带有拒绝的单机和同型机排序问题

研究了带有拒绝的单机和同型机排序问题. 对于单机情形, 工件的惩罚费用是对应加工时间的\alpha倍.如果工件有到达时间, 目标为最小化时间表长与惩罚费用之和, 证明了这个问题是可解的.如果所有工件在零时刻到达, 目标为最小化总完工时间与惩罚费用之和, 也证明了该问题是可解的.对于同型机排序问题, 研究了工件分两批在线实时到达的情形, 目标为最小化时间表长与惩罚费用之和.针对机器台数2和m, 分别给出了竞争比为2和4-2/m的在线算法.     

具有模糊行程的城市物流动态费用多车型车辆调度问题研究

针对城市物流配送中广泛存在的多车型问题,以及由于交通路况等因素导致的配送行程模糊化现象,给出了一种基于梯形模糊数的,以最小化行程费用为目标的具有模糊行程的动态费用多车型车辆调度问题模型.在问题求解方面,针对基本粒子群算法容易陷入局部最优的情况,引入混沌局部搜索策略,给出了一种基于混沌优化技术的混合粒子群算法.仿真实验表明,该算法具有可行性和有效性.     

不确定并串联系统的贮备冗余优化

在可靠性工程中,可靠性优化设计是系统设计阶段需要解决的一个重要问题.文章针对不确定并串联系统,研究了具有不确定寿命和不确定费用的贮备冗余优化问题.以最大化系统可靠性,最大化系统寿命和最小化系统费用为目标,构建了3种不同的贮备冗余优化模型.在不确定理论框架下,给出了3种模型的等价模型,且根据决策者的偏好构建了3种带有优先级的模型.此外,给出的数值算例说明了所构建模型的合理性.     

系统可靠度最优分配的一种算法

可靠度最优分配是系统设计、研制过程中需考虑的一个重要问题,其目的是从整体出发,将有限资源加以最有效地利用。本文将部件(元件)概率重要度应用于复杂系统(如网络系统)可靠性设计中,提出了一种系统可靠度最优分配问题中费用最小化的启发式算法。本算法直观、简单,易于在计算机上实现,而且系统设计者能全面了解整个优化过程,适合工程应用。本文还举例对算法进行了说明和比较,并表明本算法是精确可靠的。     

可拒绝的同类机在线排序(英文)

考虑了带拒绝费用的在线同类机排序模型.工件一个一个的到达,到达后或被接受,或以一定的费用被拒绝,目标是最小化最大完工时间与总的拒绝费用之和.我们提供了一个在线算法和分析了算法的竞赛比.     

关于可靠性设施布局问题的近似算法

设施布局问题的研究始于20世纪60年代,主要研究选择修建设施的位置和数量,以及与需要得到服务的城市之间的分配关系,使得设施的修建费用和设施与城市之间的连接费用之和达到最小.现实生活中, 受自然灾害、工人罢工、恐怖袭击等因素的影响,修建的设施可能会出现故障, 故连接到它的城市无法得到供应,这就直接影响到了整个系统的可靠性.针对如何以相对较小的代价换取设施布局可靠性的提升,研究人员提出了可靠性设施布局问题.参考经典设施布局问题的贪婪算法、原始对偶算法和容错性问题中分阶段分层次处理的思想,设计了可靠性设施布局问题的一个组合算法.该算法不仅在理论上具有很好的常数近似度,而且还具有运算复杂性低的优点.这对于之前的可靠性设施布局问题只有数值实验算法, 是一个很大的进步.     

最小化提前/延误赋权工件数及时窗惩罚的排序问题

研究赋权提前/延误工件数的公共时窗单机排序问题,时窗的位置和大小待定且由惩罚费用衡量.首先给出最优排序的一些性质,进而提出一个多项式时间算法以最小化这些费用的和.     

区际救援物资中转调度的动态决策模型与算法

考虑灾害救援中灾区对应急物资的持续消耗,研究了区际多品种救援物资的动态中转调度问题.综合考虑各阶段调度费用、运输费用和库存费用总和最小化的救援物资中转调度安排和库存规划,建立了一个区际救援物资中转调度动态决策模型,并设计了一种矩阵编码的协进化遗传算法.最后通过一个算例验证了模型和算法的有效性.     

具有指数和位置学习效应的机器排序问题

本文考虑指数学习效应和位置学习效应同时发生的新的排序模型.工件的实际加工时间不仅依赖于已经加工过工件正常加工时间之和的指数函数,而且依赖于该工件所在的位置.单机排序情形下,对于最大完工时间和总完工时间最小化问题给出多项式时间算法.此外某些特殊情况下,总权完工时间和最大延迟最小化问题也给出了多项时间算法.流水机排序情形,对最大完工时间和总完工时间最小化问题在某些特殊情形下给出多项时间算法.     

同时最小化最大费用和最大完工时间的双代理无界平行分批排序

有两个代理A和B, 每个代理都各自有一个工件集. 同一个代理的工件可以在同一批中加工, 而且每一个代理都有一个需要最小化的函数. 研究在无界平行分批处理机上同时最小化代理A的最大费用和代理B的最大完工时间问题, 并给出一个算法, 它可在多项式时间内找到关于这个问题的所有Pareto最优点.     

