71 research outputs found
On the representation of the search region in multi-objective optimization
Given a finite set of feasible points of a multi-objective optimization
(MOO) problem, the search region corresponds to the part of the objective space
containing all the points that are not dominated by any point of , i.e. the
part of the objective space which may contain further nondominated points. In
this paper, we consider a representation of the search region by a set of tight
local upper bounds (in the minimization case) that can be derived from the
points of . Local upper bounds play an important role in methods for
generating or approximating the nondominated set of an MOO problem, yet few
works in the field of MOO address their efficient incremental determination. We
relate this issue to the state of the art in computational geometry and provide
several equivalent definitions of local upper bounds that are meaningful in
MOO. We discuss the complexity of this representation in arbitrary dimension,
which yields an improved upper bound on the number of solver calls in
epsilon-constraint-like methods to generate the nondominated set of a discrete
MOO problem. We analyze and enhance a first incremental approach which operates
by eliminating redundancies among local upper bounds. We also study some
properties of local upper bounds, especially concerning the issue of redundant
local upper bounds, that give rise to a new incremental approach which avoids
such redundancies. Finally, the complexities of the incremental approaches are
compared from the theoretical and empirical points of view.Comment: 27 pages, to appear in European Journal of Operational Researc
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
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
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