Steelmaking-continuous Casting Production Research Articles

A robust optimization approach for steeling-continuous casting charge batch planning with uncertain slab weight

The volatility of slab weight in steelmaking-continuous casting (SCC) production, attributed to factors such as flexible order demand, is addressed in this paper. A robust optimization mathematical model for charge batch planning (CBP) with uncertain slab weight is established, and a collaborative optimization method using the surrogate Lagrangian relaxation (SLR) framework and improved objective feasibility pump (IOFP) is developed to solve the problem. In the SLR method, new step-size updating conditions are developed, eliminating the need for pre-estimating the optimal dual value. Additionally, only a subset of subproblems that satisfy the optimality conditions of the surrogate needs to be solved to overcome the low optimization efficiency resulting from oscillations in the feasible domain during internal searches in traditional Lagrangian relaxation (LR) methods. The IOFP method is employed to match the structure of the subproblem model of 0–1 mixed integer programming (MIP). During the search for integer solutions, a weighted objective function is added to the auxiliary model to improve the quality of solutions. Furthermore, it combines a variable neighborhood branching method to prevent the algorithm from entering into cycles. Finally, the effectiveness of the proposed model and the performance of the algorithm are validated through simulation experiments.

A decomposition-based two-stage online scheduling approach and its integrated system in the hybrid flow shop of steel industry

Steelmaking-continuous casting (SCC) is one of the most critical building blocks in the modern steel industry. Many random events occur in the real-world SCC production system. In this paper, we propose a two-stage online scheduling policy that protects the baseline schedule by the slacks provided by intra-flow times and casting speeds. The main task of the two-stage online scheduling model is: (1) to make “here-and-now” decisions for minimizing economic costs and penalties caused by constraint violations; (2) make “wait-and-see” decisions for online scheduling. Afterward, we propose a decomposition-based optimization algorithm that divides the online scheduling problem into a master problem (MP) to seek partial solutions at the last processing stage and a slave problem (SP) to check optimal solutions for upstream processing stages. Then, we employ the IBM ILOG CPLEX to solve MP and use the constraint programming (CP) optimizer to solve SP. Sensitivity analyses and algorithm comparisons are conducted on a set of well-synthetic and realistic instances to validate the proposed model and algorithm. The results show that the proposed online scheduling model and algorithm can solve realistic industrial case studies. Finally, we also develop a scheduling system integrating the proposed model and algorithm.

An Efficient and Effective Approach for the Scheduling of Steelmaking-continuous Casting Process With Multi Different Refining Routes

With the rapid development of market-oriented demand of iron and steel enterprises towards multi variety, small batch and on-time delivery, the functional requirements of steelmaking-continuous casting (SCC) production process with multi different refining routes for the dynamic balance of logistics, resources and time increase sharply. An effective scheduling of SCC process is important significance for improving the efficiency of steelmaking production and reducing the material and energy consumption. This paper develops an improved Lagrangian relaxation (LR) approach to address this problem based on time-indexed formulation while considering SCC scheduling performance indexes: sojourn time and tardiness of each job in the last stage. A direction controllable target estimation level adjustment strategy with tighter lower bound is addressed to overcome the premature convergence and weaken the oscillation in LR iteration. Computational experiment is verified based on the actual steelmaking plant in China. The computational results show that the approach improves the schedule strategy for the actual SCC process, and promotes the development of the schedule theory with the separate structure characteristics.

An integrated production batch planning approach for steelmaking-continuous casting with cast batching plan as the core

The development of the high-efficiency continuous casting technology makes it possible to continuously cast with multi-cast batching plans. The preparation of such steelmaking-continuous casting (SCC) production batching plan has become a new requirement to promote the efficient steel production. From the perspective of overall production system, an integrated approach with the cast batching plan as the core was proposed, which changes the step-by-step optimization way of combination and sequencing for preparing charge batching plan and cast batching plan sequentially. This approach, which can perform integrated combination and sequencing, directly prepares the SCC production batching plan with multiple cast batching plans that can be continuously cast, and takes into account the charge batching plans. Taking minimizing the weight of unplanned slabs, maximizing the production efficiency of continuous casters, and minimizing the penalty value for the change of dimensions of the adjacent slabs as the objectives, a multi-objective mixed-integer programming model was established. An improved NSGA-II combined with a local search strategy was designed, and the practical aspects such as multiple grades continuous casting rules and on-line width adjustable rules were considered. The test result with data from a steel plant in China indicated that the improved algorithm could obtain better slab combination sequence results compared with the NSGA-II and SPEA2. Simultaneously, compared with the manual approach and the traditional approach of preparing the charge batching plan and cast batching plan sequentially, the integrated approach can not only reduce the residual material rate by 4.96% and 0.42%, improve the quality of the solution, but also improve the efficiency of planning.

