Casting Scheduling Research Articles

A hybrid particle swarm optimisation for flexible casting job shop scheduling problem with batch processing machine

AbstractA flexible casting job shop scheduling problem (FCJSP) with batch processing machines is proposed based on the analysis of the flexible job shop scheduling problem (FJSP) and the study of the expendable casting process. Considering the makespan under the influence of the energy consumption, the authors apply the time execution window to the FCJSP model in conjunction with the characteristics of casting production. A hybrid particle swarm optimisation algorithm (HPSO) is developed to solve the FCJSP. The HPSO employs a block integration decoding rule to address scheduling integration. Particle swarm optimisation is used for global search, employing both discrete and continuous search strategies. Furthermore, the local search employs tabu search with neighbourhood operations based on knowledge‐driven techniques. Simulation experiments demonstrate the feasibility of the proposed optimisation model. In the end, the HPSO algorithm has been successfully applied to the real expendable casting scheduling. The results demonstrate that it is more efficient and robust than previously reported algorithms.

Towards sustainable production with resource efficiency: An empirical study of steelmaking continuous casting scheduling

Traditional heavy industries that are energy-intensive have much potential for energy saving and carbon emission reduction. Focusing on the production scheduling of steelmaking continuous casting, this study aims to propose a twin transformation strategy and investigate the impact on sustainable indicators while considering resource efficiency and productivity. Continuous casting is energy-intensive and the bottleneck for steelmaking. The batching and sequencing of the charges are crucial for energy resource management. This study developed a hybrid genetic algorithm that integrated charge batching decisions to minimize makespan and the total weighted tardiness for continuous casting while minimizing energy consumption for a circular supply chain. An empirical study is conducted to estimate the validity of this approach under various scenarios in real settings. The results have shown practical viability of the developed solution that has been implemented in this case company, while the developed solutions can be effectively employed in other industries for sustainability.

Research on Continuous Casting–Hot Rolling Scheduling Model Involving Reheating Furnace Conversion Mode and Improved Bat Optimization Solution Algorithm

As the main energy-consuming equipment, the reheating furnace plays an important role in the scheduling of continuous casting and hot rolling for a steel mill. This paper studies the energy consumption of cold and hot slab conversion mode in a reheating furnace, forming four conversion relationships, with the goal of minimizing the coupling function between the maximum completion time of the hot rolling and the energy waste of the reheating furnace, and modelling the scheduling of a continuous casting–hot rolling process. An improved ordered pair bat algorithm is used to solve for special process conditions of the proposed scheduling model. The effectiveness of the proposed model and algorithm is verified by solving the different slab charging sequence and conversion mode. Moreover, a comparative study of different types of batches is also conducted, and it is found that the model can save more than 5000 GJ per month for the steel mill, which can achieve the goal of effective energy saving and increasing enterprise profit.

Deep reinforcement learning for solving steelmaking-continuous casting scheduling problems under time-of-use tariffs

This paper proposes a novel intelligent scheduling method based on deep reinforcement learning (DRL) to solve the multi-objective steelmaking-continuous casting (SCC) scheduling problem, under time-of-use (TOU) tariffs for the first time. The intelligent scheduling system architecture is designed, and a mathematical model is established to minimise the total sojourn time and electricity cost. To effectively reduce production costs by avoiding peak periods of electricity consumption, the ‘start time’ of the system is generated based on the Markov Decision Process (MDP), and heuristic scheduling rules related to power cost are used as the action space, with corresponding reward functions designed according to the characteristics of these two objectives. To satisfy the continuous casting which is a particular SCC constraint, a backward strategy is developed. Additionally, a branching duelling double deep Q-network (BD3QN) is adapted to guide action selection and avoid blind search in the iteration process, and then applied to real-time scheduling. Numerical experiments demonstrate that the proposed method outperforms comparison algorithms in terms of solution quality and CPU times by a large margin.

Optimizing steel coil production schedules under continuous casting and hot rolling

In continuous steel casting operations, heats of molten steel are alloyed and refined in ladles, continuously cast and cut into slabs, and hot-rolled into coils. We present a mixed-integer program that produces a daily casting schedule and that is solved using state-of-the-art software for a 100% direct-charge steel mill; two casters concurrently produce slabs, which are rolled into coils at a single hot rolling mill. This model minimizes penalties incurred by violating plant best practices while strictly adhering to safety and logical constraints to manage risk associated with manufacturing incidents. An efficient formulation, combined with variable reduction and cutting planes, expedites solutions for small instances containing hundreds of variables and thousands of constraints by factors of at least two or three (and sometimes even 100); instances an order of magnitude larger along both problem dimensions suggest solutions that reduce costs incurred using plant best practices by as much as 40%.

