90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING
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We consider a system dynamics model that describes the effect of human activity on natural resources. The central stocks are the accumulated profit, the industry structures, and the water resources. The model can be controlled through two time-dependent parameters. The goal in this paper is to find a parameter setting that leads to a maximization of a performance index, which reflects both environmental and economic aspects. Thus, the goal is to identify the most sustainable stock of industry structures within the model's constraints and assumptions. In order to find a proven global optimal parameter set, we formulate the System Dynamics Optimization model as a mixed-integer nonlinear problem that is accessible for numerical solvers. Due to the dynamic structure of the model, certain steps of the solution process must be handled with greater care, compared to standard non-dynamic problems. We describe our approach of solving the industry structure model and present computational results. In addition, we discuss the limitations of the approach and next steps.
A common technique in the solution of large or complex optimization problems is the use of micro-macro transformations. In this paper, we carry out a theoretical analysis of such transformations for the track allocation problem in railway networks. We prove that the cumulative rounding technique of Schlechte et al. satisfies two of three natural optimality criteria and that this performance cannot be improved. We also show that under extreme circumstances, this technique can perform inconvieniently by underestimating the global optimal value.
We provide an overview of our main results about studying Linear Programming Problems whose coefficient matrix is subject to uncertainty and the uncertainty is modeled through a multi-band set. Such an uncertainty set generalizes the classical one proposed by Bertsimas and Sim and is particularly suitable in the common case of arbitrary non-symmetric distributions of the parameters. Our investigations were inspired by practical needs of our industrial partner in ongoing projects with focus on the design of robust telecommunications networks.
The rapid technological evolution of telecommunication networks demands service providers to regularly update their technology, with the aim of remaining competitive in the marketplace. However, upgrading the technology in a network is not a trivial task. New hardware components need to be installed in the network and during the installation network connectivity may be temporarily compromised. The Wavelength Division Multiplexing (WDM) technology, whose upgrade is considered in here, shares fiber links among several optical connections and tearing down a single link may disrupt several optical connections at once. When the upgrades involve large parts of a network, typically not all links can be upgraded in parallel, which may lead to an unavoidable longer disruption of some connections. A bad scheduling of the overall endeavor, however, can dramatically increase the disconnection time of parts of the networks, causing extended service disruption. In this contribution, we study the problem of finding a schedule of the fiber link upgrades that minimizes the total service disruption time. To the best of our knowledge, this problem has not yet been formalized and investigated. The aim of our work is to close this gap by presenting a mathematical optimization model for the problem and an innovative solution algorithm that tackles the intrinsic difficulties of the problem. Computational experience on realistic instances completes our study. Our original investigations have been driven by real needs of DFN, operator of the German National Research and Education Network and our partner in the BMBF research project ROBUKOM (http://www.robukom.de/).
We propose a novel optimization model for resource assignment in heterogeneous wireless network. The model adopts two objective functions maximizing the number of served users and the minimum granted utility at once. A distinctive feature of our new model is to consider two consecutive time slots, in order to include handover as an additional decision dimension.
Furthermore, the solution algorithm that we propose refines a heuristic solution approach recently proposed in literature, by considering a real joint optimization of the considered resources. The simulation study shows that the new model leads to a significant reduction in handover frequency, when compared to a traditional scheme based on maximum SNR.
Recently, parallel computing environments have become significantly popular. In order to obtain the benefit of using parallel computing environments, we have to deploy our programs for these effectively. This paper focuses on a parallelization of SCIP (Solving Constraint Integer Programs), which is a MIP solver and constraint integer programming framework available in source code. There is a parallel extension of SCIP named ParaSCIP, which parallelizes SCIP on massively parallel distributed memory computing environments. This paper describes FiberSCIP, which is yet another parallel extension of SCIP to utilize multi-threaded parallel computation on shared memory computing environments, and has the following contributions: First, the basic concept of having two parallel extensions and the relationship between them and the parallelization framework provided by UG (Ubiquity Generator) is presented, including an implementation of deterministic parallelization. Second, the difficulties to achieve a good performance that utilizes all resources on an actual computing environment and the difficulties of performance evaluation of the parallel solvers are discussed. Third, a way to evaluate the performance of new algorithms and parameter settings of the parallel extensions is presented. Finally, current performance of FiberSCIP for solving mixed-integer linear programs (MIPs) and mixed-integer non-linear programs (MINLPs) in parallel is demonstrated.
The Rolling Stock Rotation Problem is to schedule rail vehicles in order to cover timetabled trips by a cost optimal set of vehicle rotations. The problem integrates several facets of railway optimization, i.e., vehicle composition, maintenance constraints, and regularity aspects.
In industrial applications existing schedules often have to be re-optimized to integrate timetable changes or construction sites.
We present an integrated modeling and algorithmic approach for this task as well as computational results for industrial problem instances of DB Fernverkehr AG.
The planning of a communication network is inevitably depending on the quality of both the planning tool and the demand forecast used. In this article, we show exemplarily how the emerging area of Robust Optimization can advance the network planning by a more accurate mathematical description of the demand uncertainty. After a general introduction of the concept and its application to a basic network design problem, we present two applications: multi-layer and mixed-line-rate network design. We conclude with a discussion of extensions of the robustness concept to increase the accuracy of handling uncertainties.
This thesis represents a game-theoretic investigation of the allocation of inspectors in a transportation network, comparing Nash and Stackelberg equilibrium strategies to a strategy in which inspections are conducted proportionally to the traffic volume. It contains specifications for the integration of space and time dependencies and extensive experimental tests for the application on the transportation network of German motorways using real data. Main results are that - although the formulated spot-checking game is not zero-sum - we are able to compute a Nash equilibrium using linear programming and secondly, that experimental results yield that a Nash equilibrium strategy represents a good trade-off for the Stackelberg equilibrium strategy between efficiency of controls and computation time.
We consider the following freight train routing problem (FTRP). Given is a
transportation network with fixed routes for passenger trains and a
set of freight trains (requests), each defined by an origin and
destination station pair. The objective is to calculate a feasible
route for each freight train such that a sum of all expected delays and
all running times is minimal. Previous research concentrated on
microscopic train routings for junctions or inside major stations. Only
recently approaches were developed to tackle larger corridors or even
networks. We investigate the routing problem from a strategic
perspective, calculating the routes in a macroscopic transportation
network of Deutsche Bahn AG. Here macroscopic refers to an aggregation of
complex real-world structures are into fewer network elements. Moreover, the
departure and arrival times of freight trains are approximated.
The problem has a strategic
character since it asks only for a coarse routing through the network
without the precise timings. We give a mixed-integer nonlinear programming~(MINLP)
formulation for FTRP, which is a multi-commodity flow model on a time-expanded
graph with additional routing constraints. The model's nonlinearities are due to
an algebraic approximation of the delays of the trains on the arcs of
the network
by capacity restraint functions. The MINLP is reduced to a mixed-integer linear model~(MILP)
by piecewise linear approximation. The latter is solved by a state of the art MILP solver for various real-world test instances.