Due-date assignment and early/tardy scheduling on identical parallel machines

This article examines the problem of simultaneously assigning a common due date to a set of independent jobs and scheduling them on identical parallel machines in such a way that the costs associated with the due date and with the earliness or tardiness of the jobs are minimized. We establish that, for certain values of the due-date cost, an optimal schedule for this problem is also optimal for an early/tardy scheduling problem studied by Emmons. We discuss the solution properties for the two problems, and show that both problems are NP-hard even for two machines. We further show that these problems become strongly NP-hard if the number of machines is allowed to be arbitrary. We provide a dynamic programming solution for the problems, the complexity of which indicates that the problems can be solved in pseudopolynomial time as long as the number of machines remains fixed. Finally, we present the results of a limited computational study. © 1994 John Wiley & Sons, Inc.     

基于神经网络的广义两点边值问题

在航天领域中 ,多数制导问题均可以抽象为广义两点边值问题。本文探讨了神经网络在广义两点边值问题求解中的应用。首先讨论了离线制导这一类静态两点边值问题的求解 ,在此基础上 ,对在线制导这一类动态两点边值问题进行了分析 ,并给出了有效的解决方法     

A versatile scheme for ranking the extreme points of an assignment polytope

A cutting plane scheme embedded in an implicit enumeration framework is proposed for ranking the extreme points of linear assignment problems. This method is capable of ranking any desired number of extreme points at each possible objective function value. The technique overcomes storage difficulties by being able to perform the ranking at any particular objective function value independently of other objective values. Computational experience on some test problems is provided.     

Minimizing sums and products of linear fractional functions over a polytope

In this paper, we develop efficient deterministic algorithms for globally minimizing the sum and the product of several linear fractional functions over a polytope. We will show that an elaborate implementation of an outer approximation algorithm applied to the master problem generated by a parametric transformation of the objective function serves as an efficient method for calculating global minima of these nonconvex minimization problems if the number of linear fractional terms in the objective function is less than four or five. It will be shown that the Charnes–Cooper transformation plays an essential role in solving these problems. Also a simple bounding technique using linear multiplicative programming techniques has remarkable effects on structured problems. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 583–596, 1999     

Transformations of node‐balanced routing problems

This article describes a polynomial transformation for a class of unit‐demand vehicle routing problems, named node‐balanced routing problems (BRP), where the number of nodes on each route is restricted to be in an interval such that the workload across the routes is balanced. The transformation is general in that it can be applied to single or multiple depot, homogeneous or heterogeneous fleet BRPs, and any combination thereof. At the heart of the procedure lies transforming the BRP into a generalized traveling salesman problem (TSP), which can then be transformed into a TSP. The transformed graph exhibits special properties which can be exploited to significantly reduce the number of arcs, and used to construct a formulation for the resulting TSP that amounts to no more than that of a constrained assignment problem. Computational results on a number of instances are presented. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 370–387, 2015     

The conjugate gradient technique for certain quadratic network problems

We consider a class of network flow problems with pure quadratic costs and demonstrate that the conjugate gradient technique is highly effective for large-scale versions. It is shown that finding a saddle point for the Lagrangian of an m constraint, n variable network problem requires only the solution of an unconstrained quadratic programming problem with only m variables. It is demonstrated that the number of iterations for the conjugate gradient algorithm is substantially smaller than the number of variables or constraints in the (primal) network problem. Forty quadratic minimum-cost flow problems of various sizes up to 100 nodes are solved. Solution time for the largest problems (4,950 variables and 99 linear constraints) averaged 4 seconds on the CBC Cyber 70 Model 72 computer.     

An algorithm for solving general fractional interval programming problems

A Linear Fractional Interval Programming problem (FIP) is the problem of extremizing a linear fractional function subject to two-sided linear inequality constraints. In this paper we develop an algorithm for solving (FIP) problems. We first apply the Charnes and Cooper transformation on (FIP) and then, by exploiting the special structure of the pair of (LP) problems derived, the algorithm produces an optimal solution to (FIP) in a finite number of iterations.     