Bounding a class of nonconvex linearly-constrained resource allocation problems via the surrogate dual

We consider a class of problems of resource allocation under economies of scale, namely that of minimizing a lower semicontinuous, isotone, and explicitly quasiconcave cost function subject to linear constraints. An important class of algorithms for the linearly constrained minimization of nonconvex cost functions utilize the branch and bound approach, using convex underestimating cost functions to compute the lower bounds.We suggest instead the use of the surrogate dual problem to bound subproblems. We show that the success of the surrogate dual in fathoming subproblems in a branch and bound algorithm may be determined without directly solving the surrogate dual itself, but that a simple test of the feasibility of a certain linear system of inequalities will suffice. This test is interpreted geometrically and used to characterize the extreme points and extreme rays of the optimal value function's level sets.Research partially supported by NSF under grant # ENG77-06555.     

Minimizing the sum of job completion times on capacitated two-parallel machines

This paper considers a scheduling problem with two identical parallel machines. One has unlimited capacity; the other can only run for a fixed time. A given set of jobs must be scheduled on the two machines with the goal of minimizing the sum of their completion times. The paper proposes an optimal branch and bound algorithm which employs three powerful elements, including an algorithm for computing the upper bound, a lower bound algorithm, and a fathoming condition. The branch and bound algorithm was tested on problems of various sizes and parameters. The results show that the algorithm is quite efficient to solve all the test problems. In particular, the total computation time for the hardest problem is less than 0.1 second for a set of 100 problem instances. An important finding of the tests is that the upper bound algorithm can actually find optimal solutions to a quite large number of problems.     

A branch and bound algorithm for mixed zero-one multiple objective linear programming

In this paper, a branch and bound algorithm for the generation of the efficient set in mixed zero-one multiple objective linear programming problems is presented. The algorithm is developed as to take account of the multiple objectives in the node fathoming procedure. In order to extend the algorithm's applicability to large sized problems from real life, an interactive procedure is introduced which systematically reduces the number of efficient points and thus saves considerable computational effort without losing essential information. The algorithm is tested in randomly generated problems along with a case study conceming the power generation sector     

The traveling salesman problem: A duality approach

In this study we formulate the dual of the traveling salesman problem, which extends in a natural way the dual problem of Held and Karp to the nonsymmetric case. The dual problem is solved by a subgradient optimization technique. A branch and bound scheme with stepped fathoming is then used to find optimal and suboptimal tours. Computational experience for the algorithm is presented.This author's work was partially supported by NSF Grant #GK-38337.     

Single machine scheduling to minimize total weighted earliness subject to minimal number of tardy jobs

Motivated by just-in-time manufacturing, we consider a single machine scheduling problem with dual criteria, i.e., the minimization of the total weighted earliness subject to minimum number of tardy jobs. We discuss several dominance properties of optimal solutions. We then develop a heuristic algorithm with time complexity O(n³) and a branch and bound algorithm to solve the problem. The computational experiments show that the heuristic algorithm is effective in terms of solution quality in many instances while the branch and bound algorithm is efficient for medium-size problems.     

Genetic Algorithm for Network Cost Minimization Using Threshold Based Discounting

We present a genetic algorithm for heuristically solving a cost minimization problem applied to communication networks with threshold based discounting. The network model assumes that every two nodes can communicate and offers incentives to combine of from different sources. Namely, there is a prescribed threshold on every link, and if the total of on a link is greater than the threshold, the cost of this of is discounted by a factor. A heuristic algorithm based on genetic strategy is developed and applied to a benchmark set of problems. The results are compared with former branch and bound results using the CPLEX(r)solver. For larger data instances we were able to obtain improved solutions using less CPU time, confirming the effectiveness of our heuristic approach.     

A Projection Method for the Integer Quadratic Knapsack Problem

In this paper we present a new branch and bound algorithm for solving a class of integer quadratic knapsack problems. A previously published algorithm solves the continuous variable subproblems in the branch and bound tree by performing a binary search over the breakpoints of a piecewise linear equation resulting from the Kuhn-Tucker conditions. Here, we first present modifications to a projection method for solving the continuous subproblems. Then we implement the modified projection method in a branch and bound framework and report computational results indicating that the new branch and bound algorithm is superior to the earlier method.     

A Branch and Bound Algorithm for Solving Low Rank Linear Multiplicative and Fractional Programming Problems

This paper is concerned with a practical algorithm for solving low rank linear multiplicative programming problems and low rank linear fractional programming problems. The former is the minimization of the sum of the product of two linear functions while the latter is the minimization of the sum of linear fractional functions over a polytope. Both of these problems are nonconvex minimization problems with a lot of practical applications. We will show that these problems can be solved in an efficient manner by adapting a branch and bound algorithm proposed by Androulakis–Maranas–Floudas for nonconvex problems containing products of two variables. Computational experiments show that this algorithm performs much better than other reported algorithms for these class of problems.     

Parallel branch and bound for multidimensional scaling with city-block distances

Multidimensional scaling is a technique for exploratory analysis of multidimensional data. The essential part of the technique is minimization of a multimodal function with unfavorable properties like invariants and non-differentiability. Recently a branch and bound algorithm for multidimensional scaling with city-block distances has been proposed for solution of medium-size problems exactly. The algorithm exploits piecewise quadratic structure of the objective function. In this paper a parallel version of the branch and bound algorithm for multidimensional scaling with city-block distances has been proposed and investigated. Parallel computing enabled solution of larger problems what was not feasible with the sequential version.     

An Extension of the Conjugate Directions Method With Orthogonalization to Large-Scale Problems With Bound Constraints

In our previous works a new method of conjugate directions for large-scale unconstrained minimization problems has been presented [1, 2]. In the paper this algorithm is extended to minimization problems with bound constraints. Because the linear minimization along the newly found conjugate vector is not needed for constructing the next conjugate vector and one arbitrarily step-size (not necessarily the optimal one) is calculated along this conjugate direction, we are able to incorporate naturally the bound constraints into the algorithm. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)