Ladle intelligent re-scheduling method in steelmaking–refining–continuous casting production process based on BP neural network working condition estimation

Frequent delays will be experienced in the start-up of molten steel on the converter equipment during the steelmaking–continuous casting (SCC) production process due to the untimely supply of molten iron or scrap, which may cause conflicts between adjacent heat on the same equipment or in the same casting. The casting machine is cut off, resulting in the failure of the static scheduling plan. SCC production ladle re-scheduling is based on the premise that the production process path remains unchanged, the operation of adjacent heat on the converter and refining furnace does not conflict, and the casting of adjacent heat within the same casting is continuous. The ladle re-scheduling of steelmaking and continuous casting production aims at continuously casting many charges with the same cast and avoiding conflicts of adjacent charges on the same machine. This mechanism proposes a method of ladle re-scheduling in the production process of steelmaking–refining–continuous casting, which is divided into two parts: plan re-scheduling and ladle optimisation scheduling. Firstly, a re-scheduling optimisation model of the steelmaking and continuous casting production is built. This model aims at minimising the waiting time of all charges. The re-scheduling strategy of steelmaking and continuous casting production is proposed by interval processing time of charges and scheduling expert experience. This strategy is composed of two parts: re-scheduling charge decision and charge processing machine decision. Then, the first-order rule learning is used to select the optimisation target to establish the ladle optimal scheduling model. The ladle matching rules are extracted on the basis of the rule reasoning of the minimum general generalisation. The ladle optimisation scheduling method that consists of the optimal selection of the ladle and the preparation of the optimal path of the ladle is proposed. Ladle selection is based on the production process and adopts rule-based reasoning to select decarburised ladle after choosing dephosphorised ladle. Ladle path preparation, which is a multi-priority heuristic method, is designed to decide the path of the ladle from the converter to the refining furnace to the continuous casting machine. Finally, this mechanism was actually verified based on the large-scale data of a steel company in Shanghai, China. Results showed that the production efficiency of steelmaking-refining-continuous casting was improved.

Research on steelmaking-continuous casting production scheduling problem with uncertain processing time based on Lagrangian relaxation framework

Research on steelmaking-continuous casting production scheduling problem with uncertain processing time based on Lagrangian relaxation framework

Research on steelmaking-continuous casting production scheduling problem with uncertain processing time based on Lagrangian relaxation framework

Research on steelmaking-continuous casting production scheduling problem with uncertain processing time based on Lagrangian relaxation framework

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.

A robust dynamic scheduling approach based on release time series forecasting for the steelmaking-continuous casting production

In this work, the dynamic scheduling problem is investigated considering the uncertainty of the job release time in steelmaking-continuous casting production processes. In contrast to existing dynamic scheduling strategies, a novel robust dynamic scheduling approach based on release time series forecasting (RDSA_RTSF) is proposed. The proposed RDSA_RTSF consists of two stages, i.e., offline preparation and online robust dynamic scheduling. In the offline preparation stage, a release time series forecasting model is established using historical data, and the forecasting accuracy of the model is calculated. In the online robust dynamic scheduling stage, a chance constrained programming (CCP) model is built first for rescheduling based on the predicted release time series and the statistical information of the forecasting accuracy. A robust schedule is subsequently generated by using a Monte Carlo simulation and an evolutionary algorithm to solve the CCP model. The evolutionary algorithm is formulated by combining a genetic algorithm with a local search strategy based on the problem characteristics. Computational experiments based on real data from a steel plant in China show that the proposed RDSA_RTSF strategy performs better than classical approaches in obtaining robust schedule results under a dynamic environment with uncertain release times.

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.

A preference-inspired multi-objective soft scheduling algorithm for the practical steelmaking-continuous casting production

Abstract Uncertainty is the most challenging problem for implementing scheduling algorithms under practical environments, since the schedule released into a shop floor with optimal objectives often deteriorates or even suffers infeasibility during its execution period. This paper focuses on the uncertain scheduling problem arising from the steelmaking-continuous casting (SCC) manufacturing system and proposes a multi-objective soft scheduling (MOSS) to overcome this challenge. In this study, a soft-form schedule including critical decisions and characteristic indicators is introduced to provide more flexibility against random disturbances. In the MOSS algorithm, we propose a preference-inspired chemical reaction optimization (PICRO) algorithm to solve the uncertain SCC scheduling problem with soft-form solutions, in which the objectives of waiting time, cast-break and over-waiting are tackled by the preference-inspired method. In the PICRO, a simulation-based T-test method is used to evaluate solutions, and a knowledge-based local search (KLS) is embedded to enhance the convergence of PICRO. Following this, a clean-up procedure is proposed for ranking and selecting the best solutions in the final population output by the PICRO. Computational experiments on the synthetic and real-world SCC scheduling instances demonstrate that the proposed MOSS algorithm can result in significantly better solutions compared to other algorithms under practical environments.

