Yet harder knapsack problems

Already 30 years ago, Chvátal has shown that some instances of the zero-one knapsack problem cannot be solved in polynomial time using a particular type of branch-and-bound algorithms based on relaxations of linear programs together with some rudimentary cutting-plane arguments as bounding rules. We extend this result by proving an exponential lower bound in a more general class of branch-and-bound and dynamic programming algorithms which are allowed to use memoization and arbitrarily powerful bound rules to detect and remove subproblems leading to no optimal solution.     

采用树表示的全局最优形状匹配算法

提出一种全局优化算法，用于相似不变地在一场景中匹配一个形状。该算法采用支撑树来表示形状，匹配问题被转化成在目标点集中定位这棵树的问题。通过最小化边的空间变换同一个全局空间变换之间的差别，树的每条边的空间变换被强制是一致的。目标函数归结为一个关于边匹配变量的凹二次函数。该函数具有低秩Hessian矩阵，可以通过分支定界法快速地解出。还提出一种新颖的求下界的方案，它可以通过动态规划高效地解出。实验结果表明，所提算法相比主流算法有更好的鲁棒性，特别对于两点集只有部分重叠的情形。     

基于分支定界-改进AO~*算法的序贯测试策略优化

针对经典AO*算法在求解序贯测试问题中复杂度太大的难题,提出测试选择与策略优化联合的方法;首先基于解析冗余关系(ARRs)把测试选择问题映射为一个特殊的0-1整数规划(IP)模型并用分支定界法求解之,得到最优测试;然后通过两步回溯改进的AO*算法确定最优测试顺序;在一个组合电路的应用表明算法优化了测试点数,减少了扩展节点数,降低了经典算法的复杂度。     

Exact and heuristic algorithms for the just-in-time scheduling problem in a batch processing system

Batch processing systems are commonly used in many different environments such as chemical and semiconductor industries. In this research, a just-in-time scheduling problem in a batch processing system is investigated. Minimization of total earliness and tardiness of the jobs with respect to a common due date is considered as the objective function. First, the research problem is formulated as a mixed integer linear programming model. Then, to find the optimal schedule for a predetermined set of batches, a dynamic programming algorithm is proposed. Based on the proposed dynamic programming algorithm, several heuristics are also developed. A lower bounding method is presented, and then a branch and bound algorithm is proposed to solve the problem optimally. To demonstrate the performance of the proposed algorithms, several computational experiments are conducted.     

Scheduling two-machine no-wait open shops to minimize makespan

This paper examines the problem of scheduling two-machine no-wait open shops to minimize makespan. The problem is known to be strongly NP-hard. An exact algorithm, based on a branch-and-bound scheme, is developed to optimally solve medium-size problems. A number of dominance rules are proposed to improve the search efficiency of the branch-and-bound algorithm. An efficient two-phase heuristic algorithm is presented for solving large-size problems. Computational results show that the branch-and-bound algorithm can solve problems with up to 100 jobs within a reasonable amount of time. For large-size problems, the solution obtained by the heuristic algorithm has an average percentage deviation of 0.24% from a lower bound value.     

复杂流程工业系统的优化综合与柔性分析

MINLP模型在优化综合与柔性分析中起着重要作用。具有两种表示方法：代数法和逻辑法,后者在模型表达与求解方面有很多优点。MINLP模型中还可以集成启发性知识,也就是工程经验,以加快求解速度,并使结果更加合理。对于凸的MINLP问题。目前比较成熟的算法有分支界定法、外近似法和广义Bender函数法。对于非凸NINLP问题,其求解算法目前尚在研究中,已提出的有罚函数法、αBB算法和符号重建算法。此外,一些基于随机搜索的方法也得到了应用,并且在实践中取得了较好的结果。     

A branch-and-bound procedure for a single-machine earliness scheduling problem with two agents

This paper addresses a two-agent scheduling problem on a single machine where the objective is to minimize the total weighted earliness cost of all jobs, while keeping the earliness cost of one agent below or at a fixed level Q. A mixed-integer programming (MIP) model is first formulated to find the optimal solution which is useful for small-size problem instances. To solve medium- to large-size problem instances, a branch-and-bound algorithm incorporating with several dominance properties and a lower bound is then provided to derive the optimal solution. A simulated annealing heuristic algorithm incorporating with a heuristic procedure is developed to derive the near-optimal solutions for the problem. A computational experiment is also conducted to evaluate the performance of the proposed algorithms.     

