钢铁企业全流程物流优化问题的建模及分支——定价算法

研究了钢铁企业的全流程物流优化问题, 该问题在确保全流程各个工序机组产能和库存能力限制以及满足客户需求的前提下, 决策炼钢、连铸、热轧及冷轧工序间的物料流向和流量, 最小化物流成本、产能损失及库存费用. 为该问题建立了混合整数规划(Mixed integer programming, MIP)模型. 在问题求解中, 首先对MIP模型进行了Dantzig-Wolfe分解, 得到一个结构相对简单但列变量数目非常多的主问题和四个描述列向量空间的子问题. 然后, 从一个包含部分列变量的限制主问题出发, 通过子问题和主问题之间的迭代来获取主问题线性松弛的最优解. 最后, 将列生成同分支—定界相结合, 即分支—定价算法, 以获取原问题的整数最优解. 对某钢铁企业的实际生产数据扩展的随机算例进行仿真实验, 结果显示所提出的算法能够在合理计算时间内获得最优解或次优解.     

整数线性规划的切割与分支算法

基于整数线性规划问题的分支定界方法,以子问题或根问题的目标最优值作为参数,构造了一种新的切割不等式,能够方便地切割子问题或根问题的非整数最优解.在分支之前进行这种切割,产生了一种新的求解整数线性规划问题的切割与分支算法.将该算法应用于求解一些经典的数值例子,实验结果表明,与经典的分支定界方法相比,该算法大大减少了分支的数量,提高了计算效率.随着问题规模的增大,该算法的计算优越性体现得更加明显.     

分支定价方法求解带二维装箱约束的车辆路径问题EI北大核心CSCD

面向家具、电器等货物的物流配送场景,研究带二维装箱约束的车辆路径问题(2L–CVRP),构建了2L–CVRP的混合整数线性规划模型.为求解大规模2L–CVRP,构建了该问题集合划分模型,提出基于分支定价的方法.针对分支节点的松弛模型,基于列生成策略将其分解为线性规划主问题、带资源和二维装箱约束的最短路径子问题,并提出基于ng-route松弛策略的标签算法和基于禁忌搜索的装箱算法有效求解复杂子问题.仿真结果表明,提出的方法可高效求解大规模2L–CVRP,其中ng-route松弛策略能有效提升算法求解效率,研究成果为装箱约束下大规模车辆路径问题的高效求解提供了有效途径.     

启发式列生成算法求解带恶化效应的同构并行机调度问题

针对实际生产中广泛存在的一类带恶化效应的同构并行机调度问题,以最小化最大完工时间为优化目标,构建该问题的整数规划模型,并提出一种启发式列生成算法(HCGA)进行求解.在HCGA中,首先,利用Dantzig-Wolfe分解方法,将原问题分解为一个主问题(MP)和多个子问题;然后,设计启发式算法获得初始列,其中每列为一台机器上的一个调度方案,基于初始列构建限制主问题(RMP)模型;接着,设计快速有效的动态规划算法求解子问题,以得到需添加至RMP的列集,同时,考虑传统列生成算法收敛速度较慢,设计一系列方法来加速列生成过程;最后,基于所获取的MP线性松弛解,设计深潜启发式算法确定原问题的整数解.HCGA与商用求解器GUROBI的对比实验结果表明,HCGA可在较短时间内获得更优的解.     

高效求解整数线性规划问题的分支算法

为了提高求解一般整数线性规划问题的效率,提出了一种基于目标函数超平面移动的分支算法。对于给定的目标函数整数值,首先利用线性规划松弛问题的最优单纯形表确定变量的上、下界,然后将变量的上、下界条件加入约束条件中对相应的目标函数超平面进行切割,最后应用分支定界算法中的分支方法来搜寻目标函数超平面上的可行解。通过对一些经典的数值例子的求解计算并与经典的分支定界算法进行比较,结果表明,该算法减少了分支数和单纯形迭代数,具有较大的实用价值。     

整数线性规划的改进分支定界算法

分支定界(B&B)算法是求解整数线性规划(ILP)问题的一种最常用的方法,如何划分问题(分支)和按何种策略选择子问题进行扩展是影响算法效率的两个重要因素.提出了一种改进的分支定界算法,采用伪费用分支策略划分问题,采用深度优先搜索(DFS)策略选择子问题进行扩展,并在Matlab中编程实现.数值实验表明,改进的算法能够有效提高求解效率,当问题规模较大时,改进效果尤其明显.     

