Multi-objective Integer Optimization For Batching Scheduling In Steelmaking Production

Steelmaking is one important production process of steel manufacturing system in which hot metal is refined into high-quality liquid steel and subsequently cast into solidified slabs.The production process has the characteristics of high volume production equipment,high temperature,and high energy consumption.The task of the batching scheduling problem in steelmaking production is to group a number of jobs(charges)to form job groups(casts)and decide when and on which equipment to process these jobs and job groups with the purpose of cutting production costs while improving energy efficiency.In steelmaking production,the conversion of mass flows from continuous liquid-state to discrete solid-state lead to multi-energy consumption.This thesis investigates a new kind of batching scheduling problems considering energy consumptions,which are derived from real steelmaking production.This work not only makes a contribution to the theoretical development of multi-objective integer optimization but also has important application values in improving production efficiency and dropping energy-related costs.This thesis investigates a charge batching and batching scheduling problem,a batching scheduling problem considering electricity consumption,and a batching scheduling problem considering multi-energy consumption.A discrete-coding-based multi-objective evolutionary algorithm is proposed for the charge batching and batching scheduling problem.An interactive multi-objective integer linear optimization method is developed for the batching scheduling problem considering electricity consumption.A projection splitting algorithm(PSA)is proposed for general multi-objective integer optimization problems.A spatial branch and bound(SBB)-based multi-objective integer nonlinear optimization method is proposed for the batching scheduling problem considering multi-energy consumption.The research content is summarized as follows:(1)A discrete-coding-based multi-objective evolutionary algorithm is proposed for the charge batching and batching scheduling problem.Given a set of customer orders with different requirements,this problem is to group the orders to form charges and establish a production timetable for these charges.We divide this problem into two sequential subproblems:a charge batching subproblem and a batching scheduling subproblem.The charge batching subproblem is to group customer orders to a set of charges in which slab specification is decided with the aim of optimizing production costs and customer satisfaction,and the batching scheduling subproblem is to group the charges to form casts and establish a timetable of the charges and casts with the objective of minimizing the total starting time and the total waiting time.For the two subproblems,we respectively formulate bi-objective integer linear models and design discrete-coding representations based on the problem structures,and we also develop a discrete-coding-based multi-objective discrete differential evolutionary algorithm.Finally,computational experiments demonstrate the efficiency of the proposed multi-objective algorithm.(2)An interactive multi-objective integer linear optimization method is developed for the batching scheduling problem considering electricity consumption.Under Time-of-Use(TOU)tariffs,the problem is to determine the schedules of the given charges with the objective of minimizing the total electricity costs and the total starting times.For this problem,a multi-objective integer linear optimization model is formulated and an interactive multi-objective optimization method is developed.In the method,the optimal Pareto set is first generated using a two-stage ?-constraint method and a best-compromise solution is then identified using an interactive cutting plane algorithm in which the trade-off weights are derived from the Pareto set.Running details of the multi-objective optimization method are explicated through an illustrative example.(3)A projection splitting algorithm is proposed to identify the complete Pareto set for general multi-objective integer linear optimization problems.This investigation is an extension of the practical multi-objective integer optimization problems,such as multi-obj ective batching scheduling problem in steelmaking production.For existing criterion space search approaches,they are either inefficient in each iteration or time-consuming because of a large number of iterations.In order to address these issues,PSA is proposed.In each iteration of PSA,the explored space is removed based on the identified nondominated solution and the unexplored space is decomposed into two sets of subspaces by taking advantage of spatial distribution characteristics of the top vertex and the bottom vertex of the explored space.PSA limits the number of subspaces without introducing any extra difficulty to the exploration of a subspace.A worst-case bound on the number of subproblems that are required to solve is given theoretically.Experiments on two sets of benchmark problems show that PSA performs significantly better than all the competitors in terms of the computation time.(4)A spatial branch and bound-based multi-objective integer nonlinear optimization method is developed for the batching scheduling problem considering multi-energy consumption.This problem considers the electricity consumption under TOU tariffs and the water consumption under adjustable casting speeds.Considering the nonlinear relationship between the amount of consumed water and casting speeds,this problem is formulated as a multi-objective integer nonlinear model with the objective of minimizing the cast break loss penalties,the sum of start casting times,the total electricity cost and the total amount of consumed water.Because of the nonconvex and the complexity,an SBB is developed for small-and medium-size instances,a three-phase MILP-NLP decomposition strategy is proposed for large-size instances.Experiments on randomly generated instances show that the SBB outperforms the state-of-the-art commercial solvers and the decomposition strategy is capable of generating near-optimal solutions in a reasonable time.