A novel method with constraints embedded into a cuckoo search for steelmaking–continuous casting scheduling

A novel method with constraints embedded into a cuckoo search for steelmaking–continuous casting scheduling

Two-stage distributionally robust integrated scheduling of oxygen distribution and steelmaking-continuous casting in steel enterprises

In the steel industry, the imbalance between fluctuating oxygen demand and stable supply generally results in excessive oxygen emissions and power waste. Independent optimal scheduling of oxygen distribution (OD) or steelmaking-continuous casting (SCC) has limited ability to handle this issue. To address this challenge, we propose an integrated scheduling model that allows for flexible interaction between OD and SCC. We first develop an SCC scheduling model that applies to machine sharing of duplex and conventional smelting, and derive an OD scheduling model. A critical demand interface is further designed to connect the scheduling models of SCC and OD, resulting in a mixed integer linear programming-based integrated scheduling model. Existing research overlooks the probability information of demand uncertainty posed by unpredictable interferences, which limits the ability to handle uncertain demands. To address this limitation, we embed demand probability distribution via a data-driven ambiguity set and upgrade the deterministic integrated scheduling model via two-stage distributionally robust optimization. Our model was tested with real data and resulted in a 15% reduction in total costs compared to independent scheduling of OD and SCC. Additionally, it effectively reduced uncertainty risk to 8.3% with low conservativeness, demonstrating superior performance compared to recent methods.

A two-stage local search heuristic for solving the steelmaking continuous casting scheduling problem with dual shared-resource and blocking constraints

A two-stage local search heuristic for solving the steelmaking continuous casting scheduling problem with dual shared-resource and blocking constraints

An enhanced cross-entropy algorithm for the green scheduling problem of steelmaking and continuous casting with uncertain processing time

Under the mainstream trend of global carbon emission reduction, this paper studies an important steelmaking-continuous casting scheduling problem (SCCSP) considering the practical technological requirements in uncertain production environment. This problem can be modeled as the green SCCSP with uncertain processing time (GSCCSP_UPTHP), whose criteria are to minimize the maximum completion time, the average waiting time, and the carbon emissions simultaneously. An enhanced cross-entropy algorithm (ECEA) is proposed for addressing it. In terms of ECEA’s coding and decoding, a two-segment coding strategy and an adaptive decoding strategy are devised according to the problem’s characteristics. In ECEA’s global search, ECEA adopts two probability models with their own self-adjustment mechanisms to collaboratively learn the valuable information from excellent individuals and quickly guide the search to the promising regions. Moreover, the novel competition and assimilation mechanisms are devised to avoid ECEA falling into local optima early. In ECEA’s local search, a problem-dependent local search based on the key points (PDLS_KP) is proposed to sequentially execute the small neighborhood search (SNS) and the large neighborhood search (LNS) starting from the promising region of each selected key point. Meanwhile, a speed-up scanning method is developed to accelerate the search process of the LNS. Extensive experiments based on both the simulation and the real-world instances from an SCC process are constructed to show the effectiveness of TSOA in solving the GSCCSP_UPTHP.

Injury characteristics in professional modern dancers: A 15-year analysis of work-related injury rates and patterns

ABSTRACT We investigated work-related-musculoskeletal-injuries (WMSI) over 15-years in professional modern dancers to determine injury rate and pattern differences due to sex and professional-experience. Injuries were coded to allow analyses by tissue-type, body-region, severity, setting, mechanism, action-causation, and repertory-style. Injury prevalence (IP) was defined as average risk of injury/dancer. Injury incidence rate (IIR) was calculated per 1000-hrs exposure/block. Negative binomial logistic regression analyses were conducted with exposure-hrs to determine IIR, p < 0.05. Multinomial logistic regressions determined differences in tissue-type, body-region, action-causation and repertory-style; Poisson loglinear regressions determined differences in severity and mechanism, p < 0.05. Females were 15-times more likely to sustain bone-injuries, p = 0.016; males 8- and 15-times more likely to sustain muscle/tendon-injuries or lacerations/contusions, p ≤ 0.016. Females were more likely to sustain severe injury resulting in more lost-workdays and missed-performances, p < 0.001. In both sexes, more time-loss-injuries (TL-inj) occurred in performance , were traumatic in nature, with an action-causation of jumping/stomping/relevé. Dancers of moderate professional-experience were 1.3-times more likely to sustain TL-inj, p = 0.026;. Identifying context-specific activities and repertory–style relationships to injury can provide insight into casting and rehearsal scheduling. Comprehending sex-specific musculoskeletal health needs allows improved dancer health management and injury prevention planning.

