Steelmaking is a typical energy-intensive process that consumes large amount of electricity and oxygen, significantly impacting the total production cost. The production of steelmaking process is characterized by its intermittent nature and variable energy demands at different production stages. Under time-of-use energy and level-of-use energy pricing, steel companies can take advantage of processing flexibility to make better use of electricity and oxygen, thereby reducing production costs. In this paper, we address a new energy-oriented scheduling problem of steelmaking production, with consideration of the variable demand and time-of-use pricing. The problem is formulated as a mixed-integer linear programming (MILP) model, and then solved by a tailored Lagrangian decomposition algorithm. A novel aspect of the proposed algorithm is the employment of a multi-agent reinforcement learning (MARL) to adaptively determine the subgradient directions and dynamically adjust step sizes. It significantly reduces reliance on intuitive parameter tuning and accelerates algorithm convergence through optimized multiplier updates during iterations. Numerical results are presented to demonstrate that the proposed algorithm can solve the addressed scheduling problem efficiently and outperforms other Lagrangian decomposition algorithms in terms of computational efficiency.

In the last decade, a variety of multiobjective evolutionary algorithms (MOEAs) with specific enhancements have been developed for solving multiobjective optimization problems (MOPs). In this article, unlike MOEAs, we provide a new artificial intelligence approach to solve MOPs, which adopts an imitation learning-based end-to-end method, namely AlphaMOEA. AlphaMOEA is entirely a model composed of neural networks that mainly follow the architecture of multitask learning (MTL). It has two training stages: the supervised learning (SL) stage and the reinforcement learning (RL) stage. In the SL stage, AlphaMOEA fits the solutions in the decision space provided by a number of selected MOEAs. Since neural networks in AlphaMOEA are composed of parameters with high dimensions, the fitting process can be viewed as a transformation of the solutions from a low-dimensional space into a high-dimensional space. This allows AlphaMOEA to obtain different valuable knowledge from a perspective of high dimensionality. Then, AlphaMOEA is trained in the RL stage to obtain good performance for MOPs with various problem characteristics in a self-driven manner. The RL stage relies on several designed components, including a similarity-based state design to measure the distance between solutions, an evolution operator-based action set to provide exploration behavior, and an indicator-guided reward to produce an incremental evaluation. Experimental results demonstrate that AlphaMOEA can learn valuable information about the decision space in high-dimensional representations, thereby achieving a desirable balance between exploration and exploitation. AlphaMOEA can further improve the performance for solving MOPs with various problem characteristics in a reasonable time.

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.

Multiobjective reinforcement learning (MORL) aims to seek a complete Pareto front (PF) with different compromise policies in multiobjective Markov decision processes (MOMDPs). However, most MORL algorithms currently have a limitation in handling the MOMDPs with nonconvex PFs. In this article, we propose a nonlinear MORL algorithm based on decomposition and variance reduction (MORL/D-VR) to overcome this limitation. MORL/D-VR adopts the Tchebycheff approach to transform a given MOMDP into a set of single-objective Markov decision processes (MDPs) and subsequently applies an improved policy gradient algorithm, called expected utility policy gradient (EUPG), to solve each single-objective MDP efficiently. We analyze the Pareto optimality of employing the Tchebycheff approach and policy gradient methods that use the full return to update policy for solving MOMDPs. The analysis shows that such a case can identify any Pareto optimal policy regardless of the shape of PFs theoretically. This can provide a theoretical guarantee for applying the Tchebycheff approach and EUPG in MORL/D-VR to obtain the policies within the nonconvex PFs. Moreover, we devise a new baseline for EUPG to reduce the variance of gradient updates and adopt a weight vector adaptation method to improve diversity. The experimental results show that MORL/D-VR achieves a desirable performance in handling problems with different convex and nonconvex PFs and outperforms current state-of-the-art MORL algorithms.

This paper studies a resource-constrained project scheduling problem, aiming to optimize the start times of project activities under resource and precedence constraints in order to minimize the makespan. To solve this complex problem more efficiently, we propose a problem-specific solution algorithm that combines hybrid metaheuristics with machine learning techniques. Specifically, a discrete differential evolution serves as the main framework, which is augmented with adaptive mutation, crossover, and parameter strategies. During the evolution phase, the differential evolution competes with a sequential pattern-based adaptive large-neighborhood search to generate offspring solutions. In the subsequent selection phase, a precedence decomposition scheme cooperates with a Hamming distance-based k-nearest neighbor model to evaluate the offspring solutions. Extensive experiments utilizing benchmark datasets demonstrate that each algorithmic component positively contributes to performance enhancement, and the proposed algorithm outperforms state-of-the-art algorithms. Furthermore, we analyze the search behavior of the algorithm from various views to assess the influence of different strategies on its overall performance.

Symmetry is a widespread phenomenon in nature. Recognizing symmetry can minimize redundancy to improve computing efficiency. In this paper, we take permutation-related combinatorial optimization problems as a starting point and explore the symmetric structure of its solution space through group theory. From a new perspective of group action, we discover that the meaningful symmetric feature within the solution space is subject to two conditions regarding the form of objective function and the number of objects to be permuted. To exploit the symmetric features, we design a half-solution-space search strategy for various search operators, which are commonly used for permutation-related combinatorial optimization problems. The half-solution-space search strategy can make these operators explore more promising regions without additional computational effort. When the condition of object number for symmetry is unsatisfied, we propose two dimension mapping approaches to construct the symmetric feature, making the half-solution-space search strategy applicable. We evaluate the proposed strategy on three classes of popular 68 benchmark instances, including the single row facility layout problem (SRFLP), traveling salesman problem (TSP), and multi-objective traveling salesman problem (MOTSP). Experimental results show that algorithms embedded with the half-solution-space search strategy can achieve a more competitive performance than those not exploiting the symmetric features.

