. Finally, an SRA-TW instance generator considering various problem features is designed, so as to comprehensively validate the algorithm’s performance. The statistical results over numerous instances demonstrate the superiority ofAHACDPover prevailing algorithms in addressing SRA-TW.

High quality product quality prediction is very important for iron and steel enterprises to ensure stable production. However, most existing prediction methods are manually designed learning models. These methods consider only macroscopic data while ignoring mesoscopic data that also have a significant impact on product quality. Thus, they are often poor at accuracy and generalization performance in practice. To address this issue, a multi-objective convolutional neural networks ensemble learning method with multi-scale data fusion (MOCNNEL-MSDF) is developed. Using data fusion of macro/meso data derived from kinetic models, MOCNNEL-MSDF first evolves a swarm of convolutional neural networks (CNNs) by knowledge-transferring based reproduction and adaptive weights initialization adjustment to improve learning performance, and then a sparse ensemble approach based on differential evolution is applied to achieve the final prediction model from the evolved CNNs. Experimental results on both benchmark data and practical data of continuous annealing show that MOCNNEL-MSDF achieves competitive or better accuracy and robustness compared with other powerful learning methods, and outperforms the existing strip quality prediction models. The proposed method can be used in the product quality modeling of each process in the iron and steel industry, where it is desirable to combine mechanism models with production process data to construct a product quality prediction model with higher accuracy and generalization.

This article studies an operation optimization problem in a steelmaking process. Shortly before the tapping of molten steel from the basic oxygen furnace (BOF), end-point control measures are applied to achieve the required final molten steel quality. While it is difficult to build an exact mathematical model for this process, the control inputs and the corresponding outputs are available by collecting production data. We build a data-driven model for the process. To optimize the control parameters, an improved estimation of distribution algorithm (EDA) is developed using a probabilistic model comprising different distributions. A resampling mechanism is incorporated into the EDA to guide the new population to a broader and more promising area when the search becomes ineffective. To further enhance the solution quality, we add a local improvement to update the current best individual through simplified gravitational search and information learning. Experiments are conducted using real data from a BOF steelmaking process. The results show that the algorithm can help to achieve the specified molten steel quality. To evaluate the proposed algorithm as a general optimization algorithm, we test it on some complex benchmark functions. The results illustrate that it outperforms other state-of-the-art algorithms across a wide range of problems.

The implicit parallelism of a population in evolutionary algorithms (EAs) provides an ideal platform for dealing with multiple tasks simultaneously. However, little effort has been made to explore what information among different tasks can be used as valuable knowledge to help the optimization of different tasks. This article proposes a multiobjective multitask optimization (MO-MTO) EA based on decomposition with dual neighborhoods (MTEA/D-DN), in which the neighborhood is used as a bridge to achieve knowledge transfer among different tasks. In MTEA/D-DN, each subproblem not only maintains a neighborhood (internal neighborhood) within its own task based on the Euclidean distance between weight vectors but also keeps a neighborhood (external neighborhood) with the subproblems of other tasks via gray relation analysis in order to mine valuable information and communicate among tasks. The experimental studies show that our proposed algorithm outperforms five other state-of-the-art algorithms on a set of benchmark test instances and a real-world problem in steel plant.

In the iron and steel industry, the hardness of steel strips is one of the key performance indicators to evaluate strip quality and guide production for the continuous annealing production line (CAPL). However, the hardness cannot be measured online in the actual production process. Consequently, the precise prediction of the strip hardness based on practical data becomes one of the key tasks during production. In this article, a multiobjective sparse nonlinear ensemble learning with evolutionary feature selection (MOSNE-EFS) method is proposed, which is data-driven modeling of the soft sensor. The method mainly consists of two stages: 1) the construction of individual learners based on multiobjective feature selection learning (MOFSL) and 2) the selection and ensemble of individual learners based on sparse nonlinear ensemble learning via differential evolution (SNEL-DE). The final ensemble model obtained by SNEL-DE is used as the prediction model for strip hardness in CAPL. The proposed method is evaluated with industrial production data. Experimental results indicate that the two strategies, i.e., evolutionary feature selection and sparse nonlinear ensemble, are effective in improving the accuracy and robustness of the prediction model, and further comparison results demonstrate the superiority of the MOSNE-EFS model over the other existing methods.Note to Practitioners—Many quality metrics in the iron and steel industry cannot be online checked, which causes great difficulties in process monitoring, control, and operation optimization. The proposed multiobjective sparse nonlinear ensemble learning with evolutionary feature selection method can help practitioners to construct quality prediction models of many other similar production lines, such as hot rolling and cold rolling, and thus, better process monitoring, control, and optimization of product quality can be achieved.

