184 research outputs found
The line planning routing game
In this paper, we propose a novel algorithmic approach to solve line planning problems. To this end, we model the line planning problem as a game where the passengers are players which aim at minimizing individual objective functions composed of travel time, transfer penalties, and a share of the overall cost of the solution. To find equilibria of this routing game, we use a best-response algorithm. We investigate, under which conditions on the line planning model a passenger’s best-response can be calculated efficiently and which properties are needed to guarantee convergence of the best-response algorithm. Furthermore, we determine the price of anarchy which bounds the objective value of an equilibrium with respect to a system- optimal solution of the line planning problem. For problems where best-responses cannot be found efficiently, we propose heuristic methods. We demonstrate our findings on some small computational examples
Optimization Approaches for the Traveling Salesman Problem with Drone
The fast and cost-efficient home delivery of goods ordered online is logistically challenging. Many companies are looking for new ways to cross the last-mile to their customers. One technology-enabled opportunity that recently has rec
Delay management including capacities of stations
The question of delay management (DM) is whether trains should wait for delayed feeder trains or should depart on time. Solutions to this problem strongly depend on the capacity constraints of the tracks making sure that no two trains can use the same piece of track at the same time. While these capacity constraints have been included in integer programming formulations for DM, the capacity constraints of the stations (only offering a limited number of platforms) have been neglected so far. This can lead to highly infeasible solutions. In order to overcome this problem we suggest two new formulations for DM both including the stations' capacities. We present numerical results showing that the assignment-based formulation is clearly superior to the packing formulation. We furthermore propose an iterative algorithm in which we improve the platform assignment with respect to the current delays of the trains at each station in each step. We will show that this subproblem asks for coloring the nodes of a graph with a given number of colors while minimizing the weight of the conflicts. We show that the graph to be colored is an interval graph and that the problem can be solved in polynomial time by presenting a totally unimodular IP formulation
A Rolling Horizon Heuristic with Optimality Guarantee for an On-Demand Vehicle Scheduling Problem
We consider a basic vehicle scheduling problem that arises in the context of travel demand models:
Given demanded vehicle trips, what is the minimal number of vehicles needed to fulfill the demand?
In this paper, we model the vehicle scheduling problem as a network flow problem. Since instances
arising in the context of travel demand models are often so big that the network flow model becomes
intractable, we propose using a rolling horizon heuristic to split huge problem instances into smaller
subproblems and solve them independently to optimality. By letting the horizons of the subproblems
overlap, it is possible to look ahead to the demand of the next subproblem. We prove that composing
the solutions of the subproblems yields an optimal solution to the whole problem if the overlap of
the horizons is sufficiently large. Our experiments show that this approach is not only suitable for
solving extremely large instances that are intractable as a whole, but it is also possible to decrease
the solution time for large instances compared to a comprehensive approach
Railway timetabling with integrated passenger distribution
Timetabling for railway services often aims at optimizing travel times for passengers. At the same
time, restricting assumptions on passenger behavior and passenger modeling are made. While research
has shown that passenger distribution on routes can be modeled with a discrete choice model, this has
not been considered in timetabling yet. We investigate how a passenger distribution can be integrated
into an optimization framework for timetabling and present two mixed-integer linear programs for
this problem. Both approaches design timetables and simultaneously find a corresponding passenger
distribution on available routes. One model uses a linear distribution model to estimate passenger
route choices, the other model uses an integrated simulation framework to approximate a passenger
distribution according to the logit model, a commonly used route choice model. We compare both
new approaches with three state-of-the-art timetabling methods and a heuristic approach on a set of
artificial instances and a partial network of Netherlands Railways (NS)
Railway timetabling with integrated passenger distribution
Timetabling for railway services often aims at optimizing travel times for passengers. At the same
time, restricting assumptions on passenger behavior and passenger modeling are made. While research
has shown that passenger distribution on routes can be modeled with a discrete choice model, this has
not been considered in timetabling yet. We investigate how a passenger distribution can be integrated
into an optimization framework for timetabling and present two mixed-integer linear programs for
this problem. Both approaches design timetables and simultaneously find a corresponding passenger
distribution on available routes. One model uses a linear distribution model to estimate passenger
