107,370 research outputs found
Workload Equity in Vehicle Routing Problems: A Survey and Analysis
Over the past two decades, equity aspects have been considered in a growing
number of models and methods for vehicle routing problems (VRPs). Equity
concerns most often relate to fairly allocating workloads and to balancing the
utilization of resources, and many practical applications have been reported in
the literature. However, there has been only limited discussion about how
workload equity should be modeled in VRPs, and various measures for optimizing
such objectives have been proposed and implemented without a critical
evaluation of their respective merits and consequences.
This article addresses this gap with an analysis of classical and alternative
equity functions for biobjective VRP models. In our survey, we review and
categorize the existing literature on equitable VRPs. In the analysis, we
identify a set of axiomatic properties that an ideal equity measure should
satisfy, collect six common measures, and point out important connections
between their properties and those of the resulting Pareto-optimal solutions.
To gauge the extent of these implications, we also conduct a numerical study on
small biobjective VRP instances solvable to optimality. Our study reveals two
undesirable consequences when optimizing equity with nonmonotonic functions:
Pareto-optimal solutions can consist of non-TSP-optimal tours, and even if all
tours are TSP optimal, Pareto-optimal solutions can be workload inconsistent,
i.e. composed of tours whose workloads are all equal to or longer than those of
other Pareto-optimal solutions. We show that the extent of these phenomena
should not be underestimated. The results of our biobjective analysis are valid
also for weighted sum, constraint-based, or single-objective models. Based on
this analysis, we conclude that monotonic equity functions are more appropriate
for certain types of VRP models, and suggest promising avenues for further
research.Comment: Accepted Manuscrip
Study on behavioral impedance for route planning techniques from the pedestrian's perspective: Part I - Theoretical contextualization and taxonomy
The interest of researchers for analyzing of best routes and shortest
paths allows a continuous technological advance in topological analysis
techniques used in the geographic information systems for
transportation. One of the topological analysis techniques is the route
planning, in which the constraint management must be considered. There
have been few studies where the constraint domain for pedestrian in an
urban transportation system was clearly stated. Consequently, more
studies need to be carried out. The aim of this paper is to provide a
theoretical contextualization on identification and management of
constraints to ascertain the behavioral impedance domain from the
pedestrian perspective. In this part of the research the grounded theory
was the research method used to develop the proposed theory. A
meta-model was used to (1) define the behavioral domain structure, (2)
hold the behavioral data collection and (3) verify the design of the
proposed taxonomic tree. The main contribution of this article is the
behavioral domain taxonomy from the pedestrian perspective, which will
be used to implement a module responsible for the constraint management
of an experimental application, named Router. Within this context, the
proposed taxonomy could be used to model cost functions more precisely.Postprint (published version
Open source environment to define constraints in route planning for GIS-T
Route planning for transportation systems is strongly related to shortest path algorithms, an optimization problem extensively studied in the literature. To find the shortest path in a network one usually assigns weights to each branch to represent the difficulty of taking such branch. The weights construct a linear preference function ordering the variety of alternatives from the most to the least attractive.Postprint (published version
Data-driven Variable Speed Limit Design for Highways via Distributionally Robust Optimization
This paper introduces an optimization problem (P) and a solution strategy to
design variable-speed-limit controls for a highway that is subject to traffic
congestion and uncertain vehicle arrival and departure. By employing a finite
data-set of samples of the uncertain variables, we aim to find a data-driven
solution that has a guaranteed out-of-sample performance. In principle, such
formulation leads to an intractable problem (P) as the distribution of the
uncertainty variable is unknown. By adopting a distributionally robust
optimization approach, this work presents a tractable reformulation of (P) and
an efficient algorithm that provides a suboptimal solution that retains the
out-of-sample performance guarantee. A simulation illustrates the effectiveness
of this method.Comment: 10 pages, 2 figures, submitted to ECC 201
Convex Integer Optimization by Constantly Many Linear Counterparts
In this article we study convex integer maximization problems with composite
objective functions of the form , where is a convex function on
and is a matrix with small or binary entries, over
finite sets of integer points presented by an oracle or by
linear inequalities.
Continuing the line of research advanced by Uri Rothblum and his colleagues
on edge-directions, we introduce here the notion of {\em edge complexity} of
, and use it to establish polynomial and constant upper bounds on the number
of vertices of the projection \conv(WS) and on the number of linear
optimization counterparts needed to solve the above convex problem.
Two typical consequences are the following. First, for any , there is a
constant such that the maximum number of vertices of the projection of
any matroid by any binary matrix is
regardless of and ; and the convex matroid problem reduces to
greedily solvable linear counterparts. In particular, . Second, for any
, there is a constant such that the maximum number of
vertices of the projection of any three-index
transportation polytope for any by any binary
matrix is ; and the convex three-index transportation problem
reduces to linear counterparts solvable in polynomial time
Macroscopic modelling and robust control of bi-modal multi-region urban road networks
The paper concerns the integration of a bi-modal Macroscopic Fundamental Diagram (MFD) modelling for mixed traffic in a robust control framework for congested single- and multi-region urban networks. The bi-modal MFD relates the accumulation of cars and buses and the outflow (or circulating flow) in homogeneous (both in the spatial distribution of congestion and the spatial mode mixture) bi-modal traffic networks. We introduce the composition of traffic in the network as a parameter that affects the shape of the bi-modal MFD. A linear parameter varying model with uncertain parameter the vehicle composition approximates the original nonlinear system of aggregated dynamics when it is near the equilibrium point for single- and multi-region cities governed by bi-modal MFDs. This model aims at designing a robust perimeter and boundary flow controller for single- and multi-region networks that guarantees robust regulation and stability, and thus smooth and efficient operations, given that vehicle composition is a slow time-varying parameter. The control gain of the robust controller is calculated off-line using convex optimisation. To evaluate the proposed scheme, an extensive simulation-based study for single- and multi-region networks is carried out. To this end, the heterogeneous network of San Francisco where buses and cars share the same infrastructure is partitioned into two homogeneous regions with different modes of composition. The proposed robust control is compared with an optimised pre-timed signal plan and a single-region perimeter control strategy. Results show that the proposed robust control can significantly: (i) reduce the overall congestion in the network; (ii) improve the traffic performance of buses in terms of travel delays and schedule reliability, and; (iii) avoid queues and gridlocks on critical paths of the network
Study on behavioral impedance for route planning techniques from the pedestrian s perspective: Part II - Mathematical approach
The theoretical foundations of the behavioral impedance domain are based
on (1) a meta-model composed of analytical and mathematical approaches
and (2) a taxonomy on the constraints involved in the decision-making
process of a pedestrian during the route selection.
The goal of this technical report is to present the mathematical model
of the behavioral impedance domain. The partial least squares approach
has been used to validate the meta-model analytical approach and develop
the proposed mathematical model.
This study contributes a mathematical model towards the implementation
of behavioral impedance domain in geographic information systems for
transportation through a constraint management module.Postprint (published version
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