This paper investigates a dynamic slab design problem in the steel industry, where order demands arrive dynamically during a given period. Slabs are the raw materials for producing order plates demanded by customers — slabs are first rolled in a rolling mill to create desired mother plates, and then the mother plates are cut into order plates. The dynamic nature of orders, along with practical considerations regarding rolling methods and nonlinear size constraints, distinguish our problem from existing ones. The goal is to determine slab design schemes to fulfill order demands for the period. However, the stochastic nature of dynamic production and the inherent complexity of slab design present significant challenges in the efficient solution. To address these challenges, we formulate a Partially Observable Markov Decision Process (POMDP) and propose a hybrid method (MARLIP) based on multi-agent reinforcement learning (MARL) and integer programming. The MARL component determines the order plate set, the slab type, and the rolling method involved in a single slab design. Then, an integer programming model is constructed to optimize the arrangement of the order plates based on MARL’s decisions. To further refine the MARLIP approach, we introduce dual factors and a soft boundary into the MARL and propose a two-core-based dynamic programming method to solve the integer programming model. Experimental results demonstrate our algorithm’s superior performance compared to several competitive reinforcement learning and mathematical programming methods in the dynamic slab design problem.

Reinforcement learning is a promising method for solving decision problems, and its potential has been increasingly recognized for large-scale combinatorial optimization problems in recent years. However, the existing studies on reinforcement learning for cutting stock problems mostly rely on sequence-to-sequence or graph neural network approaches that use the learned experience to make decisions while neglecting the combination features of cutting stock problems. In this paper, we propose a novel reinforcement learning framework for cutting stock problems that integrate integer programming and monotone comparative statics to construct a Markov decision process with a high-quality action space. We start by constructing a new Markov decision process that considers the diagonal structure of the integer programming model for combinatorial optimization problems, and then use column generation to obtain each action by combining multiple decision variables. Furthermore, we design a bipartite graph and related bipartite graph convolutional network to find the solutions. The results show that the proposed reinforcement learning framework provides a high-quality action space, and the designed bipartite graph convolutional network can effectively select the best actions from the action set.Note to Practitioners—This article was motivated by the cutting stock problems that exist in various industrial scenarios such as the wood, steel, paper, and glass industries. We improve the reinforcement learning for the cutting stock problem that can be adopted in industrial scenarios, which can increase the profile and reduce the production cost of industrial enterprises. Our improvement can also be referred to when solving other combinatorial optimization problems that can promote making decisions in industrial production.

Reinforcement learning (RL) has been widely used in recent years to solve combinatorial optimization problems; however, it has some limitations when solving such problems with practical features. It is difficult for RL to ensure the feasibility of solutions when solving optimization problems with complex constraints, which limits its industrial application. Using a two-dimensional cutting stock problem derived from the practical plate design process in the steel industry as an example, we propose a learning and searching framework that enables RL to obtain a feasible solution that obeys complex constraints. We first formulate the two-dimensional cutting stock problem as a Markov decision process (MDP) and then design a tree-search-based reinforcement learning (TSRL) algorithm within the proposed learning and searching framework. In the learning process, we establish the approximate stage-independent Bellman equation (ASIB) of the MDP and obtain the agent decision model by solving the ASIB with approximate linear programming and column generation. In the search process, based on the obtained approximate value function, an efficient parallel two-stage tree search is developed as the agent decision generator of RL to obtain near-optimal plate design schemes. The experimental results show that the proposed TSRL algorithm outperforms baselines in terms of the capacity to obtain a feasible solution, computational time, and solution quality. Note to Practitioners—This article was motivated by the slab design problem in the steel industry but it also applied to other two-dimensional cutting stock problems with complex constraints. This work promotes making decisions in industrial production. Our key contribution is to provide a good-enough solution in a short time, which can improve the resource utilization and reduce the production cost of industrial enterprises. In terms of methodology, we provide new insight into reinforcement learning, which makes reinforcement learning more applicable to practice scenarios.

Density functional theory (DFT) forms the foundation for computing the electronic structure of many-electron systems through the Kohn-Sham (KS) equations, with electron densityn(r) serving as the fundamental variable. This approach allows for the understanding and manipulation of material properties at the atomic and electronic levels. However, the exchange-correlation (XC) functional in DFT is not known in an exact form and is typically approximated using analytical models, which limits the accuracy of DFT calculations. The recent advancements in data analytics techniques, such as machine learning, which excel in pattern recognition, offer new opportunities for more effective approximations of the XC functional. In this study, we introduce a novel approach for XC functional modeling by fusing shared representation learning. This method leverages information sharing across tasks to improve the fused XC (FXC) functional model generalization. To improve the robustness of the FXC functional model, we further develop a multi-objective constrained multitask adjustment mechanism. Additionally, to expedite the determination of the optimal FXC model, we propose a group-theory-based multi-objective optimization (MOO) algorithm, which enables faster exploration of the solution space. Our experimental results demonstrate that the KS equations incorporating the FXC functional substantially improve the accuracy of molecular atomization energies, ionization potentials, and electron density calculations. Moreover, the method exhibits applicability to the computation of isomerization reaction energies in large molecules. These findings validate the effectiveness of our data analytics and optimization-based approach in enhancing the precision of the XC functional approximation.

