Design of a distributed fiber transport network with hubbing topology

This paper deals with the comprehensive design of a distributed network, whose structure includes a large-scale fiber transport network where switching centers are interconnected via optical fiber cable. For real-world applicability, this design study covers in an integrated framework all three major decision sets: locating hub facilities, placing conduits and installing cables therein. The complex problem is formulated as a simple variant of the classical network design model by judiciously redefining commodity-Rows. Exploiting the special structure of the problem, a dual-based heuristic is then developed which yields near-optimal design plans. Computational experiments show that the performance of the proposed heuristic is satisfactory in both speed and the quality of the design solutions generated.     

Solving Posynomial Geometric Programming Problems via Generalized Linear Programming

This paper revisits an efficient procedure for solving posynomial geometric programming (GP) problems, which was initially developed by Avriel et al. The procedure, which used the concept of condensation, was embedded within an algorithm for the more general (signomial) GP problem. It is shown here that a computationally equivalent dual-based algorithm may be independently derived based on some more recent work where the GP primal-dual pair was reformulated as a set of inexact linear programs. The constraint structure of the reformulation provides insight into why the algorithm is successful in avoiding all of the computational problems traditionally associated with dual-based algorithms. Test results indicate that the algorithm can be used to successfully solve large-scale geometric programming problems on a desktop computer.     

A comparison of two dual-based procedures for solving the p-median problem

We compare two dual-based procedures for solving the p-median problem. They rely upon alternative Lagrangean relaxations of the problem. We describe the algorithms and report on our computational experiments.     

最短路博弈群体单调分配方案构造

群体单调分配方案(Population Monotonic Allocation Scheme, 后简称PMAS)是合作博弈的一类分配机制。在合作博弈中, PMAS为每一个子博弈提供一个满足群体单调性的核中的分配方案, 从而保证大联盟的动态稳定性。本文主要贡献为利用线性规划与对偶理论构造与求解一类基于最短路问题的合作博弈(最短路博弈)的PMAS。我们首先借助对偶理论, 利用组合方法为最短路博弈构造了一个基于平均分摊思想的PMAS。然后借鉴计算核仁的Maschler方案, 将PMAS的存在性问题转化为一个指数规模的线性规划的求解问题, 并通过巧妙的求解得到了与之前组合方法相同的最短路博弈的PMAS。     

最短路博弈群体单调分配方案构造

群体单调分配方案(Population Monotonic Allocation Scheme, 后简称PMAS)是合作博弈的一类分配机制。在合作博弈中, PMAS为每一个子博弈提供一个满足群体单调性的核中的分配方案, 从而保证大联盟的动态稳定性。本文主要贡献为利用线性规划与对偶理论构造与求解一类基于最短路问题的合作博弈(最短路博弈)的PMAS。我们首先借助对偶理论, 利用组合方法为最短路博弈构造了一个基于平均分摊思想的PMAS。然后借鉴计算核仁的Maschler方案, 将PMAS的存在性问题转化为一个指数规模的线性规划的求解问题, 并通过巧妙的求解得到了与之前组合方法相同的最短路博弈的PMAS。     

Yet another geometric programming dual algorithm

We describe an algorithm for the geometric programming dual problem which uses an adaptation of the generalized LP algorithm, proposed by Dantzig et al. twenty-five years ago for the chemical equilibrium problem, and show the slack primal constraints pose no numerical difficulties for this algorithm as they do for previous dual-based algorithms.     

A note on duality gap in the simple plant location problem

This paper studies the duality gap in the simple plant location problem, and presents general formulas for the gap when certain complementary slackness conditions are satisfied. We show that the duality gap derived by Erlenkotter [A dual-based procedure for uncapacitated facility location, Operations Research 26 (1978) 992–1009], and which has been widely used in the literature, is a special case of the formulas presented here. A counterexample demonstrates that an underlying assumption in Erlenkotter may be violated. The results may be used to obtain improved lower bounds for branch-and-bound algorithms.     

