Computing latest starting times of activities in interval-valued networks with minimal time lags

This paper deals with problems of determining possible values of earliest and latest starting times of an activity in networks with minimal time lags and imprecise durations that are represented by means of interval or fuzzy numbers. Although minimal time lags are practical in different projects, former researchers have not considered these problems.After proposing propositions which reduce the search space, a novel polynomial algorithm is presented to compute intervals of possible values of latest starting times in interval-valued networks with minimal time lags. Then, the results are extended to networks with fuzzy durations.     

用最少的虚工序构建等效多阶段工序网络

运用网络计划可以直观地表示项目管理中的诸多疑难问题, 便于分析和求解. 但是它也存在明显的缺点, 如, (1) 工序网络的有向无回路性表明很多时候适合运用动态规划法, 但它在通常情况下的无阶段性使得该方法无法直接应用; (2) 任意构建的工序网络容易表现得错综复杂, 不利于研究; (3) 用最少的虚工序表示双代号网络是NP-难问题, 因此对一个工序系统可能构建出多个差别迥异的工序网络, 有碍于进度计划管理研究, 等等. 如果能将工序网络构建成等效的多阶段网络, 各工序分别表示在相应的阶段中, 无疑有助于上述问题的解决. 构建等效多阶段工序网络需要添加虚工序. 通过添加最少的虚工序将工序网络构建成等效多阶段网络, 从而有助于建立更合理的工序网络表示法.     

Approximating Networks and Extended Ritz Method for the Solution of Functional Optimization Problems

Functional optimization problems can be solved analytically only if special assumptions are verified; otherwise, approximations are needed. The approximate method that we propose is based on two steps. First, the decision functions are constrained to take on the structure of linear combinations of basis functions containing free parameters to be optimized (hence, this step can be considered as an extension to the Ritz method, for which fixed basis functions are used). Then, the functional optimization problem can be approximated by nonlinear programming problems. Linear combinations of basis functions are called approximating networks when they benefit from suitable density properties. We term such networks nonlinear (linear) approximating networks if their basis functions contain (do not contain) free parameters. For certain classes of d-variable functions to be approximated, nonlinear approximating networks may require a number of parameters increasing moderately with d, whereas linear approximating networks may be ruled out by the curse of dimensionality. Since the cost functions of the resulting nonlinear programming problems include complex averaging operations, we minimize such functions by stochastic approximation algorithms. As important special cases, we consider stochastic optimal control and estimation problems. Numerical examples show the effectiveness of the method in solving optimization problems stated in high-dimensional settings, involving for instance several tens of state variables.     

资源有限网络计划启发式方法的评价（上）：理论分析与试验设计

在对网络计划问题分析的基础上,提出了两个衡量资源约束网络计划问题复杂性特征的度量指标-网络复杂性系数CNC及有资源约束网络的复杂性系数CRNC,并基于此设计了一种产生给定网络复杂性要求的随机活动网络发生器GRAN,最后针对资源约束的网络计划问题设计了一种评价与分析其启发式算法效果的试验模型。     

Synchronization criterions and pinning control of general complex networks with time delay

The problems of synchronization and pinning control for general time-delay complex dynamical networks are investigated. In this paper, less conservative criterions for both continuous-time and discrete-time complex dynamical networks with time delay are obtained. Pinning control strategies are respectively, designed to make these complex dynamical networks synchronized. Moreover, the problems of designing controllers are converted into solving optimal problems of a series of linear matrix inequalities, which reduces the computation complexity. Finally, numerical simulations verify the effectiveness of our methodology.     

Time complexity of single- and identical parallel-machine scheduling with GERT network precedence constraints

In this paper we deal with the time complexity of single- and identical parallel-machine scheduling problems in which the durations and precedence constraints of the activities are stochastic. The stochastic precedence constraints are given by GERT networks. First, we sketch the basic concepts of GERT networks and machine scheduling with GERT network precedence constraints. Second, we discuss the time complexity of some open single-machine scheduling problems with GERT network precedence constraints. Third, we investigate the time complexity of identical parallel-machine scheduling problems with GERT network precedence constraints. Finally, we present an efficient reduction algorithm for the problem of computing the expected makespan for the latter type of scheduling problem.     