Most of the current research on dynamic multiobjective optimization problems (DMOPs) assumes that environmental changes can be detectable. However, undetectable changes are frequently encountered in real-world applications, which pose a serious challenge for the existing methods. Because undetectable changes can lead to the failure of change detection techniques, thereby making it difficult to adapt to environmental changes for most algorithms. Therefore, to effectively deal with DMOPs with undetectable changes, this work proposes a dual mutation-based dynamic multiobjective evolutionary algorithm (DM-DMOEA). The proposed DM-DMOEA incorporates the following two main components. First, based on the exploration level of the population, an adaptive selection strategy is proposed, which enables the adaptive identification of individuals for mutation. Second, a dual mutation scheme is developed, utilizing both the polynomial mutation and the Gaussian mutation. These mutation operations are applied on the selected individuals to generate the mutated individuals, allowing for diverse exploration in the search space. After conducting the above two strategies, the population will evolve by the evolutionary criterion of multiobjective optimization. As a result, the algorithm can effectively adapt to undetectable changes in the environment. Comprehensive empirical studies are conducted on different benchmark functions and a real-world application to evaluate the performance of DM-DMOEA. Experimental results have demonstrated that DM-DMOEA is competitive in tracking the Pareto front over time when facing undetectable changes.

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.

The surface quality of steel materials is significantly influenced by processing conditions, which may result in roughness, flatness deviations, and various surface defects. However, the diversity of defect types and the limited size of labeled datasets pose challenges for accurate and efficient defect identification. To address these challenges, this paper proposes a multiobjective evolutionary multiscale Transformer incorporating fractal features for surface quality analytics of steel materials. Specifically, a multiscale Transformer is constructed, consisting of the convolutional tokenization architecture embedded with the multiscale attention module (MAM) and stacked Transformer encoders, enabling the model to effectively capture both morphological patterns and local defect details. In addition, a novel fractal dimension feature fusion module (FDFFM) is introduced to describe the irregularity of defect textures, enhancing feature representation. To achieve a balance between recognition accuracy and model complexity, a multiobjective evolutionary algorithm (MOEA) is employed, with the final model selected based on a knee point selection strategy to support decision-making. Experimental results validate the superior performance and efficiency of MOEA-FM-Trans compared to state-of-the-art methods.

In this article, an adaptive optimization method is proposed for the dynamic resource allocation problem (RAP) with multiple objectives in the manufacturing industry. In the proposed method, a novel reinforcement learning method (DSAC-ERCE) is designed to adaptively set the weights for multiple objectives, and then the optimization method is adopted to generate the noninferior solutions in each time period. To ensure DSAC-ERCE's performance in dynamic and complex resource allocation environments, we develop a state-encoding network with a proposed information entropy attention mechanism to encode the state. Then, we introduce a new reward function to escape from the local optima of the policy and further present a conditional entropy policy to enhance the policy network. In addition, we demonstrate the feasibility of improving the quality of actions and present a boundary method for high-quality actions. We also introduce an optimization model to automatically adjust the temperature parameter in DSAC-ERCE. Furthermore, we compare and analyze our approach with other state-of-the-art reinforcement learning methods. The experiments illustrate that DSAC-ERCE outperforms state-of-the-art reinforcement learning methods. Moreover, DSAC-ERCE can be generalized to solve optimization problems with two to five objectives, problems with linear, quadratic, cubic, logarithmic, or inverse objectives, and problems with diverse structures.

In industrial production processes, the mechanical properties of materials will directly determine the stability and consistency of product quality. However, detecting the current mechanical property is time-consuming and labor-intensive, and the material quality cannot be controlled in time. To achieve high-quality steel materials, developing a novel intelligent manufacturing technology that can satisfy multitask predictions for material properties has become a new research trend. This article proposes a multiobjective evolutionary learning method based on a two-stage model with topological sparse autoencoder (TSAE) and ensemble learning. For the structure characteristics of a typical autoencoder (AE), a topology-related constraint is incorporated into the loss function of the AE, thus maintaining the global relationship among multistage input data to improve the data reconstruction quality. Then, a sparse representation of the data is added to the AE to achieve dimensionality reduction. Moreover, the extreme gradient boosting (XGBoost) method is applied to predict the mechanical properties of steel materials through collaboration learning mechanisms. To enhance the model accuracy, a multiobjective evolutionary algorithm (MOEA) with a knee solution strategy is used to optimize the network structure and hyperparameters of the two-stage model. Experiments are conducted using real steel production data from a continuous annealing process (CAP). The results verify that the proposed method obtains a higher prediction accuracy than other state-of-the-art methods and can guide practical production and new material design.

For mobile devices with limited computing capabilities, offloading time-sensitive tasks to edge servers is a feasible approach in reducing energy consumption and computation time of tasks. In this paper, non-orthogonal multiple access (NOMA) technology is used to enable communication between mobile devices and SBSs. To minimize total offloading time and energy consumption of mobile devices, a joint allocation problem of communication and computing resources is proposed while satisfying the constraints on the maximum computation time of the task. In the multi-cell mobile edge computing (MEC) system, we consider interference from different cells on the same sub-channel. For task offloading, we consider simultaneously offloading tasks to different servers. To solve an allocation problem on communication and computing resource, we propose the MOEAD-Epsilon algorithm based on dynamic resource allocation (DRA-MOEAD-Epsilon). Simulation results verify the validity of DRA-MOEAD-Epsilon and demonstrate that it effectively improves the offloading benefits for mobile devices.

