Accurate scalar products and optimization

This paper describes a procedure for computing accurate scalar products of real-valued vectors. Anada implementation of this procedure is used to demonstrate the extent to which the technique can improve the convergence of the conjugate gradient algorithm. We also give a brief discussion of the costs and limitations of accurate arithmetic operations.     

The method of layer potentials for non-smooth domains with arbitrary topology

In this paper we discuss the solvability of boundary value problems for the Laplace operator on Lipschitz domains with arbitrary topology via boundary layers. An application to hydrodynamics is included.Partially supported by a UMC Research Board grant and UMC Summer Research Fellowship     

The chebop system for automatic solution of differential equations

In Matlab, it would be good to be able to solve a linear differential equation by typing u = L\f, where f, u, and L are representations of the right-hand side, the solution, and the differential operator with boundary conditions. Similarly it would be good to be able to exponentiate an operator with expm(L) or determine eigenvalues and eigenfunctions with eigs(L). A system is described in which such calculations are indeed possible, at least in one space dimension, based on the previously developed chebfun system in object-oriented Matlab. The algorithms involved amount to spectral collocation methods on Chebyshev grids of automatically determined resolution. AMS subject classification (2000)  65L10, 65M70, 65N35     

Modelling the dynamics of stochastic local search on <Emphasis Type="Italic">k</Emphasis>-<Emphasis Type="SmallCaps">sat</Emphasis>

A new analytical tool is presented to provide a better understanding of the search space of k-sat. This tool, termed the local value distribution , describes the probability of finding assignments of any value q′ in the neighbourhood of assignments of value q. The local value distribution is then used to define a Markov model to model the dynamics of a corresponding stochastic local search algorithm for k-sat. The model is evaluated by comparing the predicted algorithm dynamics to experimental results. In most cases the fit of the model to the experimental results is very good, but limitations are also recognised.     

Machine scheduling with resource dependent processing times

We consider machine scheduling on unrelated parallel machines with the objective to minimize the schedule makespan. We assume that, in addition to its machine dependence, the processing time of any job is dependent on the usage of a discrete renewable resource, e.g. workers. A given amount of that resource can be distributed over the jobs in process at any time, and the more of that resource is allocated to a job, the smaller is its processing time. This model generalizes the classical unrelated parallel machine scheduling problem by adding a time-resource tradeoff. It is also a natural variant of a generalized assignment problem studied previously by Shmoys and Tardos. On the basis of an integer linear programming formulation for a relaxation of the problem, we use LP rounding techniques to allocate resources to jobs, and to assign jobs to machines. Combined with Graham’s list scheduling, we show how to derive a 4-approximation algorithm. We also show how to tune our approach to yield a 3.75-approximation algorithm. This is achieved by applying the same rounding technique to a slightly modified linear programming relaxation, and by using a more sophisticated scheduling algorithm that is inspired by the harmonic algorithm for bin packing. We finally derive inapproximability results for two special cases, and discuss tightness of the integer linear programming relaxations.     

Approximation in the mean by bounded analytic functions

Let 1<p< and . LetC _q denote the Bessel capacity in the plane. Let be the set of homomorphisms ofH (G) such that (z)= and letNP denote the set of points in G for which is not a peak set forH (G). In this note, we show that ifC _q (NP)=0, thenH (G) is dense inL _a ^p (G), the Bergman space overG.Partially supported by NSF DMS-9401234     

On the unique finite (SI) decomposition of the Jordan operator ⊕ i=1 n S(θ) for certain inner function θ

In this paper, we have proven that for the Jordan blockS() withS() (SI), _i=1 ⁿ S() =S() ⁽ⁿ⁾ (n 1) has unique finite (SI) decomposition up to a similarity. As result, we obtain that ifV is a Volterra operator onH=L ²([0, 1]), thenV ⁽ⁿ⁾ has unique finite (SI) decomposition.This project was supported by National Natural Science Foundation of China.     

Higher degree layer potentials for non-smooth domains with arbitrary topology

We consider layer potentials associated with the Hodge-Laplacian acting on differential forms of arbitrary degree defined on Lipschitz subdomains of a Riemannian manifold. The main emphasis is on the interplay between the mapping properties of such layer potentials and the topology of the underlying domain.Partially supported by a UMC Research Board GrantPartially supported by NSF grant DMS-9870018     

遗传算法对车间作业调度的研究

应用遗传算法对车间作业调度问题进行研究,针对ＪＳＳＰ的具体特性,文中提出变异函数和二次编码的思想,获得较好的仿真结果。     

An approximation algorithm for the m-machine permutation flow shop scheduling problem with controllable processing times

The paper deals with the m-machine permutation flow shop scheduling problem in which job processing times, along with a processing order, are decision variables. It is assumed that the cost of processing a job on each machine is a linear function of its processing time and the overall schedule cost to be minimized is the total processing cost plus maximum completion time cost. A algorithm for the problem with m = 2 is provided; the best approximation algorithm until now has a worst-case performance ratio equal to . An extension to the m-machine (m ≥2) permutation flow shop problem yields an approximation algorithm with a worst-case bound equal to

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, where is the worst-case performance ratio of a procedure used, in the proposed algorithm, for solving the (pure) sequencing problem. Moreover, examples which achieve this bound for = 1 are also presented.     

