162 research outputs found
Adapting Branching and Queuing for Multi-objective Branch and Bound
Branch and bound algorithms have to cope with several additional difficulties
in the multi-objective case. Not only the bounding procedure is considerably
weaker, but also the handling of upper and lower bound sets requires much more
computational effort since both sets can be of exponential size. Thus, the
order in which the subproblems are considered is of particular importance.
Thereby, it is crucial not only to find efficient solutions as soon as possible
but also to find a set of (efficient) solutions whose images are well
distributed along the non-dominated frontier. In this paper we evaluate the
performance of multi-objective branch and bound algorithms depending on
branching and queuing of subproblems. We use, e.g., the hypervolume indicator
as a measure for the gap between lower and upper bound set to implement a
multi-objective best-first strategy. We test our approaches on multi-objective
knapsack and generalized assignment problems
Solving the Dynamic Dial-a-Ride Problem Using a Rolling-Horizon Event-Based Graph
In many ridepooling applications transportation requests arrive throughout the day and have to be answered and integrated into the existing (and operated) vehicle routing. To solve this dynamic dial-a-ride problem we present a rolling-horizon algorithm that dynamically updates the current solution by solving an MILP formulation. The MILP model is based on an event-based graph with nodes representing pick-up and drop-off events associated with feasible user allocations in the vehicles. The proposed solution approach is validated on a set of real-word instances with more than 500 requests. In 99.5% of all iterations the rolling-horizon algorithm returned optimal insertion positions w.r.t. the current schedule in a time-limit of 30 seconds. On average, incoming requests are answered within 2.8 seconds
Determining Cost-Efficient Controls of Electrical Energy Storages Using Dynamic Programming
Volatile electrical energy prices are a challenge and an opportunity for
small and medium-size companies in energy-intensive industries. By using
electrical energy storage and/or an adaptation of production processes,
companies can significantly profit from time-depending energy prices and reduce
their energy costs.
We consider a time-discrete optimal control problem to reach a desired final
state of the energy storage at a certain time step. Thereby, the energy input
is discrete since only multiples of 100 kWh can be purchased at the EPEX SPOT
market. We use available price estimations to minimize the total energy cost by
a rounding based dynamic programming approach. With our model non-linear energy
loss functions of the storage can be considered and we obtain a significant
speed-up compared to the integer (linear) programming formulation
Network Simulation for Pedestrian Flows with HyDEFS
The reliable simulation of pedestrian movement is an essential tool for the security aware design and analysis of buildings and infrastructure. We developed HyDEFS, an event-driven dynamic flow simulation software which is designed to simulate pedestrian movement depending on varying routing decisions of the individual users and varying constraints. HyDEFS uses given density depending velocities to model congestions and evaluates flow distributions with respect to average and maximum travel time. This is of particular importance when considering evacuation scenarios. We apply HyDEFS on two small networks and cross validate its results by time-discrete and time-continuous calculations
A Tight Formulation for the Dial-a-Ride Problem
Ridepooling services play an increasingly important role in modern
transportation systems. With soaring demand and growing fleet sizes, the
underlying route planning problems become increasingly challenging. In this
context, we consider the dial-a-ride problem (DARP): Given a set of
transportation requests with pick-up and delivery locations, passenger numbers,
time windows, and maximum ride times, an optimal routing for a fleet of
vehicles, including an optimized passenger assignment, needs to be determined.
We present tight mixed-integer linear programming (MILP) formulations for the
DARP by combining two state-of-the-art models into novel
location-augmented-event-based formulations. Strong valid inequalities and
lower and upper bounding techniques are derived to further improve the
formulations. We then demonstrate the theoretical and computational superiority
of the new model: First, the formulation is tight in the sense that, if time
windows shrink to a single point in time, the linear programming relaxation
yields integer (and hence optimal) solutions. Second, extensive numerical
experiments on benchmark instances show that computational times are on average
reduced by 49.7% compared to state-of-the-art event-based approaches
Ridepooling and public bus services: A comparative case-study
This case-study aims at a comparison of the service quality of time-tabled
buses as compared to on-demand ridepooling cabs in the late evening hours in
the city of Wuppertal, Germany. To evaluate the service quality of ridepooling
as compared to bus services, and to simulate bus rides during the evening
hours, transport requests are generated using a predictive simulation. To this
end, a framework in the programming language R is created, which automatically
combines generalized linear models for count regression to model the demand at
each bus stop. Furthermore, we use classification models for the prediction of
trip destinations. To solve the resulting dynamic dial-a-ride problem, a
rolling-horizon algorithm based on the iterative solution of Mixed-Integer
Linear Programming Models (MILP) is used. A feasible-path heuristic is used to
enhance the performance of the algorithm in presence of high request densities.
This allows an estimation of the number of cabs needed depending on the weekday
to realize the same or a better general service quality as the bus system
Optimal control for port-Hamiltonian systems and a new perspective on dynamic network flow problems
We formulate open-loop optimal control problems for general port-Hamiltonian
systems with possibly state-dependent system matrices and prove their
well-posedness. The optimal controls are characterized by the first-order
optimality system, which is the starting point for the derivation of an
adjoint-based gradient descent algorithm. Moreover, we discuss the relationship
of port-Hamiltonian dynamics and minimum cost network flow problems. Our
analysis is underpinned by a proof of concept, where we apply the proposed
algorithm to static minimum cost flow problems and dynamic minimum cost flow
problems with a simple directed acyclic graph. The numerical results validate
the approach
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