Accurate segmentation of the microvascular component of the retinal fundus image is of great significance for the clinical diagnosis. Currently, deep learning-based methods are often employed for retinal fundus image segmentation. However, most deep learning models manually designed by experts are not suitable for task-specific applications. Therefore, we propose a novel retinal image segmentation method that integrates a neural architecture search framework with a non-subsampled multiscale decomposition (NSMD-NAS) technique. Specifically, the feature extraction layer includes the convolutional layer and the transformer layer. In addition, the non-subsampling filter bank is embedded into the convolutional and the transformer modules respectively to generate a new network module for exploring multiscale, multi-frequency, and multi-directional information. Unlike previous wavelet-based network modules, non-subsampling network modules have translation invariance. Subsequently, the components of the network are specified by the elaborated encoding strategy, and then the network with the highest adaptation is searched by a genetic evolutionary algorithm (GA) to finally obtain the best network structure. Experimental results demonstrate the effectiveness of each component in the proposed model on the public benchmark datasets.

This study addresses the quay crane scheduling problem (QCSP), which involves scheduling a fixed number of quay cranes to load and unload containers from ships in a maritime container terminal. The objective is to minimize the completion time while adhering to precedence, safety margin, and noncrossing constraints. Efficient scheduling of quay cranes plays a crucial role in reducing the time vessels spend at terminals. To solve the QCSP, we explore different schedule directions for the quay cranes. Specifically, we consider three directions: unidirectional, where the quay cranes maintain a consistent movement direction from upper to lower bays or vice versa after initial repositioning; bidirectional, allowing the cranes to change direction once during operations; and multidirectional, permitting freely changing movement direction during operations. For the bidirectional QCSP, we propose a new compact mathematical formulation. To obtain valid lower bounds on the optimal completion time, we derive various relaxations of this new formulation based on the different schedule directions. Our solution framework employs logic-based Benders decomposition, decomposing the problem into an assignment master problem and operation-sequence slave subproblems. Extensive computational experiments using benchmark instances from existing literature and newly generated instances validate the efficiency and effectiveness of the lower bounds and the exact solution approach. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by the Major Program of the National Natural Science Foundation of China [Grants 72192830 and 72192831], the National Natural Science Foundation of China [Grant 72102034], and the 111 Project [Grant B16009]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0298

This paper studies a multi-objective scheduling problem in a continuous annealing operation of the steel industry, which is to simultaneously determine the production batch sizes for coils and their schedules so as to minimize the cost of setup, earliness, and tardiness. A large batch can reduce the setup costs but lead to a cost increase in earliness and tardiness. Thus, the conflict objectives of minimizing setup cost, earliness, and tardiness can be formulated separately. In this paper, we formulate a multi-objective optimization model for the problem and develop an adaptive multi-objective differential evolutionary based on deep reinforcement learning (AMODE-DRL) for effectively obtaining the Pareto solutions. In the proposed AMODE-RDL, DRL is integrated into the MODE algorithm as a controller, which can adaptively select mutation operators and parameters according to different search domains. Computational results on randomly generated instances and the practical problem instances show that DRL can effectively guide MODE to select mutation operators and parameters. The proposed algorithm can obtain better solutions compared to other powerful multi-objective evolutionary and adaptive MODE algorithms. Note to Practitioners—Setup usually leads to a decrease in production capacity and an increase in production costs. Similarly, earliness and tardiness costs are also crucial. These costs correspond to production, customer demand, and inventory, which are common objectives in production systems. However, the three objectives are generally conflicting, and it is very hard for practitioners to make appropriate decisions with manual experience. The multi-objective optimization methods can provide different scheduling for practitioners who may choose the suitable one according to current working conditions. Accordingly, the proposed model and algorithm can extend to other fields with similar characteristic problems.

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 a dynamic operation optimization problem for a steelmaking process. The problem is defined to determine optimal operation parameters that bring smelting process indices close to their desired values. The operation optimization technologies have been applied successfully for endpoint steelmaking, but it is still challenging for the dynamic smelting process because of the high temperature and complex physical and chemical reactions. A framework of deep deterministic policy gradient is applied to solve the dynamic operation optimization problem in the steelmaking process. Then, an energy-informed restricted Boltzmann machine method with physical interpretability is developed to construct the actor and critic networks in reinforcement learning (RL) for dynamic decision-making operations. It can provide a posterior probability for each action to guide training in each state. Furthermore, in terms of the design of neural network (NN) architecture, a multiobjective evolutionary algorithm is used to optimize the model hyperparameters, and a knee solution strategy is designed to balance the model accuracy and complexity of neural networks. Experiments are conducted on real data from a steelmaking production process to verify the practicability of the developed model. The experimental results show the advantages and effectiveness of the proposed method compared with other methods. It can meet the requirements of the specified quality of molten steel.

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.

