4,615 research outputs found
On limited-memory quasi-Newton methods for minimizing a quadratic function
The main focus in this paper is exact linesearch methods for minimizing a
quadratic function whose Hessian is positive definite. We give two classes of
limited-memory quasi-Newton Hessian approximations that generate search
directions parallel to those of the method of preconditioned conjugate
gradients, and hence give finite termination on quadratic optimization
problems. The Hessian approximations are described by a novel compact
representation which provides a dynamical framework. We also discuss possible
extensions of these classes and show their behavior on randomly generated
quadratic optimization problems. The methods behave numerically similar to
L-BFGS. Inclusion of information from the first iteration in the limited-memory
Hessian approximation and L-BFGS significantly reduces the effects of round-off
errors on the considered problems. In addition, we give our compact
representation of the Hessian approximations in the full Broyden class for the
general unconstrained optimization problem. This representation consists of
explicit matrices and gradients only as vector components
The Maraca: a tool for minimizing resource conflicts in a non-periodic railway timetable
While mathematical optimization and operations research receive growing attention in the railway sector, computerized timetabling tools that actually make significant use of optimization remain relatively rare. SICS has developed a prototype tool for non-periodic timetabling that minimizes resource conflicts, enabling the user to focus on the strategic decisions. The prototype is called the Maraca and has been used and evaluated during the railway timetabling construction phase at the Swedish Transport Administration between April and September 2010
Opportunities and challenges with new railway planning approach in Sweden
Long lead times in railway planning can give rise to a significant discrepancy between the original plan and the traffic eventually operated, resulting in inefficient utilization of capacity. Research shows that the railway sector in Sweden would benefit from a different planning approach in which capacity consuming decisions are pushed forward in time whenever possible. This approach is currently being implemented at Trafikverket, the Swedish Transport Administration. With it follows a number of mathematical opportunities and challenges, some of which will be presented in this paper
On the delivery robustness of train timetables with respect to production replanning possibilities
Measuring timetable robustness is a complex task. Previous efforts have mainly
been focused on simulation studies or measurements of time supplements.
However, these measurements don't capture the production flexibility of a
timetable, which is essential for measuring the robustness with regard to the
trains' commercial activity commitments, and also for merging the goals of
robustness and efficiency. In this article we differentiate between production
timetables and delivery timetables. A production timetable contains all stops,
meetings and switch crossings, while a delivery timetable only contains stops for
commercial activities. If a production timetable is constructed such that it can
easily be replanned to cope with delays without breaking any commercial activity
commitments it provides delivery robustness without compromising travel
efficiency. Changing meeting locations is one of the replanning tools available
during operation, and this paper presents a new framework for heuristically
optimising a given production timetable with regard to the number of alternative
meeting locations. Mixed integer programming is used to find two delivery feasible
production solutions, one early and one late. The area between the two solutions
represents alternative meeting locations and therefore also the replanning
enabled robustness. A case study from Sweden demonstrates how the method
can be used to develop better production timetables
Explicit optimization of plan quality measures in intensity-modulated radiation therapy treatment planning
Conventional planning objectives in optimization of intensity-modulated
radiotherapy treatment (IMRT) plans are designed to minimize the violation of
dose-volume histogram (DVH) thresholds using penalty functions. Although
successful in guiding the DVH curve towards these thresholds, conventional
planning objectives offer limited control of the individual points on the DVH
curve (doses-at-volume) used to evaluate plan quality. In this study, we
abandon the usual penalty-function framework and propose planning objectives
that more explicitly relate to DVH statistics. The proposed planning objectives
are based on mean-tail-dose, resulting in convex optimization. We also
demonstrate how to adapt a standard optimization method to the proposed
formulation in order to obtain a substantial reduction in computational cost.
We investigate the potential of the proposed planning objectives as tools for
optimizing DVH statistics through juxtaposition with the conventional planning
objectives on two patient cases. Sets of treatment plans with differently
balanced planning objectives are generated using either the proposed or the
conventional approach. Dominance in the sense of better distributed
doses-at-volume is observed in plans optimized within the proposed framework,
indicating that the DVH statistics are better optimized and more efficiently
balanced using the proposed planning objectives
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