Domination Analysis of Greedy Heuristics For The Frequency Assignment Problem

We introduce the greedy expectation algorithm for the fixed spectrum version of the frequency assignment problem. This algorithm was previously studied for the travelling salesman problem. We show that the domination number of this algorithm is at least $\sigma^{n-\lceil\log_2 n\rceil-1}$ where $\sigma$ is the available span and $n$ the number of vertices in the constraint graph. In contrast to this we show that the standard greedy algorithm has domination number strictly less than $\sigma^{n}e^{-\frac{5(n-1)}{144}}$ for large n and fixed $\sigma$

Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization

The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition

Modelling of Bicycle Manufacturing via Multi-criteria Mixed Integer Programming

AbstractSustainable manufacturing considers the economic, environmental and social dimensions as equally important. For any product, like the common bicycles, a holistic view on the different life cycle phases has to be taken in order to ensure that resources are utilised adequately. Preferences on the three dimensions might lead to different selections of materials, used equipment or required education for fulfilling the considered objectives.In a first approach, bicycle manufacturing alternatives are identified and modelled via bi-criteria mixed integer programming. The material usage is used to represent the economic dimension and the carbon dioxide equivalent is used to represent the environmental dimension. The computed supported efficient solutions provide reasonable trade-off solutions for the considered bicycle manufacturing problem

Deutsche Bahn Schedules Train Rotations Using Hypergraph Optimization

Deutsche Bahn (DB) operates a large fleet of rolling stock (locomotives, wagons, and train sets) that must be combined into trains to perform rolling stock rotations. This train composition is a special characteristic of railway operations that distinguishes rolling stock rotation planning from the vehicle scheduling problems prevalent in other industries. DB models train compositions using hyperarcs. The resulting hypergraph models are addressed using a novel coarse-to-fine method that implements a hierarchical column generation over three levels of detail. This algorithm is the mathematical core of DB's fleet employment optimization (FEO) system for rolling stock rotation planning. FEO's impact within DB's planning departments has been revolutionary. DB has used it to support the company's procurements of its newest high-speed passenger train fleet and its intermodal cargo locomotive fleet for crossborder operations. FEO is the key to successful tendering in regional transport and to construction site management in daily operations. DB's planning departments appreciate FEO's high-quality results, ability to reoptimize (quickly), and ease of use. Both employees and customers benefit from the increased regularity of operations. DB attributes annual savings of 74 million euro, an annual reduction of 34,000 tons of CO2 emissions, and the elimination of 600 coupling operations in crossborder operations to the implementation of FEO

Travelling on Graphs with Small Highway Dimension

We study the Travelling Salesperson (TSP) and the Steiner Tree problem (STP) in graphs of low highway dimension. This graph parameter was introduced by Abraham et al. [SODA 2010] as a model for transportation networks, on which TSP and STP naturally occur for various applications in logistics. It was previously shown [Feldmann et al. ICALP 2015] that these problems admit a quasi-polynomial time approximation scheme (QPTAS) on graphs of constant highway dimension. We demonstrate that a significant improvement is possible in the special case when the highway dimension is 1, for which we present a fully-polynomial time approximation scheme (FPTAS). We also prove that STP is weakly NP-hard for these restricted graphs. For TSP we show NP-hardness for graphs of highway dimension 6, which answers an open problem posed in [Feldmann et al. ICALP 2015]

Integrating body movement into attractiveness research

People judge attractiveness and make trait inferences from the physical appearance of others, and research reveals high agreement among observers making such judgments. Evolutionary psychologists have argued that interest in physical appearance and beauty reflects adaptations that motivate the search for desirable qualities in a potential partner. Although men more than women value the physical appearance of a partner, appearance universally affects social perception in both sexes. Most studies of attractiveness perceptions have focused on third party assessments of static representations of the face and body. Corroborating evidence suggests that body movement, such as dance, also conveys information about mate quality. Here we review evidence that dynamic cues (e.g., gait, dance) also influence perceptions of mate quality, including personality traits, strength, and overall attractiveness. We recommend that attractiveness research considers the informational value of body movement in addition to static cues, to present an integrated perspective on human social perception

Line planning on path networks with application to the Istanbul Metrobüs

Bus rapid transit systems in developing and newly industrialized countries often consist of a trunk with a path topology. On this trunk, several overlapping lines are operated which provide direct connections. The demand varies heavily over the day, with morning and afternoon peaks typically in reverse directions. We propose an integer programming model for this problem, derive a structural property of line plans in the static (or single period) “unimodal demand” case, and consider approaches to the solution of the multi-period version that rely on clustering the demand into peak and off-peak service periods. An application to the Metrobüs system of Istanbul is discussed

Planning rapid transit networks

[EN] Rapid transit construction projects are major endeavours that require long-term planning by several players, including politicians, urban planners, engineers, management consultants, and citizen groups. Traditionally, operations research methods have not played a major role at the planning level but several tools developed in recent years can assist the decision process and help produce tentative network designs that can be submitted to the planners for further evaluation. This article reviews some indices for the quality of a rapid transit network, as well as mathematical models and heuristics that can be used to design networks. © 2011 Elsevier Ltd.This research was partly funded by the Canadian Natural Sciences and Engineering Research Council under grant no. 39682-10, the Spanish Ministry of Science and Innovation under grant no. MTM 2009-14243 and the Junta de Andalucía, Spain, under grant no. P09-TEP-5022. This support is gratefully acknowledged. Fig. 10 was kindly provided by Giuseppe Bruno. Thanks are due to a referee who provided several valuable comments on an earlier version of this paper.Laporte, G.; Mesa, J.; Ortega, F.; Perea Rojas Marcos, F. (2011). Planning rapid transit networks. Socio-Economic Planning Sciences. 45(3):95-104. https://doi.org/10.1016/j.seps.2011.02.001S9510445