Irina S. Dolinskaya

Optimal Recharging Policies for Electric Vehicles

Recharging decisions for electric vehicles require many special considerations because of battery dynamics. Battery longevity is prolonged by recharging less frequently and at slower rates, and also by not charging the battery too close to its maximum capacity. In this paper, we address the problem of finding an optimal recharging policy for an electric vehicle along a given path. The path consists of a sequence of nodes, each representing a charging station, and the driver must decide where to stop and how much to recharge at each stop. We present efficient algorithms for finding an optimal policy in general instances with deterministic travel costs and homogeneous charging stations, and also for two specialized cases—one where the vehicle can stop anywhere along the path to recharge and another with equidistant charging stations along the path. In addition, we develop two heuristic procedures that we characterize analytically and explore empirically. We further analyze and test our solution methods on m...

Time-optimal trajectories with bounded curvature in anisotropic media

This paper characterizes time-optimal trajectories in anisotropic (direction-dependent) environments where path curvatures are bounded by the inverse of the minimum-turning radius of a mobile agent. Such problems are often faced in the navigation of aerial, ground and naval vehicles when a mobile agent cannot instantaneously change its heading angle. The work presented is a generalization of the Dubins car problem, which considers the fastest paths with bounded curvature while assuming constant speed and minimum-turning radius. We relax this assumption and discuss fastest-path finding problems for the generalized direction-dependent speed and minimum-turning radius functions, to account for the effects of waves, winds and slope of the terrain on the agent’s motions. We establish that there exists an optimal path such that it is a portion of a path of the type CSCSC where C denotes a sharpest-turn curve and S a straight-line segment. We further analyze a special case wherein the speed polar plot is convex, and show that in that case there exists an optimal path with the same structure as for the Dubins problem: CCC or CSC . An algorithm that implements our results for the convex speed polar plot is also presented.

Network repair crew scheduling and routing for emergency relief distribution problem

Every year, hundreds of thousands of people are affected by natural disasters. The number of casualties is usually increased by lack of clean water, food, shelter, and adequate medical care during the aftermath. One of the main problems influencing relief distribution is the state of the post-disaster road network. In this paper, we consider the problem of scheduling the emergency repair of a rural road network that has been damaged by the occurrence of a natural disaster. This problem, which we call the Network Repair Crew Scheduling and Routing Problem addresses the scheduling and routing of a repair crew optimizing accessibility to the towns and villages that demand humanitarian relief by repairing roads. We develop both an exact dynamic programming (DP) algorithm and an iterated greedy-randomized constructive procedure to solve the problem and compare the performance of both approaches on small- to medium-scale instances. Our numerical analysis of the solution structure validates the optimization model and provides managerial insights into the problem and its solutions.

Adaptive Routing and Recharging Policies for Electric Vehicles

Planning a trip with an electric vehicle requires consideration of both battery dynamics and the availability of charging infrastructure. Recharging costs for an electric vehicle, which increase as the battery’s charge level increases, are fundamentally different than refueling costs for conventional vehicles, which do not depend on the amount of fuel already in the tank. Furthermore, the viability of any route requiring recharging is sensitive to the availability of charging stations along the way. In this paper, we study the problem of finding an optimal adaptive routing and recharging policy for an electric vehicle in a network. Each node in the network represents a charging station and has an associated probability of being available at any point in time or occupied by another vehicle. We develop efficient algorithms for finding an optimal a priori routing and recharging policy and then present solution approaches to an adaptive problem that build on a priori policy. We present two heuristic methods f...

Fastest-Path Planning for Direction-Dependent Speed Functions

We discuss path planning in a direction-dependent environment illustrated by the fastest-path problem with anisotropic speed function. The difficulty of optimal-path finding in a direction-dependent medium comes from the fact that our travel-time function is asymmetric and, in general, violates the triangle inequality. We present an analytical form solution for the fastest-path finding problem in an obstacle-free domain without making any assumptions on the structure of the speed function. Subsequently, we merge these results with visibility graph search methods to develop an obstacle-avoiding fastest-path finding algorithm for an anisotropic speed function. Optimal routing of a vessel in a stationary random seaway is discussed throughout the paper to motivate and demonstrate applications of our work.

Construction of Fastest Curvature-Constrained Paths in Direction-Dependent Media

This paper presents an algorithm that constructs a fastest curvature-constrained path in a direction-dependent environment for given initial and target locations and heading angles. The problem studied here is a generalization of the classical Dubins car problem, where the vehicle speed and minimum turning radius are assumed to be constant. This assumption is relaxed and the settings where the two parameters are arbitrary functions of the agent’s heading angle are considered, such as a maneuvering sailboat for example. This paper is concerned with the extension and implementation of the authors’ earlier results that establish the fastest path between two positions in the plane for a Dubins-like vehicle in a (possibly) anisotropic medium to be of the form CSCSC (or any subset of this word) where C denotes a sharpest turn and S denotes a straight line segment. While the authors’ preceding work has derived the structure of a fastest path, the actual implementation of the results presents a significant challe...

Multi-depot vessel routing problem in a direction dependent wavefield

Considerable research has been done on the vehicle routing problem and its variants; however only limited amount of existing work deals with possible environmental conditions and their effects on the vehicle routes. This paper presents the multiple-depot vehicle routing problem for surface vessels, where the vehicles must traverse a time-invariant direction-dependent medium. Our model captures environmental effects and vessel dynamics on the considered paths. Three heuristic solution methods are developed and tested on simulated scenarios. The first approach exactly solves an approximate formulation of the problem, the second approximately solves an approximate problem formulation, while the third approximately solves the exact problem. Performance of the algorithms are compared to assess the tradeoff between computational cost and quality of the found solutions.

A Derivative-Free Trust-Region Algorithm for the Optimization of Functions Smoothed via Gaussian Convolution Using Adaptive Multiple Importance Sampling

In this paper we consider the optimization of a functional

Incomplete information imputation in limited data environments with application to disaster response

F

Parameter-Free Sampled Fictitious Play for Solving Deterministic Dynamic Programming Problems

defined as the convolution of a function