Uniqueness of the solution for optimal static routing in open BCMP queueing networks

Optimal static routing problems in open BCMP queueing networks with state-independent arrival and service rates are studied. They include static routing problems in communication networks and optimal static load balancing problems in distributed computer systems. We consider an overall optimal policy that is the routing policy whereby the overall mean response (or sojourn) time of a job is minimized. We obtain the routing decisions of the overall optimal policy and show that they may not be unique, but that the utilization of each service center is uniquely determined by the overall optimal policy. We also consider an individually optimal policy whereby jobs are routed so that each job may feel that its own expected response time is minimized if it knows the mean delay time for each path.     

Management of water resource systems in the presence of uncertainties by nonlinear approximation techniques and deterministic sampling

Two methods of approximate solution are developed for T-stage stochastic optimal control (SOC) problems, aimed at obtaining finite-horizon management policies for water resource systems. The presence of uncertainties, such as river and rain inflows, is considered. Both approaches are based on the use of families of nonlinear functions, called “one-hidden-layer networks” (OHL networks), made up of linear combinations of simple basis functions containing parameters to be optimized. The first method exploits OHL networks to obtain an accurate approximation of the cost-to-go functions in the dynamic programming procedure for SOC problems. The approximation capabilities of OHL networks are combined with the properties of deterministic sampling techniques aimed at obtaining uniform samplings of high-dimensional domains. In the second method, admissible solutions to SOC problems are constrained to take on the form of OHL networks, whose parameters are determined in such a way to minimize the cost functional associated with SOC problems. Exploiting these tools, the two methods are able to cope with the so-called “curse of dimensionality,” which strongly limits the applicability of existing techniques to high-dimensional water resources management in the presence of uncertainties. The theoretical bases of the two approaches are investigated. Simulation results show that the proposed methods are effective for water resource systems of high dimension.     

Topological design of telecommunication networks-local access design methods

Computer communication networks and telecommunication systems are growing at an explosive rate. Some of the major factors influencing this phenomenal growth rate have been technology driven, deregulation of the telecommunication industry and the breakup of AT&T, product and service introductions and competition, new application areas, price reductions and improved services. Corporations have discovered how to use telecommunication-based systems and computer networks as a strategic competitive weapon. Modern computer networks consist of backbone networks which serve as major highways to transfer large volumes of communication traffic, and local access networks which feed traffic between the backbone network and end user nodes. The design of the local access network is a complex process which builds on many difficult combinatorial optimization problems. This paper surveys many of the problems, presents the state of the art in solving them, and demonstrates a variety of solution procedures. The paper concludes with a list of open problems and areas open for further investigation.This research was partially supported by a Dean's grant for faculty research at the Owen Graduate School of Management, Vanderbilt University, Nashville, TN 37204, USA.     

A simplicial decomposition algorithm for solving the variational inequality formulation of the general traffic assignment problem for large scale networks

Summary The class of simplicial decomposition methods has been shown to constitute efficient tools for the solution of the variational inequality formulation of the general traffic assignment problem. This paper presents a particular implementation of such an algorithm, with emphasis on its ability to solve large scale problems efficiently. The convergence of the algorithm is monitored by the primal gap function, which arises naturally in simplicial decomposition schemes. The gap function also serves as an instrument for maintaining a reasonable subproblem size, through its use in column dropping criteria. The small dimension and special structure of the subproblems also allows for the use of very efficient algorithms; several algorithms in the class of linearization methods are presented. When restricting the number of retained extremal flows in a simplicial decomposition scheme, the number of major iterations tends to increase. For large networks the shortest path calculations, leading to new extremal flow generation, require a large amount of the total computation time. A special study is therefore made in order to choose the most efficient extremal flow generation technique. Computational results on symmetric problems are presented for networks of some large cities, and on asymmetric problems for some of the networks used in the literature. Computational results for bimodal models of some large cities leading to asymmetric problems are also discussed.     