Production scheduling problems of steelmaking-continuous casting process in dynamic production environment

A concept of production scenario for the steelmaking-continuous casting production process and the mathematical description of such concept were proposed. The production scenario was described with the variation of the equipment status and the production material properties based on the executing production schedule. Then, the dynamic characteristics of the production process could be described with the evolution process of production scenario. Through analyzing the influence of the dynamic production scenario on production scheduling, three key points about the scheduling problems were identified: the problem for integrating the schedules of different batches that is non-neglected when making a schedule, the problem for matching the material flow with the schedule that should be solved when implementing a schedule, and the problem for eliminating the deviations between the initial schedule and implemented schedule that should be solved when rescheduling in a disturbed environment. Finally, a set of experiments were conducted, and the results demonstrated that making the production schedule and solving the rescheduling problem for steelmaking-continuous casting process with addressing the above three problems improve the adaptability of the schedule in dynamic environment.

A Two-Phase Soft Optimization Method for the Uncertain Scheduling Problem in the Steelmaking Industry

In this paper, an uncertain scheduling problem arising from the steelmaking-continuous casting (SCC) production system is investigated. For the practical SCC production system, it is difficult to obtain a schedule with better performance using traditional deterministic scheduling methods since there exists uncertainty in processing times. According to the analysis on characteristics of the uncertain SCC scheduling problem (SCCSP), we construct a soft-form schedule which includes slack ratios as characteristic indexes and the job sequence at the casting stage as key decision variables to cope with the uncertainty in processing times, and propose a two-phase soft optimization method to solve the uncertain SCCSP with the just-in-time and the waiting time objectives under the break probability. In the first phase, the continuous estimation distribution algorithm (EDA) with the ordinal optimization policy is proposed to optimize slack ratios under the chance constraint, in which the optimal computing budget allocation with constrained optimization is applied to reduce the computational burden. In the second phase, based on the above optimized characteristic indexes, the discrete EDA with a local search procedure is proposed to optimize the job sequence at the casting stage. Finally, computational experiments with various scales and noise levels are performed to validate the effectiveness of the proposed algorithm.

Dynamic scheduling in steelmaking-continuous casting production for continuous caster breakdown

In the steelmaking-continuous casting (SCC) production process, machine breakdown is one of the most common disturbances which may make the current schedule unrealisable. Existing rescheduling models for machine breakdown only employ one constraint that charges cannot be processed on this machine in its failure period. However, this method is effective for steelmaking furnace breakdown and refining furnace breakdown but invalid for continuous caster breakdown. Due to the production characteristics of continuous caster, reallocating a casting order and a continuous caster for each unfinished charge on the broken down continuous caster is necessary before making a new schedule. Different reallocation strategies have different impacts on charge’s processing time and processing stage route in the dynamic scheduling process. Therefore, SCC dynamic scheduling for the continuous caster breakdown is different from the other machines. In this paper, the impacts of these strategies are studied, and a dynamic scheduling model which can be used to generate a new schedule for each strategy is built. To obtain a high-quality solution in acceptable computational time for this model with NP-hard feature, a hybrid algorithm featuring a genetic algorithm combined with a general variable neighbourhood search is developed based on the problem-specific characteristics. Computational experiments on practical production data show that the proposed rescheduling method is effective for SCC dynamic scheduling with continuous caster breakdown.

A prediction-based online soft scheduling algorithm for the real-world steelmaking-continuous casting production

Optimal scheduling of steelmaking production contributes to boosting productivity, reducing costs and achieving sustainable manufacturing for an integrated steel company. However, the optimal schedule is always difficult to implement in the real-world production system, because its optimality and feasibility are affected by various uncertain factors. In this paper, we study an uncertain scheduling problem arising from the steelmaking-continuous casting (SCC) production process which considers the cost and penalty objectives. To solve this problem, we propose a prediction-based online soft scheduling (OLSS) algorithm which belongs to predictive-reactive approach. In the proposed algorithm, a surrogate model named Gaussian process regression (GPR) is used to predict the characteristic index, slack ratio, which is able to trade off the objectives between the cost and the penalty of cast-breaks. When new batches are released to the shop floor, the soft schedule including critical decisions and characteristic indexes is determined by a dynamic optimization algorithm based on the predicted value. In the reactive phase, a heuristic method is presented to determine other non-critical decisions. Finally, the computational results show that the OLSS outperforms other algorithms in penalty objective, and obtains approximate effects in cost objective.

