双层束搜索算法优化机器人制造单元调度问题

针对混流生产阻塞机器人制造单元调度问题，给出了可行机器人运动插入法，构建可行解。依据可行机器人运动插入法，提出双层过滤变宽度束搜索算法进行求解。搜索过程利用局部评价函数和全局评价函数对节点进行两次择优选取。通过计算随机生成算例，仿真结果表明，相对于以分支定界算法产生的可行解进行变邻域搜索、分支定界算法、局部评价函数束搜索算法、全局评价函数束搜索算法和双层过滤定宽度束搜索算法，双层过滤变宽度束搜索算法不但能显著提高搜索效率，而且解的平均改进度分别为3.07%、6.07%、7.79%、12.62%、14.47%。     

复合并行机排序问题的启发式算法研究

为有效解决复合并行机排序的极小化最大完成时间问题,提出了分支定界算法和改进的启发式动态规划算法。利用分支定界算法的3个工具:分支模型、边界和优先规则,构建出分支搜索树。按优先规则进行定界搜索,从而减小了问题求解规模。将原始作业转换为虚拟作业,根据Johnson法则,求解出原问题的最优排序。改进的动态规划算法复杂度分析和计算实验表明,这两个算法可靠性高并且可以解决实际问题。     

多工件类型的无等待机器人制造单元调度研究

首先将加工多工件类型的无等待机器人制造单元调度问题分解为两个相互联系的子问题：（1）多类型工件进入系统的排序问题;（2）机器人搬运作业的排序问题。从解决工件使用工作站和机器人可能发生的冲突入手,以工件进入系统的时间为决策变量,利用禁止区间法建立了问题的数学模型,并开发了一基于图论的动态分枝定界最优算法。最后,通过一自动化印刷电路板（PCB）生产线和随机算例验证了算法的有效性。     

一种求解共享单车再平衡问题的遗传算法

共享单车再平衡问题(BRP)是单一商品旅行商问题(1-PDTSP)的扩展,是一类NP难问题。针对已有算法求解速度慢,不利于实现实时调度优化的缺点,提出一种求解BRP的非代际遗传算法。基于个体搜索机制保留优异个体,设计线路交叉算子和k点破坏修复变异算子,引入破坏修复机制,当算法收敛变慢时自动生成新个体进入种群以避免陷入局部最优解。应用BRP标准算例测试表明:在小规模算例上该算法均能找到最优解,平均CPU消耗为3.8 s;在中等规模与大规模算例上,该算法找到9个算例的最优解,并且其运算速度相较于分支定界算法和线路破坏与修复启发式算法提升77%以上。     

连铸-轧制混流生产模式下轧批调度问题的分支-定价算法

研究了连铸——轧制在热装、温装和冷装混流生产模式下的一类新型轧批调度问题.以最小化温装钢坯（热钢锭）缓冷（等待）导致的热能损失和连轧机架切换带来的产能损失为目标,建立了整数规划模型.由于商业优化软件难以在有限时间内直接求得模型的最优解甚至可行解,提出利用Dantzig-Wolfe分解技术将原模型分解为主问题和子问题,采用列生成算法对主问题和子问题进行迭代求解得到原问题的紧下界,最后以列生成算法作为定界机制嵌入分支——定界框架中形成分支——定价算法,执行分支搜索过程以获得整数最优解.本文还从影响分支——定价算法性能的要素出发提出改进策略.针对主问题,提出列生成和拉格朗日松弛混合求解策略来抑制单一列生成算法的尾效应.针对价格子问题,在动态规划算法中提出了基于占优规则和标号下界计算方法来及早消除无效状态空间,加速求解过程.以钢铁企业的实际生产数据和扩展的随机算例进行了数值实验,结果显示所提出改进策略能够突破求解能力的限制,使分支——定价算法在可接受计算时间内求得工业规模问题的最优解.     

修改D-W分解求具有需求时间窗和投机性成本的批量问题

研究多产品具有能力约束、需求时间窗、允许延期交货和投机性成本的批量问题.分析无能力约束凸包极点的特征,采用修正的Dantzig-Wolfe分解对原问题进行等价变换.使用列生成获得下界,同时采用启发式分支定界寻找近优解.对随机算例进行了测试与比较,计算结果表明上界与下界之间的间隙非常小;另外分析了当能力参数和订单规模变化时解的质量和计算时间.     