A new branch-and-bound algorithm for standard quadratic programming problems

In this paper we propose convex and LP bounds for standard quadratic programming (StQP) problems and employ them within a branch-and-bound approach. We first compare different bounding strategies for StQPs in terms both of the quality of the bound and of the computation times. It turns out that the polyhedral bounding strategy is the best one to be used within a branch-and-bound scheme. Indeed, it guarantees a good quality of the bound at the expense of a very limited computation time. The proposed branch-and-bound algorithm performs an implicit enumeration of all the KKT (stationary) points of the problem. We compare different branching strategies exploiting the structure of the problem. Numerical results on randomly generated problems (with varying density of the underlying convexity graph) are reported which show the effectiveness of the proposed approach, in particular in limiting the growth of the number of nodes in the branch-and-bound tree as the density of the underlying graph increases.     

基于蚁群算法的Web集群文档优化分布方案

在Web集群中优化分布海量级的Web文档是一个急需解决的问题.提出了一种以减少系统平均响应时间为目的的Web集群文档优化分布方案.该方案合适地拷贝网页簇,并通过对服务器进行建模将网页簇的分布问题转化为0-1整数规划问题.针对该问题的特点,设计实现了一种基于蚁群算法的求解方案,算法中蚂蚁对路径的选择分两步进行,并设置合适的启发值以加快收敛速度.实验结果表明了应用蚁群算法求解Web集群文档优化分布问题的可行性与有效性.     

一类控制受约束非线性系统的基于单网络贪婪迭代DHP算法的近似最优镇定

提出一种贪婪迭代DHP (Dual heuristic programming)算法, 解决了一类控制受约束非线性系统的近似最优镇定问题. 针对系统的控制约束, 首先引入一个非二次泛函把约束问题转换为无约束问题, 然后基于协状态函数提出一种贪婪迭代DHP算法以求解系统的HJB (Hamilton-Jacobi-Bellman)方程. 在算法的每个迭代步, 利用一个神经网络来近似系统的协状态函数, 而后根据协状态函数直接计算系统的最优控制策略, 从而消除了常规近似动态规划方法中的控制网络. 最后通过两个仿真例子证明了本文提出的最优控制方案的有效性和可行性.     

Minimizing makespan in three-machine flow shops with deteriorating jobs

In this paper, a three-machine permutation flow shop scheduling problem with time-dependent processing times is considered. By the time-dependent processing times we mean that the job's processing time is an increasing function of its starting time. The objective is to find a sequence that minimizes the makespan. This problem is well known to be NP-hard. Several dominance properties and a lower bound are derived to speed up the elimination process of a branch-and-bound algorithm. Moreover, two heuristic algorithms are proposed to overcome the inefficiency of the branch-and-bound algorithm. Computational experiments on randomly generated problems are conducted to evaluate the branch-and-bound algorithm and heuristic algorithm. Computational results show that the proposed heuristic algorithm M-NEH perform effectively and efficiently.     

A branch and bound algorithm for minimizing makespan on a single machine with unequal release times under learning effect and deteriorating jobs

We present a single-machine problem with the unequal release times under learning effect and deteriorating jobs when the objective is minimizing the makespan. In this study, we introduced a scheduling model with unequal release times in which both job deterioration and learning exist simultaneously. By the effects of learning and deterioration, we mean that the processing time of a job is defined by increasing function of its execution start time and position in the sequence. A branch-and-bound algorithm incorporating with several dominance properties and lower bounds is developed to derive the optimal solution. A heuristic algorithm is proposed to obtain a near-optimal solution. The computational experiments show that the branch-and-bound algorithm can solve instances up to 30 jobs, and the average error percentage of the proposed heuristic is less than 0.16%.     