Steelmaking-continuous casting scheduling problem with multi-position refining furnaces under time-of-use tariffs

Steelmaking-continuous casting scheduling problem with multi-position refining furnaces under time-of-use tariffs

Scheduling of steelmaking-continuous casting process with different processing routes using effective surrogate Lagrangian relaxation approach and improved concave–convex procedure

This paper studies a steelmaking-continuous casting scheduling problem with different processing routes. We model this problem as a mixed-integer nonlinear programming problem. Next, Lagrangian relaxation approach is introduced to solve this problem by relaxing the coupling constraints. Due to the nonseparability in Lagrangian functions, we design an improved concave–convex procedure to decompose the Lagrangian relaxation problem into three tractable subproblems and analyse the convergence of the improved concave–convex procedure under some assumptions. Furthermore, we present an effective surrogate subgradient algorithm with global convergence to solve the Lagrangian dual problem. Lastly, computational experiments on the practical production data show the effectiveness of the proposed surrogate subgradient method for solving this steelmaking-continuous casting scheduling problem.

Energy-efficient steelmaking-continuous casting scheduling problem with temperature constraints and its solution using a multi-objective hybrid genetic algorithm with local search

With the increasing energy price and the urgent demand of manufacturing enterprises for energy conservation, energy-efficient scheduling (EES) technology has been widely investigated and applied in industry and academia. The steelmaking-continuous casting (SCC) production is the main energy-consuming sector and the key process for quality control of steel manufacturing. Due to the high-temperature characteristics of SCC production, the temperature drop deriving from non-processing process could directly lead to energy loss and increase the energy consumption of each procedure, which has important influence on the total energy consumption. Therefore, the energy-efficient steelmaking-continuous casting scheduling problem with temperature constraints (EESCCSPT) was concerned and a multi-objective mathematical programming model was introduced to minimize the penalty of due date deviation and the extra energy consumption measured by temperature drop. Comparing to the general scheduling problem, the constraint of minimum casting superheat and the constraint of target tapping temperature generated by the high-temperature technical requirements were directly considered to ensure schedule feasibility in terms of temperature. A multi-objective hybrid genetic algorithm combined with local search (MOHGALS) was presented, in which the enhanced evolutionary mechanisms combined with the improved genetic operators and the local search were also designed. Results of computational experiments showed that MOHGALS was more feasible and effective than NSGA-II and SPEA2 on the EESCCSPT.

An optimised steelmaking-continuous casting scheduling simulation system with unity 3D

This work considers the transportation time involved in ladle allocation during the steelmaking-continuous casting production. The optimisation problem of equipment allocation is presented, the optimal production sequence is determined and a schedule for charges is determined. In order to ensure that the operation time and the energy consumption are minimised, a solution methodology combining heuristic algorithm and conflict elimination algorithm is developed. The simulation experiment based on actual production data shows that this methodology can effectively solve the steelmaking and continuous casting scheduling problem. To validate the scheduling plan more intuitively and modify it further, we present an optimisation system based on unity 3D simulation platform. The system can effectively evaluate the optimisation of the solution and adjust the related data to modify the scheduling plan and ultimately get a reasonable rescheduling plan.