变邻域搜索算法求解机器人制造单元调度问题——排序依赖转换时间

针对排序依赖转换时间的两机器机器人制造单元调度问题的NP难特性,设计了变邻域搜索算法求解。为了加快算法收敛速度,设计了工件阻塞时间最小化生成初始解;为了搜索到更好解,分析了算法的参数取值。通过随机产生算例测试,提出算法优于模拟退火算法,证实了提出算法的有效性。     

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型和子问题模型,提出了满足问题特性的分支定界和列生成相结合的精确型分支定价算法。在列生成算法中,给出了适合本问题的列选取策略;在分支定界算法中,设计了广度优先策略来提升求解效率。采用多组算例来验证了方案与算法的有效性,并通过不同规模算例分析了进出港时段长度变化对方案的影响,可为港口的实际作业安排提供参考。     

分支定界算法的分布并行化研究

介绍了一种专用于计算分支定界算法的机群计算平台，其中所使用的分布并行策略减少了分支定界算法计算时间复杂度，减小了问题的规模；可以把计算平台机群中的任何一台计算机上计算出的当前全局最佳本分值，实时地广播给所有其他并行的计算机，并作为它们新的最佳本分值，实现分支节点的快速并行淘汰；应用启发式算法修改了分支定界算法，提高了分支节点的淘汰效率。选用旅行商问题实例作为测试基准。计算表明，在保证求得最优解的前提下，该平台能很好地提高分支定界算法的效率。     

求解带硬时间窗车辆路径问题的时差插入启发式算法

针对已有求解带硬时间窗车辆路径问题时插入启发式算法结构复杂、参数多、求解效率不高的缺点,提出了求解该问题的时差插入启发式算法。该算法引入时差的概念,将时差作为启发规则的评价指标。相比已有求解该问题的经典启发式算法,该算法有参数个数少、算法结构简单等特点。应用标准测试算例测试表明,所提算法的求解质量优于Solomon的插入启发式算法和Potvin的平行插入启发式算法。     

Branch-and-bound algorithm for the maximum triangle packing problem

This work addresses the problem of finding the maximum number of unweighted vertex-disjoint triangles in an undirected graph G. It is a challenging NP-hard combinatorial problem and it is well-known to be APX-hard. A branch-and-bound algorithm which uses a lower bound based on neighborhood degree is presented. A naive upper bound is proposed as well as another one based on a surrogate relaxation of the related integer linear program which is analogous to a multidimensional knapsack problem. Further, a Greedy Search algorithm and a genetic algorithm are described to improve the lower bound. A computational comparison of lower bounds, branch-and-bound algorithm and CPLEX solver is provided using randomly generated benchmarks and well-known DIMACS implementation challenges. The empirical study shows that the branch-and-bound finds the optimal triangle packing solution for small randomly generated MTP instances (up to 100 vertices and 200 triangles) and some DIMACS graphs. For some larger instances and DIMACS challenges graphs, we remark that our lower bound outperforms CPLEX solver regarding the triangle packing solution and the computation time.     

A recombination‐based matheuristic for mixed integer programming problems with binary variables

This work introduces a heuristic for mixed integer programming (MIP) problems with binary variables, based on information obtained from differences between feasible solutions as well as solutions from the linear relaxation. This information is used to build a neighborhood that is explored as a sub‐MIP problem. The proposed heuristic is evaluated using 45 problems from the MIPLIB repository. Its performance, in terms of solution improvement over the results obtained after exploring 50,000 nodes of the branch‐and‐bound tree, is compared against that of Solution Polishing, which is another recombination‐based heuristic for MIP problems used within the CPLEX solver; as well as against the solution obtained by running the default CPLEX branch‐and‐cut (B&C) method under a same time limit. The computational results indicate that the proposed method is able to yield results that are significantly better than those obtained by the default CPLEX B&C approach and comparable to those of Solution Polishing in terms of the mean solution quality. This equivalence of expected solution quality, coupled with a simpler implementation, suggests the use of the proposed approach as a possible alternative for improving the quality of solutions in MIP problems.     

Extensions to the repetitive branch and bound algorithm for globally optimal clusterwise regression

A branch and bound strategy is proposed for solving the clusterwise regression problem, extending Brusco's repetitive branch and bound algorithm (RBBA). The resulting strategy relies upon iterative heuristic optimization, new ways of observation sequencing, and branch and bound optimization of a limited number of ending subsets. These three key features lead to significantly faster optimization of the complete set and the strategy has more general applications than only for clusterwise regression. Additionally, an efficient implementation of incremental calculations within the branch and bound search algorithm eliminates most of the redundant ones. Experiments using both real and synthetic data compare the various features of the proposed optimization algorithm and contrasts them against a benchmark mixed logical-quadratic programming formulation optimized by CPLEX. The results indicate that all components of the proposed algorithm provide significant improvements in processing times, and, when combined, generally provide the best performance, significantly outperforming CPLEX.     