Local networks for computer communications: A. WEST and P. JANSON (Eds.) Proceedings of the IFIP Working Group 6.4, International Workshop on Local Networks,Zürich,Switzerland, August 27–29, 1980, North-Holland,Amsterdam, 1981, xiii + 470 pages,Dfl.125.00

In this paper we present two lower bounds for the p-median problem, the problem of locating p facilities (medians) on a network. These bounds are based on two separate lagrangean relaxations of a zero-one formulation of the problem with subgradient optimisation being used to maximise these bounds. Penalty tests based on these lower bounds and a heuristically determined upper bound to the problem are developed and shown to result in a large reduction in problem size. The incorporation of the lower bounds and the penalty tests into a tree search procedure is described and computational results are given for problems with an arbitrary number of medians and having up to 200 vertices. A comparison is also made between these algorithms and the dual-based algorithm of Erlenkotter.     

On solving the discrete location problems when the facilities are prone to failure

The classical discrete location problem is extended here, where the candidate facilities are subject to failure. The unreliable location problem is defined by introducing the probability that a facility may become inactive. The formulation and the solution procedure have been motivated by an application to model and solve a large size problem for locating base stations in a cellular communication network. We formulate the unreliable discrete location problems as 0–1 integer programming models, and implement an enhanced dual-based solution method to determine locations of these facilities to minimize the sum of fixed cost and expected operating (transportation) cost. Computational tests of some well-known problems have shown that the heuristic is efficient and effective for solving these unreliable location problems.     

An Analysis of Partially Clairvoyant Scheduling

Real-time scheduling problems confront two issues not addressed by traditional scheduling models, viz., parameter variability and the existence of complex relationships constraining the executions of jobs. Accordingly, modeling becomes crucial in the specification of scheduling problems in such systems. In this paper, we analyze scheduling algorithms in Partially Clairvoyant Real-time scheduling systems and present a new dual-based algorithm for the feasibility problem in the case of strict relative constraints. We also study the problem of online dispatching in Partially Clairvoyant systems and show that the complexity of dispatching is logarithmically related to the complexity of the schedulability problem.     

The hub location and network design problem with fixed and variable arc costs: formulation and dual-based solution heuristic

Many air, less-than-truck load and intermodal transportation and telecommunication networks incorporate hubs in an effort to reduce total cost. These hubs function as make bulk/break bulk or consolidation/deconsolidation centres. In this paper, a new hub location and network design formulation is presented that considers the fixed costs of establishing the hubs and the arcs in the network, and the variable costs associated with the demands on the arcs. The problem is formulated as a mixed integer programming problem embedding a multi-commodity flow model. The formulation can be transformed into some previously modelled hub network design problems. We develop a dual-based heuristic that exploits the multi-commodity flow problem structure embedded in the formulation. The test results indicate that the heuristic is an effective way to solve this computationally complex problem.     

Lagrangian-relaxation-based solution procedures for a multiproduct capacitated facility location problem with choice of facility type

This paper presents exact and heuristic solution procedures for a multiproduct capacitated facility location (MPCFL) problem in which the demand for a number of different product families must be supplied from a set of facility sites, and each site offers a choice of facility types exhibiting different capacities. MPCFL generalizes both the uncapacitated (or simple) facility location (UFL) problem and the pure-integer capacitated facility location problem. We define a branch-and-bound algorithm for MPCFL that utilizes bounds formed by a Lagrangian relaxation of MPCFL which decomposes the problem into UFL subproblems and easily solvable 0-1 knapsack subproblems. The UFL subproblems are solved by the dual-based procedure of Erlenkotter. We also present a subgradient optimization-Lagrangian relaxation-based heuristic for MPCFL. Computational experience with the algorithm and heuristic are reported. The MPCFL heuristic is seen to be extremely effective, generating solutions to the test problems that are on average within 2% of optimality, and the branch-and-bound algorithm is successful in solving all of the test problems to optimality.     

A 2-block semi-proximal ADMM for solving the H-weighted nearest correlation matrix problem

Higham considered two types of nearest correlation matrix (NCM) problems, namely the W-weighted case and the H-weighted case. Since there exists well-defined computable formula for the projection onto the symmetric positive semidefinite cone under the W-weighting, it has been well studied to make several Lagrangian dual-based efficient numerical methods available. But these methods are not applicable for the H-weighted case mainly due to the lack of a computable formula. The H-weighted case remains numerically challenging, especially for the highly ill-conditioned weight matrix H. In this paper, we aim to solve the dual form of the H-weighted NCM problem, which has three separable blocks in the objective function with the second part being linear. Based on the linear part, we reformulate it as a new problem with two separable blocks, and introduce the 2-block semi-proximal alternating direction method of multipliers to deal with it. The efficiency of the proposed algorithms is demonstrated on the random test problems, whose weight matrix H are highly ill-conditioned or rank deficient.     

