110,232 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
An Adversarial Interpretation of Information-Theoretic Bounded Rationality
Recently, there has been a growing interest in modeling planning with
information constraints. Accordingly, an agent maximizes a regularized expected
utility known as the free energy, where the regularizer is given by the
information divergence from a prior to a posterior policy. While this approach
can be justified in various ways, including from statistical mechanics and
information theory, it is still unclear how it relates to decision-making
against adversarial environments. This connection has previously been suggested
in work relating the free energy to risk-sensitive control and to extensive
form games. Here, we show that a single-agent free energy optimization is
equivalent to a game between the agent and an imaginary adversary. The
adversary can, by paying an exponential penalty, generate costs that diminish
the decision maker's payoffs. It turns out that the optimal strategy of the
adversary consists in choosing costs so as to render the decision maker
indifferent among its choices, which is a definining property of a Nash
equilibrium, thus tightening the connection between free energy optimization
and game theory.Comment: 7 pages, 4 figures. Proceedings of AAAI-1
Beyond the One Step Greedy Approach in Reinforcement Learning
The famous Policy Iteration algorithm alternates between policy improvement
and policy evaluation. Implementations of this algorithm with several variants
of the latter evaluation stage, e.g, -step and trace-based returns, have
been analyzed in previous works. However, the case of multiple-step lookahead
policy improvement, despite the recent increase in empirical evidence of its
strength, has to our knowledge not been carefully analyzed yet. In this work,
we introduce the first such analysis. Namely, we formulate variants of
multiple-step policy improvement, derive new algorithms using these definitions
and prove their convergence. Moreover, we show that recent prominent
Reinforcement Learning algorithms are, in fact, instances of our framework. We
thus shed light on their empirical success and give a recipe for deriving new
algorithms for future study.Comment: ICML 201
On Time-optimal Trajectories for a Car-like Robot with One Trailer
In addition to the theoretical value of challenging optimal control problmes,
recent progress in autonomous vehicles mandates further research in optimal
motion planning for wheeled vehicles. Since current numerical optimal control
techniques suffer from either the curse of dimens ionality, e.g. the
Hamilton-Jacobi-Bellman equation, or the curse of complexity, e.g.
pseudospectral optimal control and max-plus methods, analytical
characterization of geodesics for wheeled vehicles becomes important not only
from a theoretical point of view but also from a prac tical one. Such an
analytical characterization provides a fast motion planning algorithm that can
be used in robust feedback loops. In this work, we use the Pontryagin Maximum
Principle to characterize extremal trajectories, i.e. candidate geodesics, for
a car-like robot with one trailer. We use time as the distance function. In
spite of partial progress, this problem has remained open in the past two
decades. Besides straight motion and turn with maximum allowed curvature, we
identify planar elastica as the third piece of motion that occurs along our
extr emals. We give a detailed characterization of such curves, a special case
of which, called \emph{merging curve}, connects maximum curvature turns to
straight line segments. The structure of extremals in our case is revealed
through analytical integration of the system and adjoint equations
Weak invariance principle in Besov spaces for stationary martingale differences
The classical Donsker weak invariance principle is extended to a Besov spaces
framework. Polygonal line processes build from partial sums of stationary
martingale differences as well independent and identically distributed random
variables are considered. The results obtained are shown to be optimal
Real-Time Planning with Multi-Fidelity Models for Agile Flights in Unknown Environments
Autonomous navigation through unknown environments is a challenging task that
entails real-time localization, perception, planning, and control. UAVs with
this capability have begun to emerge in the literature with advances in
lightweight sensing and computing. Although the planning methodologies vary
from platform to platform, many algorithms adopt a hierarchical planning
architecture where a slow, low-fidelity global planner guides a fast,
high-fidelity local planner. However, in unknown environments, this approach
can lead to erratic or unstable behavior due to the interaction between the
global planner, whose solution is changing constantly, and the local planner; a
consequence of not capturing higher-order dynamics in the global plan. This
work proposes a planning framework in which multi-fidelity models are used to
reduce the discrepancy between the local and global planner. Our approach uses
high-, medium-, and low-fidelity models to compose a path that captures
higher-order dynamics while remaining computationally tractable. In addition,
we address the interaction between a fast planner and a slower mapper by
considering the sensor data not yet fused into the map during the collision
check. This novel mapping and planning framework for agile flights is validated
in simulation and hardware experiments, showing replanning times of 5-40 ms in
cluttered environments.Comment: ICRA 201
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