基于一种新型分支定价算法的电动车支线镇际快递配送路径规划研究

针对由电动汽车支持的支线镇际快递配送系统,提出一类新型的分支定价算法实现对车辆和货物的路径规划。研究利用时空网络将时间离散化构建模型,同时考虑了车辆资源、仓储资源和充电桩资源的管理问题。在分支定价算法中,分支策略和割平面策略的结合有效削弱了时间离散化所带来的对称性问题。强化策略则通过对生成路径变量进行有效筛选,并利用求解器帮助算法快速找到高质量可行解。实验将分支定价算法和商用求解器求解以及基于列生成的启发式算法进行对比,结果表明分支定价算法在精确求解小规模问题和启发求解中等规模问题时都具有明显优势,从而能有效地对该问题进行求解。     

调速泵结构配置协调分解优化算法及实现

建立多级调速泵结构配置连续非线性规划和整数非线性规划二阶段模型.非线性整数规划子问题采用外逼近算法求解.针对连续非线性规划主问题,提出基于割角法的可行域协调分解优化算法,证明割角法陷阱问题并建立判断准则排除已知的陷阱区域,在此基础上构建系列松弛问题得到原优化问题渐进收紧的下界估计,并最终收敛到原优化问题全局最优解.三级调速泵结构配置实例验证了算法的有效性,并给出与其他算法的比较结果.     

最小化全局完成时间的成像卫星任务规划算法

成像侦察卫星任务规划问题是一类典型多约束组合优化问题.最小化全局完成时间是任务规划领域时效性要求较高情况下的一种优化目标.提出一种整合整数规划与约束规划方法,在最小化任务规划方案全局完成时间的目标下,求解成像侦察卫星任务规划问题的组合算法.该算法通过应用Benders分解将原约束整数规划模型划分为主问题与子问题两部分,采用软件MOSEK与GECODE对主、子问题分别求解.根据子问题求解结果生成剪枝约束,返回主问题迭代,直到获得优化解.算法有效性通过仿真实验进行了检验并取得预期效果.     

一类非线性两层规划问题的递阶优化解法

提出一种求解一类非线性两层规划问题的新方法．通过引入解耦向量将非线性两层规划问题分解为独立且易于求解的子问题，利用两级递阶结构第1级求解若干优化的子问题，而在第2级利用第1级求解的结果调整解耦向量．所提出的方法借助于分解一协调原理并按迭代方式最终求得问题的最优解．对于含整数的规划问题，通过连续化处理后也可按该方法方便地求解．算例表明所提出的算法是简便而有效的．     

Group-scheduling problems in electronics manufacturing

This paper addresses the flowshop group-scheduling problems typically encountered in the assembly of printed circuit boards in electronics manufacturing. A mathematical programming model is formulated to capture the characteristics inherent to group-scheduling problems experienced in electronics manufacturing as well as those common to a wide range of group-scheduling problems encountered in other production environments. Several heuristics, each incorporating different components that underlie the tabu search concept, are developed to solve this strongly NP-hard problem effectively in a timely manner. In order to investigate the quality of the heuristic solutions with respect to tight lower bounds, an effective and efficient decomposition approach is developed. The problem is decomposed into a master problem and single-machine subproblems, and a column generation algorithm is developed to solve the linear programming relaxation of the master problem. Branching schemes, compatible with the column generation subproblems, are employed to partition the solution space when the solution to the linear programming relaxation is not integral. Furthermore, tabu search based fast heuristics are implemented to solve the subproblems, and an effective stabilization method is developed to accelerate the column generation approach. An experimental design with both fixed and random factors accompanied by rigorous statistical analyses of computational tests conducted on randomly generated test problems as well as on a large size real industry problem confirm the high performance of the proposed approach in identifying quality lower bounds and strongly suggest its flexibility and applicability to a wide range of real problems.     