This paper investigates a dynamic analytics and operation optimization method for the basic oxygen furnace (BOF) steelmaking process, which is a multi-stage process. First, based on reaction kinetics, fluid dynamics and conservation of mass, that a novel discrete-time nonlinear system with process disturbance, time delay and the constrained operation input is established characterizes the dynamics of the quality (the carbon content and the temperature) of molten steel in the BOF steelmaking process. It is difficult and complicated to realize analytics and operation optimization for the BOF steelmaking process by using the established nonlinear system directly, so a surrogate-model-based discrete-time switched system with time delay and actuator saturation is given to describe the multi-stage BOF steelmaking process. Then, sufficient conditions are derived under which the stability is guaranteed and the tracking performance is achieved. The parameters of analytics-based operation optimization algorithm can be obtained by solving linear matrix inequality problems (LMIPs). Finally, the effectiveness of the proposed method is verified by a BOF steelmaking numerical experiment example. Note to Practitioners—This paper deals with the problem of dynamic analytics and operation optimization arising from the BOF steelmaking process. Based on the real-time estimation of the carbon content and the temperature of molten steel, the plan for the operation of oxygen lance and the addition of auxiliary materials is given to produce the qualified molten steel. This paper establishes a system model based on the mechanism, and the model parameters are derived from papers verified by a large amount of data to ensure the correctness of the model. In addition, actuator saturation is applied to describe the phenomenon of restricted operation variables. Through a surrogate model approximation and theoretical analysis, the parameters of dynamic analytics and operation optimization algorithm can be obtained by solving LMIPs, which is a convex optimization problem that is easy to solve. The numerical experiment results show that the proposed method can give operators some desired references.

The single-row facility layout problem (SRFLP) is concerned with arranging facilities along a straight line so as to minimize the sum of the products of the flow costs and distances among all facility pairs. SRFLP has rich practical applications and is however NP-hard. In this article, we first investigate a dedicated symmetry-breaking approach based on the permutation group theory for reducing the solution space of SRFLP. Relevant symmetry properties are identified through the alternating group of the original solution space or the corresponding coordinate rotation space. Then, a memetic algorithm is proposed to explore promising search regions regarding the reduced solution space. The memetic algorithm employs a problem-specific crossover operator guided by${k}$-medoids clustering technique to produce meaningful offspring solutions. The algorithm additionally uses a simulated annealing procedure to intensively exploit a given search region and a distance-and-quality-based population management strategy to ensure a reasonable diversity of the population. Experimental results on commonly used benchmark instances and newly introduced large-scale instances with sizes up to 2000 facilities show that the proposed algorithm competes favorably with state-of-the-art SRFLP algorithms. It attains all but one previous best known upper bounds (BKS) and discovers new upper bounds for 33 instances out of the 93 popular benchmark instances.

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.

Reinforcement learning (RL) is a promising approach to tackling learning and decision-making problems in a dynamic environment. Most studies on RL focus on the improvement of state evaluation or action evaluation. In this article, we investigate how to reduce action space by using supermodularity. We consider the decision tasks in the multistage decision process as a collection of parameterized optimization problems, where state parameters dynamically vary along with the time or stage. The optimal solutions of these parameterized optimization problems correspond to the optimal actions in RL. For a given Markov decision process (MDP) with supermodularity, the monotonicity of the optimal action set and the optimal selection with respect to state parameters can be obtained by using the monotone comparative statics. Accordingly, we propose a monotonicity cut to remove unpromising actions from the action space. Taking bin packing problem (BPP) as an example, we show how the supermodularity and monotonicity cut work in RL. Finally, we evaluate the monotonicity cut on the benchmark datasets reported in the literature and compare the proposed RL with some popular baseline algorithms. The results show that the monotonicity cut can effectively improve the performance of RL.

The task assignment problem (TAP) is concerned with assigning a set of tasks to a set of agents subject to the limited processing and memory capacities of each agent. The objective to be minimized is the total assignment cost and total communication cost. TAP is a relevant model for many practical applications, yet solving the problem is computationally challenging. Most of the current metaheuristic algorithms for TAP adopt population-based search frameworks, whose search behaviors are usually difficult to analyze and understand due to their complex features. In this work, unlike previous population-based solution methods, we concentrate on a single trajectory stochastic local search model to solve TAP. Especially, we consider TAP from the perspective of a grouping problem and introduce the first probability learning-based local search algorithm for the problem. The proposed algorithm relies on a dual probability learning procedure to discover promising search regions and a gain-based neighborhood search procedure to intensively exploit a given search region. We perform extensive computational experiments on a set of 180 benchmark instances with the proposed algorithm and the general mixed integer programming solver CPLEX. We assess the composing ingredients of the proposed algorithm to shed light on their impacts on the performance of the algorithm.Note to Practitioners—This work is motivated by the problem of program modules designing and task allocation in parallel and distribution systems. It can also be applied to deal with job (task) grouping problems in practical industrial applications. This article presents a novel and effective learning-based local search algorithm to obtain high-quality solutions for the considered problem. The results of numerical experiments and comparisons show that our algorithm can achieve good search performances on problem instances of different scales and difficulties. Afterward, we use the proposed solution method to solve a real-life open-order slab assignment problem, which is derived from the production planning of silicon steel for an iron and steel company. The learning techniques of the proposed algorithm are of general interest and can be used in search algorithms for solving other real-life optimization problems with grouping features. For future research, we will design solution methods based on these learning techniques to address other practical optimization problems.

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.

The multidimensional knapsack problem (MKP) is a well-known combinatorial optimization problem with many real-life applications. In this article, a memetic algorithm based on probability learning (MA/PL) is proposed to solve MKP. The main highlights of this article are two-fold: 1) problem-dependent heuristics for MKP and 2) a novel framework of MA/PL. For the problem-dependent heuristics, we first propose two kinds of logarithmic utility functions (LUFs) based on the special structure of MKP, in which the profit value and weight vector of each item are considered simultaneously. Then, LUFs are applied to effectively guide the repair operator for infeasible solutions and the local search operator. For the framework of MA/PL, we propose two problem-dependent probability distributions to extract the special knowledge of MKP, that is, the marginal probability distribution (MPD) of each item and the joint probability distribution (JPD) of two conjoint items. Next, learning rules for MPD and JPD, which borrow ideas from competitive learning and binary Markov chain, are proposed. Thereafter, we generate MA/PL's offspring by integrating MPD and JPD, such that the univariate probability information of each item as well as the dependency of conjoint items can be sufficiently used. Results of experiments on 179 benchmark instances and a real-life case study demonstrate the effectiveness and practical values of the proposed MKP.