A variational inequality formulation of equilibrium models for end-of-life products with nonlinear constraints

Variational inequality theory facilitates the formulation of equilibrium problems in economic networks. Examples of successful applications include models of supply chains, financial networks, transportation networks, and electricity networks. Previous economic network equilibrium models that were formulated as variational inequalities only included linear constraints; in this case the equivalence between equilibrium problems and variational inequality problems is achieved with a standard procedure because of the linearity of the constraints. However, in reality, often nonlinear constraints can be observed in the context of economic networks. In this paper, we first highlight with an application from the context of reverse logistics why the introduction of nonlinear constraints is beneficial. We then show mathematical conditions, including a constraint qualification and convexity of the feasible set, which allow us to characterize the economic problem by using a variational inequality formulation. Then, we provide numerical examples that highlight the applicability of the model to real-world problems. The numerical examples provide specific insights related to the role of collection targets in achieving sustainability goals.     

Stability Analysis of Gradient-Based Neural Networks for Optimization Problems

The paper introduces a new approach to analyze the stability of neural network models without using any Lyapunov function. With the new approach, we investigate the stability properties of the general gradient-based neural network model for optimization problems. Our discussion includes both isolated equilibrium points and connected equilibrium sets which could be unbounded. For a general optimization problem, if the objective function is bounded below and its gradient is Lipschitz continuous, we prove that (a) any trajectory of the gradient-based neural network converges to an equilibrium point, and (b) the Lyapunov stability is equivalent to the asymptotical stability in the gradient-based neural networks. For a convex optimization problem, under the same assumptions, we show that any trajectory of gradient-based neural networks will converge to an asymptotically stable equilibrium point of the neural networks. For a general nonlinear objective function, we propose a refined gradient-based neural network, whose trajectory with any arbitrary initial point will converge to an equilibrium point, which satisfies the second order necessary optimality conditions for optimization problems. Promising simulation results of a refined gradient-based neural network on some problems are also reported.     

An approach to the modeling and analysis of multiobjective generalized networks

Generalized networks can often provide substantial advantages in both the modeling and solution of integer programming problems. In this paper we present a straightforward approach which combines generalized networks with goal programming so as to achieve a modeling and solution methodology for multiobjective generalized networks. Such an approach also encompasses the solution to weighted integer foal programming as well as lexicographic integer goal programming problems. In ongoing research, the resulting hybrid algorithms have indicated superior performance, for a number of problems, over that obtained by more conventional approaches. A particularly attractive feature of the methodology is its relative simplicity and robustness.     

演化博弈与自组织合作

主要研究复杂网络上的演化博弈.首先研究具有社团结构的无标度网络上的演化囚徒困境博弈及Newman-Watts小世界网络中异质性对合作演化的影响.然后考察了在不同合作者和作弊者初始分布配置情况下,不同的初始比例条件对合作水平的影响,且在社会网络上研究了雪堆博弈中的合作演化.进一步地,讨论了网络拓扑和博弈动力学的共同演化问题和网络上演化囚徒困境中的强化学习问题.最后给出了复杂网络上演化博弈论的未来发展方向与应用前景.     