A computational study of constraint satisfaction for multiple capacitated job shop scheduling

We introduce the multiple capacitated job shop scheduling problem as a generalization of the job shop scheduling problem. In this problem machines may process several operations simultaneously. We present an algorithm based on constraint satisfaction techniques to handle the problem effectively. The most important novel feature of our algorithm is the consistency checking. An empirical performance analysis is performed using a well-known set of instances of the job shop scheduling problem and a newly constructed set of instances of the multiple capacitated job shop scheduling problem. We show that our algorithm performs well for both sets of instances.     

A New Approach to Pattern Matching in Degenerate DNA/RNA Sequences and Distributed Pattern Matching

In this paper, we consider the pattern matching problem in DNA and RNA sequences where either the pattern or the text can be degenerate, i.e., contain sets of characters. We present an asymptotically faster algorithm for the above problem that works in O(n log m) time, where n and m is the length of the text and the pattern respectively. We also suggest an efficient implementation of our algorithm, which works in linear time when the pattern size is small. Finally, we also describe how our approach can be used to solve the distributed pattern matching problem. The preliminary version of this paper appeared in [26].     

A note on holomorphic approximation in Banach spaces

Given a complex Banach space X and a holomorphic function f on its unit ball B, we discuss the problem whether f can be approximated, uniformly on smaller balls, by functions g holomorphic on all of X. Research partially supported by NSF grant DMS0700281.     

Interactive optimization

Optimization algorithms or heuristics in which the user interacts significantly either during the solution process or as part of post-optimality analysis are becoming increasingly popular. An important underlying premise of such man/ machine systems is that there are some steps in solving a problem in which the computer has an advantage and other steps in which a human has an advantage. This paper first discusses how man/machine systems can be useful in facilitating model specification and revision, coping with aspects of a problem that are difficult to quantify and assisting in the solution process. We then survey successful systems that have been developed in the areas of vehicle scheduling, location problems, job shop scheduling, course scheduling, and planning language-based optimization.     

Interactive optimization

Optimization algorithms or heuristics in which the user interacts significantly either during the solution process or as part of post-optimality analysis are becoming increasingly popular. An important underlying premise of such man/machine systems is that there are some steps in solving a problem in which the computer has an advantage and other steps in which a human has an advantage. This paper first discusses how man/machine systems can be useful in facilitating model specification and revision, coping with aspects of a problem that are difficult to quantify and assisting in the solution process. We then survey successful systems that have been developed in the areas of vehicle scheduling, location problems, job shop scheduling, course scheduling, and planning language-based optimization.     

安装、加工和拆卸时间分离的两台机器混合作业问题

混合作业是经典的自由作业和异序作业的一种综合,其中一些工件可以按任意的机器顺序进行处理,而另一些工件必须遵守预先指定的机器顺序.本文研究安装、加工和拆卸时间分离的两台机器混合作业排序问题,该问题已经被知道是强NP困难的,本文把流水作业中的同顺序作业概念推广到混合作业,并得到这个混合作业问题在同顺序意义下的最优解,这个解对于一般情形是3/2近似解,但对于一些有意义的特殊情形是整体最优的.     

基于遗传算法的多目标柔性工作车间调度问题求解

本文针对柔性工作车间调度问题给出了一个有意义的综合目标尽可能缩短制造周期的同时尽可能的减少机器负荷。由于传统遗传算法在多目标柔性工作车间调度问题上的局限性，我们提出了一种改进遗传算法：首先，我们给出了针对综合目标的工序调度算法获得初始集合；接着，针对柔性工作车间调度问题的特点，我们在常用的基于工序顺序的编码方法上融入了基于机器分配的编码方法，并据此设计了相应的交叉变异操作；最后借鉴了物种进化现象中的环境迁移思想设计了解决多目标优化问题的迁移操作。实验结果表明，改进的遗传算法在多目标柔性工作车间调度问题的解决上要优于传统遗传算法。     

A note on the generalized min-sum set cover problem

In this paper, we consider the generalized min-sum set cover problem, introduced by Azar, Gamzu, and Yin (STOC 2009). Bansal, Gupta, and Krishnaswamy (SODA 2010) give a 485-approximation algorithm for the problem. We are able to alter their algorithm and analysis to obtain a 28-approximation algorithm, improving the performance guarantee by an order of magnitude. We use concepts from α-point scheduling to obtain our improvements.     

A branch and bound algorithm for scheduling trains in a railway network

The paper studies a train scheduling problem faced by railway infrastructure managers during real-time traffic control. When train operations are perturbed, a new conflict-free timetable of feasible arrival and departure times needs to be re-computed, such that the deviation from the original one is minimized. The problem can be viewed as a huge job shop scheduling problem with no-store constraints. We make use of a careful estimation of time separation among trains, and model the scheduling problem with an alternative graph formulation. We develop a branch and bound algorithm which includes implication rules enabling to speed up the computation. An experimental study, based on a bottleneck area of the Dutch rail network, shows that a truncated version of the algorithm provides proven optimal or near optimal solutions within short time limits.     

Combinatorial and Geometric Methods in Topology

Starting from the (apparently) elementary problem of deciding how many different topological spaces can be obtained by gluing together in pairs the faces of an octahedron, we will describe the central r?le played by hyperbolic geometry within three-dimensional topology. We will also point out the striking difference with the two dimensional case, and we will review some of the results of the combinatorial and computational approach to three-manifolds developed by different mathematicians over the last several years. Lecture held by Carlo Petronio in the Seminario Matematico e Fisico di Milano on April 23, 2007