An optimised steelmaking-continuous casting scheduling simulation system with unity 3D

An optimised steelmaking-continuous casting scheduling simulation system with unity 3D

Electrical load tracking scheduling of steel plants under time-of-use tariffs

Electrical load tracking is a critical strategy for energy intensive industries to provide demand response (DR) in today’s electricity markets. It can take advantage of time-of-use (TOU) tariffs in steelmaking-refining-continuous casting (SRCC) scheduling. In this paper, we develop a continuous-time mixed integer nonlinear programming (MINLP) model subject to energy-awareness and TOU tariffs to manage the electrical load tracking scheduling of SRCC. Due to the complex cases among load intervals of electrical load tracking, time-slots of TOU tariffs and processing cycles of jobs result from different time granularities of the electrical load tracking and TOU tariffs, we formulate the objective functions with derived general formulations that can apply to all cases. An improved strength Pareto evolutionary algorithm 2, AHSPEA2, is developed to solve this proposed model, whose search ability and population diversity are enhanced greatly by two strategies, the arithmetic crossover operator and the improved hybrid self-adaptive mutation operators. The computational results demonstrate that AHSPEA2 is far superior and prove its effectiveness in providing high-quality scheduling plans which follow the pre-contracted load curve carefully to decrease deviations and reduce electricity costs simultaneously.

Research on Steelmaking-Continuous Casting Production Scheduling Problem Based on Augmented Lagrangian Relaxation Algorithm under Multi-Coupling Constraints

Abstract Steelmaking - continuous casting production scheduling is an important part of steelmaking production system. A scientific and reasonable steelmaking - continuous casting production scheduling is the key to improve the production efficiency of the steelmaking - continuous casting production system. In this paper, with the shortest total charge waiting time and the castings that are processed on time as the optimization goal, with the charges that are casted continuous within same casting and machine capacity constraints and so on as the constraints to established a mixed integer programming mathematical model. The augmented Lagrangian relaxation algorithm is used to solved the scheduling problem. The diagonal quadratic approximation method is used to linearize quadratic term so that it can be transformed into a problem to be solved with separable structure. Experiments show that the algorithm proposed has the advantages of fast convergence and short solution time for solving the steel-continuous casting scheduling problem compared to the traditional Lagrange algorithm, and the superiority is more obvious when the scale of the problem is increased.

Modeling and solving the steelmaking and casting scheduling problem

AbstractWe propose a general model for the problem of planning and scheduling steelmaking and casting activities obtained by combining common features and constraints of the operations from a real plant and the literature. For tackling the problem, we develop a simulated annealing approach based on a solution space made of job permutations, which uses as submodule a chronological constructive procedure that assigns processing times and resources to jobs. Our technique, properly tuned in a statistically principled way, is able to find good solutions for a large range of different settings and horizons. In addition, it outperforms both a greedy procedure and a constraint‐based solver developed for comparison purposes on almost all instances. Finally, we have collected several real‐world instances that we make available on the web along with the solution validator and our best results.

An improved artificial bee colony algorithm for steelmaking–refining–continuous casting scheduling problem

Abstract Steelmaking–refining–Continuous Casting (SCC) scheduling is a worldwide problem, which is NP-hard. Effective SCC scheduling algorithms can help to enhance productivity, and thus make significant monetary savings. This paper develops an Improved Artificial Bee Colony (IABC) algorithm for the SCC scheduling. In the proposed IABC, charge permutation is employed to represent the solutions. In the population initialization, several solutions with certain quality are produced by a heuristic while others are generated randomly. Two variable neighborhood search neighborhood operators are devised to generate new high-quality solutions for the employed bee and onlooker bee phases, respectively. Meanwhile, in order to enhance the exploitation ability, a control parameter is introduced to conduct the search of onlooker bee phase. Moreover, to enhance the exploration ability, the new generated solutions are accepted with a control acceptance criterion. In the scout bee phase, the solution corresponding to a scout bee is updated by performing three swap operators and three insert operators with equal probability. Computational comparisons against several recent algorithms and a state-of-the-art SCC scheduling algorithm have demonstrated the strength and superiority of the IABC.

Solving a real world steel stacking problem

We present a real world steel slab stacking problem. The problem features continuous production and retrieval and non-instantaneous crane movements. There are stacking constraints, based on dimensions, weight and temperature of the slabs and temporal constraints based on the casting schedule, the delivery due times as well as the availability of rolling pallets for transport. We present a prioritisation heuristic for the possible crane movements. Based on this heuristic we build a branch and bound solver as well as a greedy look-ahead heuristic. We evaluate the heuristics using randomly generated problem instances of various sizes with the same characteristics as the real world problem and find that the greedy look-ahead heuristic outperforms the branch and bound approach when using realistic time limits.