演变图上的连接子图演变模式挖掘

探讨演变图(即随时间变化的图)的挖掘,重点研究在演变图中挖掘连接子图的演变模式集合.提出一种连接子图的相似度函数及其快速计算算法.基于该相似度函数,提出一种发现演变模式集合的多项式时间复杂度的动态规划算法.模拟数据集上的实验结果表明,该算法具有较低的误差率和较高的效率.真实数据集上的实验结果表明,挖掘结果在真实应用中具有实际意义.     

传搁时间约束下的运输与批处理机生产协调调度

针对炼钢模铸系统钢锭高温运作的特点,提出带有传搁时间约束的生产前运输与批处理机生产协调的调度问题.工件的加工时间依赖于其传搁时间,每批工件的加工时间为该批工件中加工时间最大值.目标函数为最小化总完工时间与生产费用的线性组合.通过复杂性分析,证明该问题是强NP难解问题.建立混合整数规划模型,基于动态规划提出两种特殊情况的最优算法,设计原问题的启发式算法并进行最坏情况下性能比分析.实验仿真结果验证了所提出启发式算法的有效性与稳定性.     

Two-machine flow shop scheduling with linear decreasing job deterioration

In this paper, we consider a two-machine flow shop scheduling problem with deteriorating jobs. By a deteriorating job, we mean that the processing time is a decreasing function of its execution start time. A proportional linear decreasing deterioration function is assumed. The objective is to find a sequence that minimizes total completion time. Optimal solutions are obtained for some special cases. For the general case, several dominance properties and some lower bounds are derived to speed up the elimination process of a branch-and-bound algorithm. A heuristic algorithm is also proposed to overcome the inefficiency of the branch-and-bound algorithm. Computational results for randomly generated problem instances are presented, which show that the heuristic algorithm effectively and efficiently in obtaining near-optimal solutions.     

Portfolio selection using neural networks

In this paper we apply a heuristic method based on artificial neural networks (NN) in order to trace out the efficient frontier associated to the portfolio selection problem. We consider a generalization of the standard Markowitz mean-variance model which includes cardinality and bounding constraints. These constraints ensure the investment in a given number of different assets and limit the amount of capital to be invested in each asset. We present some experimental results obtained with the NN heuristic and we compare them to those obtained with three previous heuristic methods. The portfolio selection problem is an instance from the family of quadratic programming problems when the standard Markowitz mean-variance model is considered. But if this model is generalized to include cardinality and bounding constraints, then the portfolio selection problem becomes a mixed quadratic and integer programming problem. When considering the latter model, there is not any exact algorithm able to solve the portfolio selection problem in an efficient way. The use of heuristic algorithms in this case is imperative. In the past some heuristic methods based mainly on evolutionary algorithms, tabu search and simulated annealing have been developed. The purpose of this paper is to consider a particular neural network (NN) model, the Hopfield network, which has been used to solve some other optimisation problems and apply it here to the portfolio selection problem, comparing the new results to those obtained with previous heuristic algorithms.     

基于BSP模型的大规模线性规划并行算法研究

在许多实际工程问题中经常遇到一些大型线形规划问题，通常的计算过程需要占用大量的计算时间，效率低下。文中提出了一种基于BSP模型的大规模线性规划并行算法——修正单纯形并行算法，分析了其代价函数和加速比，在所研制的集群计算机上进行了实现和测试。结果表明：当问题规模比较大时，此并行算法能获得较好的加速比。     

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.     

Degree-constrained minimum spanning tree

In this paper the problem of a degree-constrained minimum spanning tree (DCMST) is defined. The problem is formulated as a linear 0–1 integer programming problem. A primal and a dual heuristic (construction) procedure and a branch-and-bound algorithm are proposed to construct a DCMST. These procedures are illustrated with a simple example. Some computational experience with these algorithms is also reported.     

The general problem solving algorithm and its implementation

By generalising problem solving techniques such as divide-and-conquer, dynamic programming, tree and graph searching, integer programming and branch-and-bound, a general problem solving algorithm is deduced. Various examples of the use of this algorithm are given and its implementation on both sequential and parallel machines, such as the cosmic cube, is discussed.