Neural Approach for Solving Several Types of Optimization Problems

Neural networks consist of highly interconnected and parallel nonlinear processing elements that are shown to be extremely effective in computation. This paper presents an architecture of recurrent neural net-works that can be used to solve several classes of optimization problems. More specifically, a modified Hopfield network is developed and its inter-nal parameters are computed explicitly using the valid-subspace technique. These parameters guarantee the convergence of the network to the equilibrium points, which represent a solution of the problem considered. The problems that can be treated by the proposed approach include combinatorial optimiza-tion problems, dynamic programming problems, and nonlinear optimization problems.Communicated by L. C. W. Dixon     

前馈神经网络和Logit回归的比较研究

近年来 ,前馈神经网络广泛地应用在 Logit回归作为标准统计方法的分析领域 .但却很少作它们之间的直接比较 ,本文是 Logit回归和前馈神经网络“比较研究”的一个尝试 ,说明了一些理论结果和特性 ,讨论了在它们的应用中碰到的一些实际问题 ,还进一步用分析的和模拟的两种方法研究了一些重要的渐近概念、过分拟合以及模型选择等问题 ,最后讨论并给出一些结论     

Sequential location-allocation problems on chains and trees with probabilistic link demands

In this paper, we consider multiperiod minisum location problems on networks in which demands can occur continuously on links according to a uniform probability density function. In addition, demands may change dynamically over time periods and at most one facility can be located per time period. Two types of networks are considered in conjunction with three behavioral strategies. The first type of network discussed is a chain graph. A myopic strategy and long-range strategy for locatingp-facilities are considered, as is a discounted present worth strategy for locating two facilities. Although these problems are generally nonconvex, effective methods are developed to readily identify all local and global minima. This analysis forms the basis for similar problems on tree graphs. In particular, we construct algorithms for the 3-facility myopic problem and the 2-facility long-range and discounted cost problems on a tree graph. Extensions and suggestions for further research on problems involving more general networks are provided.     

Novel Algorithms for Noisy Minimization Problems with Applications to Neural Networks Training

The supervisor and searcher cooperation framework (SSC), introduced in Refs. 1 and 2, provides an effective way to design efficient optimization algorithms combining the desirable features of the two existing ones. This work aims to develop efficient algorithms for a wide range of noisy optimization problems including those posed by feedforward neural networks training. It introduces two basic SSC algorithms. The first seems suited for generic problems. The second is motivated by neural networks training problems. It introduces also inexact variants of the two algorithms, which seem to possess desirable properties. It establishes general theoretical results about the convergence and speed of SSC algorithms and illustrates their appealing attributes through numerical tests on deterministic, stochastic, and neural networks training problems.     

A new path-based cutting plane approach for the discrete time-cost tradeoff problem

Determining discrete time-cost tradeoffs in project networks allows for the control of the processing time of an activity via the amount of non-renewable resources allocated to it. Larger resource allocations with associated higher costs reduce activities’ durations. Given a set of execution modes (time-cost pairs) for each activity, the discrete time-cost tradeoff problem (DTCTP) involves selecting a mode for each activity so that either: (i) the project completion time is minimized, given a budget, or (ii) the total project cost is minimized, given a deadline, or (iii) the complete and efficient project cost curve is constructed over all feasible project durations. The DTCTP is a problem with great applicability prospects but at the same time a strongly N P{\mathcal N}\,P-hard optimization problem; solving it exactly has been a real challenge. Known optimal solution methodologies are limited to networks with no more than 50 activities and only lower bounds can be computed for larger, realistically sized, project instances. In this paper, we study a path-based approach to the DTCTP, in which a new path-based formulation in activity-on-node project networks is presented. This formulation is subsequently solved using an exact cutting plane algorithm enhanced with speed-up techniques. Extensive computational results reported for almost 5,000 benchmark test problems demonstrate the effectiveness of the proposed algorithm in solving to optimality for the first time some of the hardest and largest instances in the literature. The promising results suggest that the algorithms may be embedded into project management software and, hence, become a useful tool for practitioners in the future.     

Ranking paths in stochastic time-dependent networks

In this paper we address optimal routing problems in networks where travel times are both stochastic and time-dependent. In these networks, the best route choice is not necessarily a path, but rather a time-adaptive strategy that assigns successors to nodes as a function of time. Nevertheless, in some particular cases an origin–destination path must be chosen a priori, since time-adaptive choices are not allowed. Unfortunately, finding the a priori shortest path is an NP-hard problem.