Minimizing greenhouse gas emissions in intermodal freight transport: an application to rail service design

Freight transport has undesirable effects on the environment. The most prominent of these is greenhouse gas emissions. Intermodal freight transport, where freight is shipped from origin to destination by a sequence of at least two transportation modes, offers the possibility of shifting freight (either partially or in full) from one mode to another in the hope of reducing the greenhouse emissions by appropriately scheduling the services and routing the freight. Traditional planning methods for scheduling services in an intermodal transportation network usually focus on minimizing travel or time-related costs of transport. This article breaks away from such an approach by addressing the issue of incorporating environment-related costs (greenhouse gases, to be specific) into freight transportation planning and proposes an integer program in the form of a linear cost, multicommodity, capacitated network design formulation that minimizes the amount of greenhouse gas emissions of transportation activities. Computational results based on an application of the proposed approach on a real-life rail freight transportation network are presented.     

Local search methods for the flowshop scheduling problem with flowtime minimization

Flowshop scheduling is a very active research area. This problem still attracts a considerable amount of interest despite the sheer amount of available results. Total flowtime minimization of a flowshop has been actively studied and many effective algorithms have been proposed in the last few years. New best solutions have been found for common benchmarks at a rapid pace. However, these improvements many times come at the cost of sophisticated algorithms. Complex methods hinder potential applications and are difficult to extend to small problem variations. Replicability of results is also a challenge. In this paper, we examine simple and easy to implement methods that at the same time result in state-of-the-art performance. The first two proposed methods are based on the well known Iterated Local Search (ILS) and Iterated Greedy (IG) frameworks, which have been applied with great success to other flowshop problems. Additionally, we present extensions of these methods that work over populations, something that we refer to as population-based ILS (pILS) and population-based IG (pIGA), respectively. We calibrate the presented algorithms by means of the Design of Experiments (DOE) approach. Extensive comparative evaluations are carried out against the most recent techniques for the considered problem in the literature. The results of a comprehensive computational and statistical analysis show that the presented algorithms are very effective. Furthermore, we show that, despite their simplicity, the presented methods are able to improve 12 out of 120 best known solutions of Taillard’s flowshop benchmark with total flowtime criterion.     

Analysis of FETI methods for multiscale PDEs. Part II: interface variation

In this article, we give a new rigorous condition number estimate of the finite element tearing and interconnecting (FETI) method and a variant thereof, all-floating FETI. We consider a scalar elliptic equation in a two- or three-dimensional domain with a highly heterogeneous (multiscale) diffusion coefficient. This coefficient is allowed to have large jumps not only across but also along subdomain interfaces and in the interior of the subdomains. In other words, the subdomain partitioning does not need to resolve any jumps in the coefficient. Under suitable assumptions, we derive bounds for the condition numbers of one-level and all-floating FETI that are robust with respect to strong variations in the contrast in the coefficient, and that are explicit in some geometric parameters associated with the coefficient variation. In particular, robustness holds for face, edge, and vertex islands in high-contrast media. As a central tool we prove and use new weighted Poincaré and discrete Sobolev type inequalities that are explicit in the weight. Our theoretical findings are confirmed in a series of numerical experiments.     

State-dependent routing on symmetric loss networks with trunk reservations. II: Asymptotics,optimal design

