3,532 research outputs found
Recommended from our members
Accommodating user preferences in the optimization of public transport travel
Recommended from our members
Time-dependent stochastic shortest path(s) algorithms for a scheduled transportation network
Following on from our work concerning travellersâ preferences in public transportation networks (Wu and Hartley, 2004), we introduce the concept of stochasticity to our algorithms. Stochasticity greatly increases the complexity of the route finding problem, so greater algorithmic efficiency becomes imperative. Public transportation networks (buses, trains) have two important features: edges can only be traversed at certain points in time and the weights of these edges change in a day and have an uncertainty associated with them. These features determine that a public transportation network is a stochastic and time-dependent network. Finding multiple shortest paths in a both stochastic and time-dependent network is currently regarded as the most difficult task in the route finding problems (Loui, 1983). This paper discusses the use of k-shortest-paths (KSP) algorithms to find optimal route(s) through a network in which the edge weights are defined by probability distributions. A comprehensive review of shortest path(s) algorithms with probabilistic graphs was conducted
Route Planning in Transportation Networks
We survey recent advances in algorithms for route planning in transportation
networks. For road networks, we show that one can compute driving directions in
milliseconds or less even at continental scale. A variety of techniques provide
different trade-offs between preprocessing effort, space requirements, and
query time. Some algorithms can answer queries in a fraction of a microsecond,
while others can deal efficiently with real-time traffic. Journey planning on
public transportation systems, although conceptually similar, is a
significantly harder problem due to its inherent time-dependent and
multicriteria nature. Although exact algorithms are fast enough for interactive
queries on metropolitan transit systems, dealing with continent-sized instances
requires simplifications or heavy preprocessing. The multimodal route planning
problem, which seeks journeys combining schedule-based transportation (buses,
trains) with unrestricted modes (walking, driving), is even harder, relying on
approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4,
previously published by Microsoft Research. This work was mostly done while
the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at
Microsoft Research Silicon Valle
Optimal Pricing to Manage Electric Vehicles in Coupled Power and Transportation Networks
We study the system-level effects of the introduction of large populations of
Electric Vehicles on the power and transportation networks. We assume that each
EV owner solves a decision problem to pick a cost-minimizing charge and travel
plan. This individual decision takes into account traffic congestion in the
transportation network, affecting travel times, as well as as congestion in the
power grid, resulting in spatial variations in electricity prices for battery
charging. We show that this decision problem is equivalent to finding the
shortest path on an "extended" transportation graph, with virtual arcs that
represent charging options. Using this extended graph, we study the collective
effects of a large number of EV owners individually solving this path planning
problem. We propose a scheme in which independent power and transportation
system operators can collaborate to manage each network towards a socially
optimum operating point while keeping the operational data of each system
private. We further study the optimal reserve capacity requirements for pricing
in the absence of such collaboration. We showcase numerically that a lack of
attention to interdependencies between the two infrastructures can have adverse
operational effects.Comment: Submitted to IEEE Transactions on Control of Network Systems on June
1st 201
Study on k-shortest paths with behavioral impedance domain from the intermodal public transportation system perspective
Behavioral impedance domain consists of a theory on route planning for pedestrians, within which constraint management is considered. The goal of this paper is to present the k-shortest path model using the behavioral impedance approach. After the mathematical model building, optimization problem and resolution problem by a behavioral impedance algorithm, it is discussed how behavioral impedance cost function is embedded in the k-shortest path model. From the pedestrian's route planning perspective, the behavioral impedance cost function could be used to calculate best subjective paths in the objective way.Postprint (published version
Recommended from our members
Network problems & algorythms
Special structure linear programming problems have received considerable attention during the last two decades and among them network problems are of particular importance and have found numerous applications in manage- ment science and technology.
The mathematical models of the shortest route, maximal flow, and pure minimum cost flow problems are presented and various interrelationships among them are investigated. Finally three algorithms due to Dijkstra and Ford and Fulkerson which deal with the solution of the above three network problems are discussed
The Time Window Assignment Vehicle Routing Problem
In many distribution networks, it is vital that time windows in which deliveries are made are assigned to customers for the long term. However, at the moment of assigning time windows demand is not known. In this paper we introduce the time window assignment vehicle routing problem, the TWAVRP. In this problem time windows have to be assigned before demand is known. Next the realization of demand is revealed and an optimal vehicle routing schedule has to be made that satisfies the time window constraints. We assume that different scenarios of demand realizations are known, as well as their probability distribution. The TWAVRP is the problem of assigning time windows such that the expected traveling costs are minimized. We propose a formulation of the TWAVRP and develop two variants of a column generation algorithm to solve the LP relaxation of this formulation. Numerical experiments show that these algorithms provide us with very tight LP-bounds to instances of moderate size in reasonable computation time. We incorporate the column generation algorithm in a branch and price algorithm and find optimal integer solutions to small instances of the TWAVRP. In our numerical experiments, the branch and price algorithm typically finds the optimal solution very early in the branching procedure and spends most time on proving optimality
- âŠ