In the blast furnace ironmaking process, accurate prediction of silicon content in molten iron is of great significance for maintaining stable furnace conditions, improving hot metal quality, and reducing energy consumption. However, most of the current research works employ linear correlation coefficient methods to select input features in modeling, which may not fully take the nonlinear and coupling relationships between features into account. Therefore, this article considers the input feature selection issue of silicon content prediction model from a new perspective and proposes a multiobjective evolutionary nonlinear ensemble learning model with evolutionary feature selection mechanism (MOENE-EFS), in which extreme learning machine is adopted as the base learner. MOENE-EFS takes the input feature scheme of each base learner as well as their network structure and parameters as decision variables and proposes a modified nondominated sorting differential evolution algorithm to optimize two conflicting objectives, i.e., accuracy and diversity of base learners, simultaneously. Through the optimization, a set of Pareto optimal base learners with high accuracy and strong diversity can be obtained. Moreover, different from the linear ensemble methods commonly used in classical evolutionary ensemble learning, this article proposes a nonlinear ensemble method to combine the obtained base learners based on differential evolution. Experimental results indicate that the two proposed strategies, i.e., evolutionary feature selection and nonlinear ensemble, are very effective in improving the accuracy and stability of the prediction model. MOENE-EFS also outperforms the other prediction models in both benchmark data and practical industrial data. Furthermore, analysis on the input features of all Pareto optimal base learners shows that the evolutionary feature selection is capable of selecting essential features and is consistent with human experience, which indicates it is a promising method to deal with the input feature selection issue in silicon content prediction.

The color-coated steel coil is a high value-added product for steel enterprises, and its production process is affected by multiple factors. How to provide operators with appropriate scheduling schemes is the key to improve the economic benefits of enterprises. In this article, for the scheduling of a single color-coating turn, we establish a multiobjective optimization model that minimizes the number of insertions of transition coils, the thickness jump penalty of adjacent coils, and the switching times of the backup rollers. To address this problem, we propose a piecewise coding approach to ensure that each individual meets the production constraints. Besides, a multiobjective evolutionary algorithm (MOEA) based on decomposition and dynamic local search (D-DLS) strategy is proposed (MOEA/D-DLS). More specifically, the color-coating multiobjective scheduling problem is decomposed into a series of single-objective subproblems and optimized simultaneously. Furthermore, based on the speed of evolution of these subproblems, local search is performed on partial subproblems dynamically. The proposed algorithm is used to solve eight multiobjective scheduling problem instances of color-coating with different scales, and the experimental results demonstrate that the proposed algorithm is very effective compared with four state-of-the-art algorithms.Note to Practitioners—Practical production scheduling problems in iron & steel industry generally need to optimize conflicting objectives simultaneously, which is very hard for practitioners to make appropriate decisions with manual experience. The decomposition-based multiobjective evolutionary algorithm (MOEA) can help practitioners of color-coating scheduling to achieve a set of Pareto optimal decisions with good distribution and tradeoff among three objectives. Since the scheduling of the other production lines shares many similarities with our problem, the proposed model and algorithm can also be applicable to these problems.

The make-to-order (MTO) manufacturers generally make production plans based on orders, which can help enterprises effectively avoid market risks, reduce market pressure and improve competitiveness. However, due to the characteristics of MTO production mode, the order static scheduling problem and rush order dynamic rescheduling problem have become more and more important for these MTO manufacturers. Therefore, in this paper, we take the packaging production line of a typical carbon black production enterprise as the research background to study the carbon black production line static and dynamic multiobjective scheduling problem. Firstly, multiobjective optimization models of both order static scheduling and rush order dynamic rescheduling are established. Then the improved MOEA/D algorithm combined the heuristic algorithm based on heuristic rules and discrete dynamic local search is developed to solve these two models. Based on the actual production data, eight instances of order static scheduling problems of different scales and four instances of rush order dynamic rescheduling problems of different scales are constructed respectively. Experimental results illustrate that the improved MOEA/D is effective and superior in solving these two problems.