We investigate a distributed, state-dependent, dynamic routing strategy for circuit-switched loss networks which we have called Aggregated-Least-Busy-Alternative (ALBA). The networks considered are symmetric and fully connected, the offered calls form Poisson streams and routes have at most two links. In ALBA(K), the states of each link are lumped intoK (K 2) aggregates and the route of each call is determined by local information on the aggregate-states of the links of the alternate routes. The last aggregate is always the set of states reserved for direct traffic and defined by the trunk reservation parameter. The particular case of ALBA in which there is no aggregation is Least-Busy-Alternative (LBA); ALBA(2) represents the other extreme of aggregation. We consider two separate asymptotic scalings based on Fixed Point Models for ALBA(K) which were obtained and investigated in an earlier paper. In the first, it is assumed that the number of network nodes, the offered traffic and trunk group size are all large; their ratios have been chosen to reflect practical interest. The results show that there exists a threshold which delineates fundamentally different behavior: for offered traffic below the threshold, the network loss probability decreases exponentially with increasing network size, while above the threshold the decrease is only polynomial. In the related second asymptotic scaling, the asymptotically optimum trunk reservation parameter is obtained as the solution of a simple equation. Such asymptotically optimal designs are compared to the outputs of exhaustive numerical searches for some realistically sized networks and found to perform very well.Dr. Gibbens' work was done while visiting AT&T Bell Laboratories. His present address: Statistical Laboratory, University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB, UK.     

统计相关性分析方法的进展

系统综述了自19世纪开始且至今常用统计相关性的方法,例如Pearson和Spearman相关系数,CorGc和CovGc 相关性及距离相关性方法。重点介绍了2011年提出的MIC方法以及由此引发的毁誉参半的大量评述,旨在揭示这一热点领域研究面貌。该领域不仅受到统计学家的关注,而且受到了分析大样本和异质数据的应用研究领域的学者们的追捧,例如基因组生物学家和网络信息研究者。这些研究者期望在众多已有方法的理解和剖析中更恰当地付诸应用,并提出新的应用问题来推动新的分析方法的创造。     

Efficient design of freight train operation with double-hump yards

This work provides a new methodology to solve the rail freight train service design problem, with the following distinctive characteristics: (1) service costs, traveling distances and capacities of different service paths in each double-hump yard are explicitly considered; and (2) the direction of train service movement through double-hump yards are determined. The problem is formulated as integer programming, aiming at minimizing the total cost of cumulative train service cost, service cost and distance-driven cost. Three examples of different scales are solved using tabu search algorithm. The results and process of the algorithm, compared with exact solutions determined by the ILOG Cplex software, demonstrate high computational efficiency and solution quality. A small- and a large-scale case study in China are used to examine the model. The results show that the methodology used could save between 8.3 and 40% of the number of shifted service cars compared with the best-known published model.     

Multiple criteria sorting models and methods. Part II: theoretical results and general issues

4OR - Multiple criteria sorting methods assign objects into ordered categories while objects are characterized by a vector of n attributes values. Categories are ordered, and the assignment of the...     

Local convergence analysis of iterative aggregation-disaggregation methods with polynomial correction

The paper introduces some new results on local convergence analysis of one class of iterative aggregation-disaggregation methods for computing a stationary probability distribution vector of an irreducible stochastic matrix. We focus on methods, where the basic iteration on the fine level corresponds to a multiplication by a polynomial of order one with nonnegative coefficients in the original matrix. We show that this process is locally convergent for matrices with positive diagonals or when the coefficients of the polynomial are positive. On the other hand there are examples for which the process may diverge in a local sense for higher degree polynomials even if it converges for a polynomial of a lower degree for the same matrix.     

Equivalential algebras. Part II: Independence

Received November 27, 1996; accepted in final form February 26, 1997.     

Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity

An Adaptive Regularisation framework using Cubics (ARC) was proposed for unconstrained optimization and analysed in Cartis, Gould and Toint (Part I, Math Program, doi:, 2009), generalizing at the same time an unpublished method due to Griewank (Technical Report NA/12, 1981, DAMTP, University of Cambridge), an algorithm by Nesterov and Polyak (Math Program 108(1):177–205, 2006) and a proposal by Weiser, Deuflhard and Erdmann (Optim Methods Softw 22(3):413–431, 2007). In this companion paper, we further the analysis by providing worst-case global iteration complexity bounds for ARC and a second-order variant to achieve approximate first-order, and for the latter second-order, criticality of the iterates. In particular, the second-order ARC algorithm requires at most O(e^-3/2){mathcal{O}(epsilon^{-3/2})} iterations, or equivalently, function- and gradient-evaluations, to drive the norm of the gradient of the objective below the desired accuracy e{epsilon}, and O(e^-3){mathcal{O}(epsilon^{-3})} iterations, to reach approximate nonnegative curvature in a subspace. The orders of these bounds match those proved for Algorithm 3.3 of Nesterov and Polyak which minimizes the cubic model globally on each iteration. Our approach is more general in that it allows the cubic model to be solved only approximately and may employ approximate Hessians.     