基于滚动变时间窗的重组批处理机调度研究

针对具有等待时间限制和工件动态到达的重组批处理机调度问题,以拖延时间和最小为目标,提出基于滚动变时间窗的三层混合调度算法。该调度算法是应用滚动时域策略,将重组批处理机调度问题分解为许多变时间窗的子问题;每个子问题调度分三层执行：即产生触发并传递参数、重组批及排序、派工并更新参数。通过实时调度仿真平台和CPLEX平台进行实例验证,结果表明基于滚动变时间窗的三层混合调度算法能够在较短计算时间内获得满意优化解。     

Exact algorithms for a scheduling problem with unrelated parallel machines and sequence and machine-dependent setup times

A scheduling problem with unrelated parallel machines, sequence and machine-dependent setup times, due dates and weighted jobs is considered in this work. A branch-and-bound algorithm (B&B) is developed and a solution provided by the metaheuristic GRASP is used as an upper bound. We also propose a set of instances for this type of problem. The results are compared to the solutions provided by two mixed integer programming models (MIP) with the solver CPLEX 9.0. We carry out computational experiments and the algorithm performs extremely well on instances with up to 30 jobs.     

A 2-phase algorithm for solving the single allocation p-hub center problem

The single allocation p-hub center problem is an NP-hard location–allocation problem which consists of locating hub facilities in a network and allocating non-hub nodes to hub nodes such that the maximum distance/cost between origin–destination pairs is minimized. In this paper we present an exact 2-phase algorithm where in the first phase we compute a set of potential optimal hub combinations using a shortest path based branch and bound. This is followed by an allocation phase using a reduced sized formulation which returns the optimal solution. In order to get a good upper bound for the branch and bound we developed a heuristic for the single allocation p-hub center problem based on an ant colony optimization approach. Numerical results on benchmark instances show that the new solution approach is superior over traditional MIP-solver like CPLEX. As a result we are able to provide new optimal solutions for larger problems than those reported previously in literature. We are able to solve problems consisting of up to 400 nodes in reasonable time. To the best of our knowledge these are the largest problems solved in the literature to date.     

钢铁企业板坯动态分配问题的建模与分散搜索算法求解

板坯动态分配问题是在一定周期内, 将炼钢-连铸工序动态产出的余材板坯合理分配给期货合同、潜在合同或自拟合同, 使加权费用和最小. 对该问题建立0-1 整数规划模型, 针对问题的NP- 难求解性, 设计基于多邻域的分散搜索算法对问题近似求解, 并加入随机策略防止算法陷入局部最优. 分别采用模拟数据和实际数据进行测试, 所提出的算法与商业软件CPLEX 相比, 可在较短时间内获得近优解, 在解的质量和计算时间方面均优于人工方法.     

An efficient approach to determine cell formation,cell layout and intracellular machine sequence in cellular manufacturing systems

Cellular manufacturing systems (CMS) are used to improve production flexibility and efficiency. They involve the identification of part families and machine cells so that intercellular movement is minimized and the utilization of the machines within a cell is maximized. Previous research has focused mainly on cell formation problems and their variants; however, only few articles have focused on more practical and complicated problems that simultaneously consider the three critical issues in the CMS-design process, i.e., cell formation, cell layout, and intracellular machine sequence. In this study, a two-stage mathematical programming model is formulated to integrate the three critical issues with the consideration of alternative process routings, operation sequences, and production volume. Next, because of the combinatorial nature of the above model, an efficient tabu search algorithm based on a generalized similarity coefficient is proposed. Computational results from test problems show that our proposed model and solution approach are both effective and efficient. When compared to the mathematical programming approach, which takes more than 112 h (LINGO) and 1139 s (CPLEX) to solve a set of ten test instances, the proposed algorithm can produce optimal solutions for the same set of test instances in less than 12 s.     

A three-stage approach for the resource-constrained shortest path as a sub-problem in column generation

This paper focuses on the common scenario in which the resource-constrained shortest path problem (RCSP) on an acyclic graph is a sub-problem in the context of column generation. It proposes a pseudo-polynomial time, three-stage solution approach. Stages 1 (preprocessing) and 2 (setup) are implemented one time to transform RCSP into a shortest path problem, which is solved by stage 3 (iterative solution) at each column generation iteration, each time with different arc costs. This paper analyzes certain properties related to each stage as well as algorithm complexity. Computational tests compare the performances of this method, a state-of-the-art label-setting algorithm, and CPLEX optimization software on four classes of instances, each of which involves either one or multiple resources, and show that the new method is effective. The new method outperforms the label-setting algorithm when resource limitations are tight—as can be expected in practice, and outperforms CPLEX for all tested instances. The label-setting algorithm outperforms CPLEX for all single-resource RCSP instances and almost all multiple-resource RCSP instances.     

Integrated sliding-mode algorithms in robot tracking applications

An integrated solution based on sliding mode ideas is proposed for robotic trajectory tracking. The proposal includes three sliding-mode algorithms for speed auto-regulation, path conditioning and redundancy resolution in order to fulfill velocity, workspace and C-space constraints, respectively. The proposed method only requires a few program lines and simplifies the robot user interface since it directly deals with the fulfillment of the constraints to find a feasible solution for the robot trajectory tracking in a short computation time. The proposed approach is evaluated in simulation on the freely accessible 6R robot model PUMA-560, for which the main features of the method are illustrated.