Sequencing surgical cases in a day-care environment: An exact branch-and-price approach

In this paper we investigate how to sequence surgical cases in a day-care facility. We specify a multi-criteria objective function in which we minimize the peak use of recovery beds, the occurrence of recovery overtime and the violation of various patient and surgeon preferences. The limited availability of resources and the occurrence of medical precautions, such as an additional cleaning of the operating room after the surgery of an infected patient, are taken into account. We apply column generation to solve this combinatorial optimization problem and propose a dynamic programming algorithm to solve the pricing problem. The computational efficiency of this dynamic programming approach is validated through comparison with a mixed integer linear programming approach. In order to obtain integer variables, we embed the column generation loop in an enumerative branch-and-price framework. We elaborate on various branching strategies and branching schemes and examine their impact on the solution quality. The test instances for the computational experiments are generated using real-life data of the surgical day-care center at the academic hospital UZ Leuven Campus Gasthuisberg (Belgium).     

A hub location problem with fully interconnected backbone and access networks

This paper considers the design of two-layered fully interconnected networks. A two-layered network consists of clusters of nodes, each defining an access network and a backbone network. We consider the integrated problem of determining the access networks and the backbone network simultaneously. A mathematical formulation is presented, but as the linear programming relaxation of the mathematical formulation is weak, a formulation based on the set partitioning model and column generation approach is also developed. The column generation subproblems are solved by solving a series of quadratic knapsack problems. We obtain superior bounds using the column generation approach than with the linear programming relaxation. The column generation method is therefore developed into an exact approach using the branch-and-price framework. With this approach we are able to solve problems consisting of up to 25 nodes in reasonable time. Given the difficulty of the problem, the results are encouraging.     

单向航道下连续泊位分配与船舶调度集成优化

为改善单向航道连续泊位港口的运营效率,研究泊位分配与船舶进出港调度集成优化.考虑潮汐、进出港时段交替与偏好泊位的影响,建立0-1整数线性规划模型,以船舶偏离偏好泊位成本和滞期成本为优化目标,确定各艘船舶的靠泊位置与进出港时刻.针对问题情境和其特有的约束条件,将原数学模型通过Dantzig-Wolfe分解方法分成主问题模...     

基于列生成算法求解动态库存板坯分配问题

针对钢铁企业中遇到的动态库存板坯分配问题进行了研究。建立了一个0-1整数规划数学模型,该模型的目标是最小化板坯与合同规格差异费用以及板坯在库停留所产生的库存成本费用之和。根据问题特点,使用Danzig-Wolfe策略将这个模型分解为一个带有集划分约束的主问题和一个具有背包特征约束的价格子问题,开发了分支价格算法进行求解。计算结果表明所开发的分支价格算法能够最优求解生产实际问题。     

Dantzig-Wolfe decomposition and branch-and-price solving in G12

The G12 project is developing a software environment for stating and solving combinatorial problems by mapping a high-level model of the problem to an efficient combination of solving methods. Model annotations are used to control this process. In this paper we explain the mapping to branch-and-price solving. Dantzig-Wolfe decomposition is automatically performed using the additional information given by the model annotations. The models obtained can then be solved using column generation and branch-and-price. G12 supports the selection of specialised subproblem solvers, the aggregation of identical subproblems to reduce symmetries, automatic disaggregation when required by branch-and-bound, the use of specialised subproblem constraint-branching rules, and different master problem solvers including a hybrid solver based on the volume algorithm. We demonstrate the benefits of the G12 framework on three examples: a trucking problem, cutting stock, and two-dimensional bin packing.     

考虑倒垛因素的轧制计划编制方法

在给定粗轧制计划的基础上考虑钢坯库倒垛优化, 编制详细的轧制计划; 建立以最小化轧制计划内钢坯出 库总倒垛次数与轧制单元之间切换机架次数为目标的多目标整数规划模型; 针对模型特征, 设计一种基于钢坯匹配的单亲遗传算法. 通过基于实际生产数据的实验验证, 相对于传统的手工计算方法, 所提出的算法在优化倒垛次数和切换机架次数上平均提升20 %, 算法和模型是可行且有效的.     

考虑轧辊成本的轧制计划编制与调整

在分析轧辊车削成本的基础上对轧制计划编制和调整问题进行深入研究, 建立以最小化轧辊车削量为目标的0-1整数规划模型. 针对问题特征, 构造基于替换邻域搜索的两阶段算法: 第1阶段, 对轧制单元实施最佳匹配和交叉使用调整; 第2阶段, 通过搜索轧制单元的轧辊替换邻域, 用车削量较少的轧辊替代车削量较大的轧辊, 从而优化第1阶段的有效解. 通过实际生产数据验证, 两阶段算法能够在满足轧制工艺规程的基础上有效降低轧辊车削量, 算法和模型均可行且有效.