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.

Estimation of distribution algorithm (EDA) is an efficient population-based stochastic search technique. Since it was proposed, many attempts have been made to improve its performance in the context of nonlinear continuous optimization. However, the success of EDA depends on the accuracy of modeling, the effectiveness of sampling, and the ability of exploration. An effective EDA often needs to take some measures to adjust the model and to guide sampling. In this article, we propose a novel EDA which applies the idea of Kalman filtering to revise the modeling data and a learning strategy to improve sampling. The filtering scheme modifies the modeling data set using an estimation error matrix based on historic solution data. During the sampling process, the learning strategy determines the region to sample next based on the sampling outcomes so far, instead of completely random sampling. The proposed EDA also employs a multivariate probabilistic model based on copula function and can quickly reach the promising area in which the optimal solution is likely to be located. A collection of general benchmark functions are used to test the performance of the proposed algorithm. Computational experiments show that the EDA is effective.Note to Practitioners—In many process industries, there exist black-box operation optimization problems and large-scale nonlinear optimization problems with variable coupling. For these problems, it is difficult to establish mechanism models between input and output. However, real-time data can be measured from the system through sensors. We can utilize this process information to optimize the system so as to attain the desired objective. In this article, we propose a novel estimation of distribution algorithm (EDA) which applies a filtering scheme to revise the modeling data and a learning strategy to improve sampling, which can solve the problems with the characteristics of nonlinearity, variable coupling, and large scale. Computational experiments show that the EDA is effective. In the future, the proposed algorithm can be applied to some practical optimization problems such as operation optimization in blast furnace, which is considered as a continuous production process with variable coupling. The algorithm has the potential to help optimizing the process control parameters.

The steelmaking process in the iron and steel industry involves complicated physicochemical reactions. The main aim of steelmaking is to adjust the quality of molten steel. During the steel-tapping process, the temperature and carbon content are the most essential quality indices for end-point prediction. This article presents a novel machine learning framework for the endpoint prediction problems in the smelting process. Considering the importance of data representation in modeling, the original data are inputted to a stacked autoencoder (SAE) to extract the essential features in an unsupervised manner. The top layer is then designed as a sparse Bayesian regression (SBR) layer to obtain the predicted mean values and error bars that measure the uncertainty in the prediction. To improve the generalization ability of the prediction model, an intelligent optimization algorithm based on improved differential evolution (DE) is used to optimize the hyperparameters of the model. The main advantage of this model is that the underlying characteristics of the samples can be learned automatically layer by layer, instead of designing them manually. Finally, the effectiveness of the proposed method is verified using real data collected from two steel plants. The experimental results show that the proposed model gives a more precise prediction than other existing models and can provide error bars for the end-point prediction.

This article studies a multiple double-load crane scheduling problem in steel slab yards. Consideration of multiple cranes and their double-load capability makes the scheduling problem more complex. This problem has not been studied previously. We first formulate the problem as a mixed-integer linear programming (MILP) model. A two-phase model-based heuristic is then proposed. To solve large problems, a pointer-based discrete differential evolution (PDDE) algorithm was developed with a dynamic programming (DP) algorithm embedded to solve the one-crane subproblem for a fixed sequence of tasks. Instances of real problems are collected from a steel company to test the performance of the solution methods. The experiment results show that the model can solve small problems optimally, and the solution greatly improves the schedule currently used in practice. The two-phase heuristic generates near-optimal solutions, but it can still only solve comparatively modest problems within reasonable (4 h) computational timeframes. The PDDE algorithm can solve large practical problems relatively quickly and provides better results than the two-phase heuristic solution, demonstrating its effectiveness and efficiency and therefore its suitability for practical use. Note to Practitioners-Bridge cranes are commonly used to move heavy items in manufacturing and logistics systems. Generally, more than one crane runs on a common track. The latest versions of such cranes, such as those used in slab yards in the steel industry, can hold two items simultaneously. Operations scheduling of multiple double-load cranes involves the assignment of tasks to the cranes, the combination of tasks to double-load operations, and sequencing of the tasks, considering the noncrossing constraint between cranes. Effective solution of this complex problem can help to fully utilize the crane capability, increase productivity, and reduce energy consumption. This article models this problem and develops a heuristic solution that combines differential evolution (DE) and DP. Experiment results show that the algorithm is effective and efficient for practical use in slab yards. It may also be applicable to other systems using similar cranes.

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.

We study integrated production- and delivery-scheduling problems that arise in practical make-to-order settings in several industries. In these problems, make-to-order products are first processed in a plant and then delivered to customer sites through two stages of shipping: first, from the plant to a pool point (e.g., a port, a distribution, or a consolidation center) and, second, from the pool point to customer sites. The objective is to obtain a joint schedule of job processing at the plant and two-stage shipping of completed jobs to customer sites to optimize a performance measure that takes into account both delivery timeliness and total transportation costs. We consider two problems in which delivery timeliness is measured by total or maximum lead time of the jobs and study both offline and online versions of these problems. For the offline problems involving a single production line at the plant, we provide optimal dynamic programming algorithms. For the more general offline problems involving multiple production lines at the plant, we propose fast heuristics and analyze their worst-case and asymptotic performances. For the online problems, we propose online algorithms and analyze their competitive ratios. By comparing our offline heuristics with lower bounds using randomly generated test instances, it is shown that these heuristics are capable of generating near-optimal solutions quickly. Using real data from Baosteel’s Meishan plant, we also show that our corresponding offline heuristic generates significantly better solutions than Baosteel’s rule-based approach. In addition, our computational results on the performance of the online algorithms relative to the offline heuristics generate important methodological insights that can be used by practitioners in choosing a specific solution approach.