An improved cross entropy algorithm for steelmaking-continuous casting production scheduling with complicated technological routes

In order to increase productivity and reduce energy consumption of steelmaking-continuous casting (SCC) production process, especially with complicated technological routes, the cross entropy (CE) method was adopted to optimize the SCC production scheduling (SCCPS) problem. Based on the CE method, a matrix encoding scheme was proposed and a backward decoding method was used to generate a reasonable schedule. To describe the distribution of the solution space, a probability distribution model was built and used to generate individuals. In addition, the probability updating mechanism of the probability distribution model was proposed which helps to find the optimal individual gradually. Because of the poor stability and premature convergence of the standard cross entropy (SCE) algorithm, the improved cross entropy (ICE) algorithm was proposed with the following improvements: individual generation mechanism combined with heuristic rules, retention mechanism of the optimal individual, local search mechanism and dynamic parameters of the algorithm. Simulation experiments validate that the CE method is effective in solving the SCCPS problem with complicated technological routes and the ICE algorithm proposed has superior performance to the SCE algorithm and the genetic algorithm (GA).

A soft-decision based two-layered scheduling approach for uncertain steelmaking-continuous casting process

Strong uncertainties is a key challenge for the application of scheduling algorithms in real-world production environments, since the optimized schedule at a time often turns to be deteriorated or even infeasible during its execution due to a large majority of unexpected events. This paper studies the uncertain scheduling problem arising from the steelmaking-continuous casting (SCC) process and develops a soft-decision based two-layered approach (SDA) to cope with the challenge. In our approach, traditional scheduling decisions, i.e. the beginning time and assigned machine for each job at each stage, are replaced with soft scheduling decisions in order to provide more flexibility towards unexpected events. Furthermore, all unexpected events are classified into two categories in terms of the impact degree on scheduling: critical events and non-critical events. In the two-layered solution framework, the upper layer is the offline optimization layer for handling critical events, in which a particle swarm optimization algorithm is proposed for generating soft scheduling decisions; while the lower layer is the online dispatching layer for handling non-critical events, where a dispatching heuristic is designed to decide in real time which charge and when to process after a machine becomes available, with the guidance of the soft schedule given by the upper layer. Computational experiments on randomly generated SCC scheduling instances and practical production data demonstrate that the proposed soft-decision based approach can obtain significantly better solutions compared to other methods under strongly uncertain SCC production environments.

A Three-level Batching Strategy for the Planning of Steelmaking-continuous Casting Production

This paper focuses on the optimal planning of steelmaking-continuous casting production in real steelmaking plant. The tasks of steelmaking planning are to make the decisions as how to determine the relation between slabs and charges, the sequence of charges in casts and the casting width of slabs while considering the known information about the contract properties, the size properties and processing properties, etc. Effective planning can satisfy the capacity of downstream and continuously casting the steel molten. A three-level batching policy consisting of charge planning, tundish planning, cast planning is proposed in this paper. The different requirement of width in charge planning, tundish planning, cast planning are considered as the performance indicators and constraints equations respectively to formulate the problems. A hybrid optimal strategy combined with the iterated local search (ILS), variable neighborhood search (VNS), and the hybrid optimal strategy with ant colony optimization is adopted. Numerical experiments are done to verify the effectiveness of the three-level batching strategy by using practical data set collected from the steelmaking plant in Baosteel which is one of the most advanced iron and steel enterprises in China. Computational experiments demonstrate that the models and algorithms developed can make an optimal planning in a computationally efficient manner to improve the steel production.

An Improved Differential Evolution Algorithm for Practical Dynamic Scheduling in Steelmaking-Continuous Casting Production

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.

Complete Modification Rescheduling Method and Its Application for Steelmaking and Continuous Casting

Delayed processing time and machine failures upset the plan in steelmaking-continuous casting (SCC) production, which make production plan infeasible. The manual repairing cannot satisfy objectives of quick response and optimal scheduling. The practical rescheduling with 1-4 refining stages cannot abstract as three stages hybrid flow shop (HFS). A method is presented for the rescheduling problem, which includes two steps. Firstly, the assigning machine strategy and its computing algorithm are given. Secondly, the mathematical models are developed as multi-objective model based on practical production constraints, so as to solve machine conflicts. The dynamic scheduling system for SCC with the rescheduling method has been successfully applied to Shanghai Baoshan steel plant, and realizes rapidly optimal rescheduling.