Differential evolution is one of the most powerful evolutionary algorithms for single objective optimization problems in the literature. Its application in the multiobjective optimization problems is also very successful, and many kinds of promising multiobjective differential evolution (MODE) algorithms have been proposed in the literature. This paper develops a new variant of MODE with two features. First, a set of personal archives are maintained to evolve the search process instead of a population with a fixed size, and a truncation procedure is used to enhance selection pressure. Second, multiple biased mutation operators incorporating the target solution quality are proposed, and an adaptive selection method is adopted to allocate the mutation operators to solutions. The proposed MODE is referred to as the MODE with personal archive and biased self-adaptive mutation selection (BiasMOSaDE). A set of 31 benchmark multiobjective problems selected from the literature are adopted to evaluate its performance. Computational results illustrate that the proposed BiasMOSaDE is competitive or even superior to several state-of-the-art MODEs in the literature.

Due to the simple but effective search framework, differential evolution (DE) has achieved successful applications in multiobjective optimization problems. However, most of the previous research on the multiobjective DE (MODE) focused on the design of control strategies of parameters and mutation operators for a given population at each generation, and ignored that the given population might have a bad distribution in the objective space. Therefore, this paper proposes a new variant of MODE in which a reference axis vicinity mechanism (RAVM) is developed to restore the good distribution of the given population and maintain its convergence before the evolution (i.e., mutation, crossover, and selection) starts at each generation. Besides the RAVM, a hybrid control strategy of parameters and mutation operators is also presented to accelerate convergence by integrating both randomness and guided information derived from solutions generated during the search process. Computational results on four series of benchmark problems illustrate that the proposed MODE with the RAVM and hybrid control strategy is competitive or even superior to some state-of-the-art multiobjective evolutionary algorithms in the literature.

Different from most of the previous multi-objective differential evolutionary (MODE) algorithms focusing on the selection of control parameters or mutation strategies, this paper developed a new MODE algorithm in which the search history of each solution is memorized to construct a good new population for the next generation. This population construction strategy based on memory is motivated by the fact that a population with good quality and diversity can generally help to generate more promising new solutions. In this strategy, the non-dominated solutions obtained by each solution are memorized in an archive and subsequently a construction method is proposed to select solutions with good quality and diversity from the union of all archives to construct the new population. This strategy is incorporated into an adaptive MODE with multiple mutation operators. Computational results on benchmark problems show that the proposed strategy can significantly improve the search efficiency of MODE with traditional population update strategy. The results also reveal that the proposed MODE is superior to some state-of-the-art MODEs and multi-objective evolutionary algorithms in the literature.

Recently, the hybridization between evolutionary algorithms and other metaheuristics has shown very good performances in many kinds of multiobjective optimization problems (MOPs), and thus has attracted considerable attentions from both academic and industrial communities. In this paper, we propose a novel hybrid multiobjective evolutionary algorithm (HMOEA) for real-valued MOPs by incorporating the concepts of personal best and global best in particle swarm optimization and multiple crossover operators to update the population. One major feature of the HMOEA is that each solution in the population maintains a nondominated archive of personal best and the update of each solution is in fact the exploration of the region between a selected personal best and a selected global best from the external archive. Before the exploration, a selfadaptive selection mechanism is developed to determine an appropriate crossover operator from several candidates so as to improve the robustness of the HMOEA for different instances of MOPs. Besides the selection of global best from the external archive, the quality of the external archive is also considered in the HMOEA through a propagating mechanism. Computational study on the biobjective and three-objective benchmark problems shows that the HMOEA is competitive or superior to previous multiobjective algorithms in the literature.

This paper proposes a hybrid differential evolution algorithm for multi-objective optimization problems. One major feature of this hybrid multi-objective differential evolution (HMODE) algorithm is that it adopts subpopulations whose sizes are dynamically adapted during the evolution process. The second feature is that the HMODE adopts a new solution update mechanism instead of the standard one used in the traditional differential evolution. The HMODE uses multiple operators and assigns an operator to each subpopulation. The update of each subpopulation is based on the assigned operator. The third feature of the HMODE is that a self-adapt local search method is used to improve the external archive. Computational study on benchmark problems shows that the HMODE is competitive or superior to previous multi-objective algorithms in the literature.

This paper studies a large-scale scheduling problem in iron and steel industry, called color-coating production scheduling for coils in inventory (CCPSCI). The problem is to select steel coils from those in the coil yard and to create a production schedule so that the productivity and product quality are maximized, while the production cost and other penalties are minimized. A tabu search (TS) algorithm is proposed for this problem. Results on real production instances show that the proposed method is much more effective and efficient than manual scheduling.