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, $N$ mobile agents are tasked with the collection of data generated at $M$ 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