Using multiple searchers in constrained-path,moving-target search problems

The search theory open literature has paid little, if any, attention to the multiple-searcher, moving-target search problem. We develop an optimal branch-and-bound procedure and six heuristics for solving constrained-path problems with multiple searchers. Our optimal procedure outperforms existing approaches when used with only a single searcher. For more than one searcher, the time needed to guarantee an optimal solution is prohibitive. Our heuristics represent a wide variety of approaches: One solves partial problems optimally, two use paths based on maximizing the expected number of detections, two are genetic algorithm implementations, and one is local search with random restarts. A heuristic based on the expected number of detections obtains solutions within 2% of the best known for each one-, two-, and three-searcher test problem considered. For one- and two-searcher problems, the same heuristic's solution time is less than that of other heuristics. For three-searcher problems, a genetic algorithm implementation obtains the best-known solution in as little as 20% of other heuristic solution times. © 1996 John Wiley & Sons, Inc.     

Sequencing independent jobs with a single resource

This paper examines problems of sequencing n jobs for processing by a single resource to minimize a function of job completion times, when the availability of the resource varies over time. A number of well-known results for single-machine problems which can be applied with little or no modification to the corresponding variable-resource problems are given. However, it is shown that the problem of minimizing the weighted sum of completion times provides an exception.     

Fuzzy数序的CV指标法及改进

确定Fuzzy数的序是一个重要的理论问题,有广泛的应用价值.CV指标法基于Fuzzy数概率分布的均值及方差对Fuzzy数进行定序,但在Fuzzy数概率分布的均值及方差的一些组合下存在失效问题,文中通过实例对此进行了分析,定义了综合Fuzzy数均值、方差及信息量的限位系数并给出了基于限位系数的Fuzzy数定序方法.     

指挥信息系统非线性最优化问题的混沌搜索解法

指挥信息系统进行辅助决策很多情况下是一个求解最优化问题的过程,指挥信息系统遇到的很多问题具有非线性,同时指挥信息系统对算法的适应性和收敛速度要求相当严格。对此,普通的优化技术只能求出局部最优解。基于混沌搜索技术的计算智能具有全局搜索能力强、算法简洁、计算量小、收敛速度快的特点,成为一种求解非线性最优化问题全局最优的有效方法。算例表明,当搜索次数达到一定数量时,混沌搜索方法可以保证算法收敛到全局最优解,且计算效率很高。     

A finite descent theory for linear programming,piecewise linear convex minimization,and the linear complementarity problem

A descent algorithm simultaneously capable of solving linear programming, piecewise linear convex minimization, and the linear complementarity problem is developed. Conditions are given under which a solution can be found in a finite number of iterations using the geometry of the problem. A computer algorithm is developed and test problems are solved by both this method and Lemke's algorithm. Current results indicate a decrease in the number of cells visited but an increase in the total number of pivots needed to solve the problem.     

A forward network simplex algorithm for solving multiperiod network flow problems

An optimization model which is frequently used to assist decision makers in the areas of resource scheduling, planning, and distribution is the minimum cost multiperiod network flow problem. This model describes network structure decision-making problems over time. Such problems arise in the areas of production/distribution systems, economic planning, communication systems, material handling systems, traffic systems, railway systems, building evacuation systems, energy systems, as well as in many others. Although existing network solution techniques are efficient, there are still limitations to the size of problems that can be solved. To date, only a few researchers have taken the multiperiod structure into consideration in devising efficient solution methods. Standard network codes are usually used because of their availability and perceived efficiency. In this paper we discuss the development, implementation, and computational testing of a new technique, the forward network simplex method, for solving linear, minimum cost, multiperiod network flow problems. The forward network simplex method is a forward algorithm which exploits the natural decomposition of multiperiod network problems by limiting its pivoting activity. A forward algorithm is an approach to solving dynamic problems by solving successively longer finite subproblems, terminating when a stopping rule can be invoked or a decision horizon found. Such procedures are available for a large number of special structure models. Here we describe the specialization of the forward simplex method of Aronson, Morton, and Thompson to solving multiperiod network network flow problems. Computational results indicate that both the solution time and pivot count are linear in the number of periods. For standard network optimization codes, which do not exploit the multiperiod structure, the pivot count is linear in the number of periods; however, the solution time is quadratic.     