This paper proposes a dynamic analytics method based on the least squares support vector machine with a hybrid kernel to address real-time prediction problems in the converter steelmaking process. The hybrid kernel function is used to enhance the performance of the existing kernels. To improve the model's accuracy, the internal parameters are optimized by a differential evolution algorithm. In light of the complex mechanisms of the converter steelmaking process, a multistage modeling strategy is designed instead of the traditional single-stage modeling method. Owing to the dynamic nature of the practical production process, great effort has been made to construct a dynamic model that uses the prediction error information based on the static model. The validity of the proposed method is verified through experiments on real-world data collected from a basic oxygen furnace steelmaking process. The results indicate that the proposed method can successfully solve dynamic prediction problems and outperforms other state-of-the-art methods in terms of prediction accuracy.

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.

We consider several integrated production, inventory, and delivery problems that arise in a number of practical settings where customer orders have pre-specified delivery time windows. These orders are first processed in a plant and then delivered to the customers by transporters (such as trains and air flights) which have fixed delivery departure times. If an order is completed but not immediately delivered by a transporter, the order is kept temporarily in inventory, which incurs an inventory cost. There is a delivery cost for delivering an order, which varies with the departure time. Given a set of orders, the objective is to find an integrated schedule for processing the orders, keeping finished orders in inventory if necessary, and delivering them to the customers such that the total inventory and delivery cost is minimum. We consider two classes of problems: where order delivery is splittable and where order delivery is nonsplittable. For each of the problems considered, we study its computational complexity by either showing that the problem is NP-hard or proposing an algorithm that can find an optimal solution. For the two most general problems, we show that any polynomial time algorithm has an arbitrarily bad worst-case performance bound, and propose combined column generation and tabu search heuristic algorithms that can find near optimal solutions for them in a reasonable computational time. The online appendix is available at https://doi.org/10.1287/ijoc.2016.0726 .

Aiming at the permutation flow-shop scheduling problem (PFSSP) with makespan criterion, a combination algorithm based on differential evolution (DE) and estimation of distribution algorithm (EDA), namely DE-EDA, is proposed. Firstly, DE-EDA combines the probability-dependent macro information extracted by EDA and the individual-dependent micro information obtained by DE to execute the exploration, which is helpful in guiding the global search to explore promising solutions. Secondly, in order to make DE well suited to solve PFSSP, a convert rule named smallest-ranked-value (SRV) is designed to generate the discrete job permutations from the continuous values. Thirdly, a sequence-learning-based Bayes posterior probability is presented to estimate EDA's probability model and sample new solutions, so that the global information of promising search regions can be learned precisely. In addition, a simple but effective two-stage local search is embedded into DE-EDA to perform the exploitation, and thereafter numerous potential solution(s) with relative better fitness can be exploited in some narrow search regions. Finally, simulation experiments and comparisons based on 29 well-known benchmark instances demonstrate the effectiveness of the proposed DE-EDA.

Due to the large amounts of energy consumption in the converter steelmaking production process, the furnace state generates a fierce chemical reaction, and accompanies with high temperature. In this paper, in order to accurately control and optimize the converter steelmaking production process, and guarantee the quality of products, the data analytics method based on least square support vector machine (LSSVM) is used to establish the operation optimization model of converter steelmaking. Meanwhile, a kind of operation optimization method based on improved estimation of distribution algorithm (IEDA) is proposed, and Gaussian model is selected as the probabilistic model. In order to increase the diversity of population, the variable scale variance strategy is developed. In addition, aiming at the local search ability, the mutation mechanism of modified differential evolution algorithm is adopted in the search process. The experimental results illustrate that the proposed method can effectively solve the end-point control problems of temperature and carbon content in BOF steelmaking process.

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.

This paper studies a scheduling problem with batching decisions in steelmaking-continuous production. The problem is to minimize the makespan by selecting machines for a set of charges and given the charges scheduling as well as batching decisions. We formulate the problem as a MILP model by considering the practical technological requirements and the rules of batching. To solve the problem, we propose a Subpopulation-based Differential Evolution (SPDE) algorithm with a real-coded representation for fitness evaluation, a classification scheme for a trade-off between exploration and exploitation and a new perturbation-based neighborhood search. Computational results on random instances show that the proposed algorithm can obtain better solutions than other DE variants tested. In addition, the proposed algorithm competes well with IBM ILOG CPLEX optimizer in solving the problem.

This paper deals with the energy consumption prediction in steel industry using particle swarm optimization-based back propagation Neural Network. More than ten types of energy including electricity, coal, power and gas are considered simultaneously. The problem is further complicated by the consumption, regeneration and conversion of energy. The objective is to estimate as accurately as possible the amount of energy to be consumed for steelmaking operation in future production horizon. The improved neural network algorithm is designed by introducing momentum term, adaptive learning rate and swarm intelligence. The test results of real data from a steel enterprise show that the proposed method outperforms the standard version back propagation with respect to prediction accuracy and running time.