Local design vs. global design: A strategic business choice

The market for a particular product consists of many customers having different needs and wants. A local design strategy attempts to increase market share and sales revenue by designing many variants of the product to exploit these differences. Such a strategy involves increased requirements for design, manufacturing, and marketing resources. A global design strategy offers a single product concept to all customers. Thus, the choice between a local design strategy and a global design strategy poses a fundamental tradeoff to the managers in many markets. Making such a decision is a complex process as it involves many design, manufacturing and marketing factors. We present a model based on optimal control theory representing major tradeoffs that exist between a local design strategy and a global design strategy. We demonstrate, through extensive computational experiments, how the model helps to gain strategic insight into the complex tradeoffs that exist between global design strategy and local design strategy alternatives under various scenarios over the life of a product.     

Lyapunov exponents for products of matrices and multifractal analysis. Part II: General matrices

We continue the study in [15, 18] on the upper Lyapunov exponents for products of matrices. Here we consider general matrices. In general, the variational formula about Lyapunov exponents we obtained in part I does not hold in this setting. In any case, we focus our interest on a special case where the matrix function M(x) takes finite values M ₁, ..., M _m . In this case, we prove the variational formula under an additional irreducibility condition. This extends a previous result of the author and Lau [18]. As an application, we prove a new multifractal formalism for a certain class of self-similar measures on ℝ with overlaps. More precisely, let μ be the self-similar measure on ℝ generated by a family of contractive similitudes {S _j = ρx + b _j } _j=1^ℓ which satisfies the finite type condition. Then we can construct a family (finite or countably infinite) of closed intervals {I _j } _j∈Λ with disjoint interiors, such that μ is supported on ⋃ _j∈Λ I _j and the restricted measure of μ on each interval I _j satisfies the complete multifractal formalism. Moreover, the dimension spectrum dim _H (α) is independent of j. The author was partially supported by the direct grant and RGC grants (Projects 400706, 401008) in CUHK, Fok Ying Tong Education Foundation and NSFC (Grant 10571100).     

In search of Thomas Knight: Part 2

Between 1809 and 1820, Thomas Knight (1775–1853) published quite a few papers on mathematics and its applications. These show him to have been surprisingly well-versed in French analytical mathematics at a time when French works were little read by his British contemporaries. In BSHM Bulletin 2, Gloria Edwards and I published a paper (Craik and Edwards 2004 Craik, Alex D D and Edwards, Gloria. 2004. “In search of Thomas Knight”. In BSHM Bulletin Vol. 2, 17–27. denoted [I] [Google Scholar]) entitled ‘In search of Thomas Knight’, designated below as ‘[1]’, that examined Knight’s life and work. This follow-up paper gives further biographical information that links him with Edinburgh; it describes some more of his publications that were previously overlooked (for notice of the latter, I am grateful to a correspondent who wishes to remain anonymous); and it records some remarks about his work by his contemporaries.     

Dual finite element analysis of three-dimensional axisymmetric elliptic problems. Part II

In Part II we derive a priori error estimates for the second type of a pure dual finite element model of a three-dimensional axisymmetric elliptic problem with mixed boundary conditions. Convergence is proved for both types of model without any regularity assumption upon the solution. An algorithm for finding a particular solution is presented. © 1993 John Wiley & Sons, Inc.