Experiments with linear fractional problems

In this paper we present the results of a limited number of experiments with linear fractional problems. Six solution procedures were tested and the results are expressed in the number of simplex-like pivots required to solve a sample of twenty problems randomly generated.     

Minimum-cost flows in convex-cost networks

An algorithm is given for solving minimum-cost flow problems where the shipping cost over an arc is a convex function of the number of units shipped along that arc. This provides a unified way of looking at many seemingly unrelated problems in different areas. In particular, it is shown how problems associated with electrical networks, with increasing the capacity of a network under a fixed budget, with Laplace equations, and with the Max-Flow Min-Cut Theorem may all be formulated into minimum-cost flow problems in convex-cost networks.     

Using grasp to solve the component grouping problem

Component grouping problems, a type of set-partitioning problem, arise in a number of different manufacturing and material logistics application areas. For example, in circuit board assembly, robotic work cells can be used to insert components onto a number of different types of circuit boards. Each type of circuit board requires particular components, with some components appearing on more than one type. The problem is to decide which components should be assigned to each work cell in order to minimize the number of visits by circuit boards to work cells. We describe two new heuristics for this problem, based on so-called greedy random adaptive search procedures (GRASP). With GRASP, a local search technique is replicated many times with different starting points. The starting points are determined by a greedy procedure with a probabilistic aspect. The best result is then kept as the solution. Computational experiments on problems based on data from actual manufacturing processes indicate that these GRASP methods outperform, both in speed and in solution quality, an earlier, network-flow-based heuristic. We also describe techniques for generating lower bounds for the component grouping problem, based on the combinatorial structure of a problem instance. The lower bounds for our real-world test problems averaged within 7%-8% of the heuristic solutions. Similar results are obtained for larger, randomly generated problems. © 1994 John Wiley & Sons. Inc.     

Entropy-based selection with multiple objectives

In this article we present an approach to determine the initially unspecified weights in an additive measurable multiattribute value function. We formulate and solve a series of nonlinear programming problems which (1) incorporate whatever partial information concerning the attribute weights or overall relative value of alternatives the decision maker chooses to provide, yet (2) yield a specific set of weights as a result. Although each formulation is rather easily solved using the nonlinear programming software GINO (general interactive optimizer), solutions in closed form dependent on a single parameter are also provided for a number of these problems.     

防空多传感器网络的拓扑优化模型

防空多传感器网络是防空网络化作战体系结构的重要组成部分。针对防空多传感器网络的网络结构模型,研究了已知网络中单元节点的位置和数量,如何最优确定网络中继器的位置、数量及其与单元节点的连接关系,即网络拓扑优化设计问题。最后给出了防空多传感器网络拓扑优化设计的数学模型及其求解方法。     

基于最少谓词思想的可达路径选择

对于结构测试中的不可达路径问题,仅仅使用传统的不可达路径排除方法存在很大的限制性,应用效果一般.积极选择可达路径的思想可有效减少不可达路径的产生.目前,基于最少谓词思想的路径生成方法得到广泛的认可.了解可达路径选择思想后,主要介绍一种基于数据流信息的,具体应用基本程序切片技术来生成可达路径的方法,该方法可生成几乎有最少谓词的路径,有较好效果.     

进城农民工子女教育问题探析

当前,随着进城务工农民数量的不断增加,跟随其进城的子女也越来越多。农民在自己进城落脚的同时,却无力解决孩子进城就读将要面临的诸多现实问题,结果造成部分进城儿童无法得到足够和平等的教育机会,只能进入农民工子弟学校就学。总体来说,由于受教育体制、观念、教育经费等多种因素的制约,进城农民工子女的教育问题已成为一项重大社会问题。本文通过对进城农民工子女教育现状的描述找出问题,并对这些问题产生的原因以及解决的对策进行了初步探讨。