In order to explore and extend the ability and application of Differential Evolution (DE), a Contribution-guided Discrete Differential Evolution (C-DDE) is proposed in this paper for the Quadratic Multiple Knapsack Problem (QMKP), which is a challenging combinatorial optimization problem with NP-Hard and a number of applications. C-DDE extends the traditional standard DE by adopting a novel hybrid mutation operation strategy, which includes “DE/rand/1” mutation and a new contribution-guided mutation operator. They are adopted interchangeably based on a uniform distribution. The definition of contribution for an object to a knapsack is presented, which is applied to guide an individual to evolve into an improved mutant individual and to accelerate the calculation of fitness value for mutant individuals. Traditional “DE/rand/1” is utilized as a dedicated perturbation strategy to ensure a global diversification of the search procedure. The contribution-guided mutation is utilized as self-evolution strategy for intensification of ability in searching for better solutions. The proposed algorithm has been tested on the set of 27 well-known benchmarks. The experimental results demonstrate the efficiency and robustness of our proposed algorithm to reach good results.

This paper studies a supply chain scheduling problem in cold rolling, which is derived from practical steel production. The problem is to make coil schedules for all the production lines involved in the supply chain, with the aim of balancing the capacity of each production line, and minimizing the total changeover cost. To describe the problem, we formulate a mixed integer linear programming (MILP) model with consideration of all practical technological requirements. The strong AP-hardness of the problem motivates us to develop an improved discrete differential evolution (DE) algorithm to solve it. We represent individuals of the population as integer-coded matrixes. In the proposed DE algorithm, an improved mutation operation and a new double-mode crossover operation which is composed of two operators with different evolution purposes are proposed. Moreover, self-adaptive control parameters cooperated with the proposed evolution strategies are adopted to enhance the performance of algorithm. By computational experiments, the results show that the proposed DE algorithm outperforms the compared DE algorithms for solving the supply chain scheduling problem. In addition, the proposed algorithm is also competitive in comparison with the commercial optimization solver CPLEX.

Differential evolution (DE) is a well-known optimization algorithm that utilizes the difference of positions between individuals to perturb base vectors and thus generate new mutant individuals. However, the difference between the fitness values of individuals, which may be helpful to improve the performance of the algorithm, has not been used to tune parameters and choose mutation strategies. In this paper, we propose a novel variant of DE with an individual-dependent mechanism that includes an individual-dependent parameter (IDP) setting and an individual-dependent mutation (IDM) strategy. In the IDP setting, control parameters are set for individuals according to the differences in their fitness values. In the IDM strategy, four mutation operators with different searching characteristics are assigned to the superior and inferior individuals, respectively, at different stages of the evolution process. The performance of the proposed algorithm is then extensively evaluated on a suite of the 28 latest benchmark functions developed for the 2013 Congress on Evolutionary Computation special session. Experimental results demonstrate the algorithm's outstanding performance.

This paper studies a challenging problem of dynamic scheduling in steelmaking-continuous casting (SCC) production. The problem is to re-optimize the assignment, sequencing, and timetable of a set of existing and new jobs among various production stages for the new environment when unforeseen changes occur in the production system. We model the problem considering the constraints of the practical technological requirements and the dynamic nature. To solve the SCC scheduling problem, we propose an improved differential evolution (DE) algorithm with a real-coded matrix representation for each individual of the population, a two-step method for generating the initial population, and a new mutation strategy. To further improve the efficiency and effectiveness of the solution process for dynamic use, an incremental mechanism is proposed to generate a new initial population for the DE whenever a real-time event arises, based on the final population in the last DE solution process. Computational experiments on randomly generated instances and the practical production data show that the proposed improved algorithm can obtain better solutions compared to other algorithms.

To solve the discrete optimization problem, the traditional continuous differential evolution (DE) algorithm has to be modified in individual representation or evolution strategy. Inspired from a pair of reciprocal operators (pointer and address-of) in computer programming language, a novel pointerbased discrete differential evolution (PDDE) is presented in this paper. Making use of the permutation of integers as the individual representation, PDDE redefines the addition and subtraction operations of traditional DE to construct discrete mutation operator. In addition, the scaling factor and crossover probability factor are redefined to fit the discrete operation. The performance of PDDE is evaluated through extensively experiments on comparing general searching ability and solving resource-constrained project scheduling problem. The computational results show that the proposed PDDE is efficient.

In many engineering applications, the dynamic optimization problems with Ordinary Differential Equations (ODE) or Differential Algebraic Equations (DAE) constraints are encountered frequently. These types of problems are solved difficultly because of the characteristic of their nonlinear, multidimensional and multimodal. In this paper, a novel hybrid Differential Evolution (DE) and Estimation of Distribution Algorithm (EDA) is proposed for the dynamic optimization problems. A novel hybrid scheme based on DE and EDA (DE-EDA) is designed to generate the offspring population. Using the DE-EDA, the population can reach a promising area in which the optimal solution is located speedily. A modified mutation scheme is proposed which can increase the diversity of the population. In addition, the modeling and sampling scheme based on empirical Copula is used to improve the speed of modeling and sampling. Eight optimal control optimization problems and one parameter estimation problem are tested to measure the performance of the algorithm. Experimental results show that the algorithm is feasible and effective.

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.

Abstract: A production scheduling problem for hot rolling seamless steel tube at Tianjin Pipe Corporation of China is studied. Considering the complexity of the problem and the acceptable time for solving it, a rule-based heuristic approach is proposed and implemented. The proposed approach is a bottleneck scheduling method and considers simultaneously all production processes in three production units and ‘optimizes’ them as a whole. Additionally, the running result shows, on average, that a 3% increase in throughput and a 5% reduction in late deliveries have been achieved since the system implementation.