Isotone relations revisited

We propose a new approach towards proving that the fixed point property for ordered sets is preserved by products. This approach uses a characterization of fixed points in products via isotone relations. First explorations of classes of isotone relations are presented. These first explorations give us hope that this approach could lead to advances on the Product Problem.     

基于行为分析的AS/RS有色赋时Petri网模型研究

为了研究如何提高AS/RS系统的性能,有必要构建其模型.提出了库所双重着色的有色赋时Petri网方法,分析了AS/RS系统活动资源的行为特点和要求,并详细阐述了使用有色赋时Petri网分别构建这些行为模型的过程,从而实现整个AS/RS系统框架模型.采用visual c++软件仿真表明,该方法在构建面向资源的离散系统模型时是有效的.     

A numerical approach to design control invariant sets for constrained nonlinear discrete-time systems with guaranteed optimality

A numerical approach to design control invariant sets for constrained nonlinear discrete-time systems with guaranteed optimality is proposed in this paper. The addressed approach is based on the fact that zonotopes are more flexible for representing sets than boxes in interval analysis. Then the solver of set inversion via interval analysis is extended to set inversion via zonotope geometry by introducing the novel idea of bisecting zonotopes. The main feature of the extended solver of set inversion is the bisection and the evolution of a zonotope rather than a box. Thus the shape of admissible domains for set inversion can be broadened from boxes to zonotopes and the wrapping effect can be reduced as well by using the zonotope evolution instead of the interval evolution. Combined with global optimization via interval analysis, the extended solver of set inversion via zonotope geometry is further applied to design control invariant sets for constrained nonlinear discrete-time systems in a numerical way. Finally, the numerical design of a control invariant set and its application to the terminal control of the dual-mode model predictive control are fulfilled on a benchmark Continuous-Stirred Tank Reactor example.     

The GUS-property of second-order cone linear complementarity problems

The globally uniquely solvable (GUS) property of the linear transformation of the linear complementarity problems over symmetric cones has been studied recently by Gowda et al. via the approach of Euclidean Jordan algebra. In this paper, we contribute a new approach to characterizing the GUS property of the linear transformation of the second-order cone linear complementarity problems (SOCLCP) via some basic linear algebra properties of the involved matrix of SOCLCP. Some more concrete and checkable sufficient and necessary conditions for the GUS property are thus derived.     

Jacobian elliptic function expansion solutions for the Wick-type stochastic coupled KdV equations

The Jacobian elliptic function expansion approach is extended and applied to construct exact solutions of the nonlinear Wick-type stochastic coupled KdV equations and some new exact solutions are obtained via the approach and Hermite transformation.     

Frequently hypercyclic subspaces

We study the existence of frequently hypercyclic subspaces for a given operator, that is, the existence of closed infinite-dimensional subspaces in which every non-zero vector is frequently hypercyclic. We attack the problem with any of the three methods that have been used for hypercyclic subspaces: a constructive approach, an approach via left-multiplication operators, and an approach via tensor products.     

Clustering Nonlinear,Nonstationary Time Series Using BSLEX

Accurate clustering of time series is a challenging problem for data arising from areas such as financial markets, biomedical studies, and environmental sciences, especially when some, or all, of the series exhibit nonlinearity and nonstationarity. When a subset of the series exhibits nonlinear characteristics, frequency domain clustering methods based on higher-order spectral properties, such as the bispectra or trispectra are useful. While these methods address nonlinearity, they rely on the assumption of series stationarity. We propose the Bispectral Smooth Localized Complex EXponential (BSLEX) approach for clustering nonlinear and nonstationary time series. BSLEX is an extension of the SLEX approach for linear, nonstationary series, and overcomes the challenges of both nonlinearity and nonstationarity through smooth partitions of the nonstationary time series into stationary subsets in a dyadic fashion. The performance of the BSLEX approach is illustrated via simulation where several nonstationary or nonlinear time series are clustered, as well as via accurate clustering of the records of 16 seismic events, eight of which are earthquakes and eight are explosions. We illustrate the utility of the approach by clustering S&P 100 financial returns.