128 research outputs found
Optimal Routing of Energy-aware Vehicles in Networks with Inhomogeneous Charging Nodes
We study the routing problem for vehicles with limited energy through a
network of inhomogeneous charging nodes. This is substantially more complicated
than the homogeneous node case studied in [1]. We seek to minimize the total
elapsed time for vehicles to reach their destinations considering both
traveling and recharging times at nodes when the vehicles do not have adequate
energy for the entire journey. We study two versions of the problem. In the
single vehicle routing problem, we formulate a mixed-integer nonlinear
programming (MINLP) problem and show that it can be reduced to a lower
dimensionality problem by exploiting properties of an optimal solution. We also
obtain a Linear Programming (LP) formulation allowing us to decompose it into
two simpler problems yielding near-optimal solutions. For a multi-vehicle
problem, where traffic congestion effects are included, we use a similar
approach by grouping vehicles into "subflows". We also provide an alternative
flow optimization formulation leading to a computationally simpler problem
solution with minimal loss in accuracy. Numerical results are included to
illustrate these approaches.Comment: To appear in proceeding of 22nd Mediterranean Conference on Control
and Automation, MED'1
Approximate IPA: Trading Unbiasedness for Simplicity
When Perturbation Analysis (PA) yields unbiased sensitivity estimators for
expected-value performance functions in discrete event dynamic systems, it can
be used for performance optimization of those functions. However, when PA is
known to be unbiased, the complexity of its estimators often does not scale
with the system's size. The purpose of this paper is to suggest an alternative
approach to optimization which balances precision with computing efforts by
trading off complicated, unbiased PA estimators for simple, biased approximate
estimators. Furthermore, we provide guidelines for developing such estimators,
that are largely based on the Stochastic Flow Modeling framework. We suggest
that if the relative error (or bias) is not too large, then optimization
algorithms such as stochastic approximation converge to a (local) minimum just
like in the case where no approximation is used. We apply this approach to an
example of balancing loss with buffer-cost in a finite-buffer queue, and prove
a crucial upper bound on the relative error. This paper presents the initial
study of the proposed approach, and we believe that if the idea gains traction
then it may lead to a significant expansion of the scope of PA in optimization
of discrete event systems.Comment: 8 pages, 8 figure
An Optimal Control Approach for the Data Harvesting Problem
We propose a new method for trajectory planning to solve the data harvesting
problem. In a two-dimensional mission space, mobile agents are tasked with
the collection of data generated at stationary sources and delivery to a
base aiming at minimizing expected delays. An optimal control formulation of
this problem provides some initial insights regarding its solution, but it is
computationally intractable, especially in the case where the data generating
processes are stochastic. We propose an agent trajectory parameterization in
terms of general function families which can be subsequently optimized on line
through the use of Infinitesimal Perturbation Analysis (IPA). Explicit results
are provided for the case of elliptical and Fourier series trajectories and
some properties of the solution are identified, including robustness with
respect to the data generation processes and scalability in the size of an
event set characterizing the underlying hybrid dynamic system
Lifetime Maximization of Wireless Sensor Networks with a Mobile Source Node
We study the problem of routing in sensor networks where the goal is to
maximize the network's lifetime. Previous work has considered this problem for
fixed-topology networks. Here, we add mobility to the source node, which
requires a new definition of the network lifetime. In particular, we redefine
lifetime to be the time until the source node depletes its energy. When the
mobile node's trajectory is unknown in advance, we formulate three versions of
an optimal control problem aiming at this lifetime maximization. We show that
in all cases, the solution can be reduced to a sequence of Non- Linear
Programming (NLP) problems solved on line as the source node trajectory
evolves.Comment: A shorter version of this work will be published in Proceedings of
2016 IEEE Conference on Decision and Contro
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