route choices, the other model uses an integrated simulation framework to approximate a passenger
distribution according to the logit model, a commonly used route choice model. We compare both
new approaches with three state-of-the-art timetabling methods and a heuristic approach on a set of
artificial instances and a partial network of Netherlands Railways (NS)
Delay Management including Capacities of Stations
The question of delay management is whether trains should wait for delayed feeder
trains or should depart on time. Solutions to this problem strongly depend on the available
capacity of the railway infrastructure. While the limited capacity of the tracks has been
considered in delay management models, the limited capacity of the stations has been
neglected so far. In this paper, we develop a model for the delay management problem that
includes the stations’ capacities. This model allows to reschedule the platform assignment
dynamically. Furthermore, we propose an iterative algorithm in which we first solve the
delay management model with a fixed platform assignment and then improve this platform
assignment in each step. We show that the latter problem can be solved in polynomial
time by presenting a totally unimodular IP formulation. Finally, we present an extension
of the model that balances the delay of the passengers on the one hand and the number of
changes in the platform assignment on the other. All models are evaluated on real-world
instances from Netherlands Railways
Delay Management with Re-Routing of Passengers
The question of delay management is whether trains should wait for a delayed feeder train
or should depart on time. In classical delay management models passengers always take
their originally planned route. In this paper, we propose a model where re-routing of
passengers is incorporated.
To describe the problem we represent it as an event-activity network similar to the one
used in classical delay management, with some additional events to incorporate origin
and destination of the passengers. We present an integer programming formulation of
this problem. Furthermore, we discuss the variant in which we assume fixed costs for
maintaining connections and we present a polynomial algorithm for the special case of
only one origin-destination pair. Finally, computational experiments based on real-world
data from Netherlands Railways show that significant improvements can be obtained by
taking the re-routing of passengers into account in the model
An iterative heuristic for passenger-centric train timetabling with integrated adaption times
In this paper we present a method to construct a periodic timetable from a tactical
planning perspective. We aim at constructing a timetable that is feasible with respect
to infrastructure constraints and minimizes average perceived passenger travel time. In
addition to in-train and transfer times, our notion of perceived passenger time includes
the adaption time (waiting time at the origin station). Adaption time minimization allows
us to avoid strict frequency regularity constraints and, at the same time, to ensure regular
connections between passengers’ origins and destinations. The combination of adaption
time minimization and infrastructure constraints satisfaction makes the problem very
challenging.
The described periodic timetabling problem can be modelled as an extension of a Peri-
odic Event Scheduling Problem (PESP) formulation, but requires huge computing times if
it is directly solved by a general-purpose solver for instances of realistic size. In this paper,
we propose a heuristic approach consisting of two phases that are executed iteratively.
First, we solve a mixed-integer linear program to determine an ideal timetable that mini-
mizes the average perceived passenger travel time but neglects infrastructure constraints.
Then, a Lagrangian-based heuristic makes the timetable feasible with respect to infras-
tructure constraints by modifying train departure and arrival times as little as possible.
The obtained feasible timetable is then evaluated to compute the resulting average per-
ceived passenger travel time, and a feedback is sent to the Lagrangian-based heuristic so as to possibly improve the obtained timetable from the passenger perspective, while
still respecting infrastructure constraints. We illustrate the proposed iterative heuristic
approach on real-life instances of Netherlands Railways and compare it to a benchmark
approach, showing that it finds a feasible timetable very close to the ideal one
Min-ordering and max-ordering scalarization methods for multi-objective robust optimization
Several robustness concepts for multi-objective uncertain optimization have been developed during the last years, but not many solution methods. In this paper we introduce two methods to find min–max robust efficient solutions based on scalarizations: the min-ordering and the max-ordering method. We show that all point-based min–max robust weakly efficient solutions can be found with the max-ordering method and that the min-ordering method finds set-based min–max robust weakly efficient solutions, some of which cannot be found with formerly developed scalarization based methods. We then show how the scalarized problems may be approached for multi-objective uncertain combinatorial optimization problems with special uncertainty sets. We develop compact mixed-integer linear programming formulations for multi-objective extensions of bounded uncertainty (also known as budgeted or Γ-uncertainty). For interval uncertainty, we show that the resulting problems reduce to well-known single-objective problems
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