We study the problem of planning a tour for an energy‐limited Unmanned Aerial Vehicle (UAV) to visit a set of sites in the least amount of time. We envision scenarios where the UAV can be recharged at a site or along an edge either by landing on stationary recharging stations or on Unmanned Ground Vehicles (UGVs) acting as mobile recharging stations. This leads to a new variant of the Traveling Salesperson Problem (TSP) with mobile recharging stations. We present an algorithm that finds not only the order in which to visit the sites but also when and where to land on the charging stations to recharge. Our algorithm plans tours for the UGVs as well as determines the best locations to place stationary charging stations. We study three variants for charging: Multiple stationary charging stations, single mobile charging station, and multiple mobile charging stations. As the problems we study are nondeterministic polynomial time (NP)‐Hard, we present a practical solution using Generalized TSP that finds the optimal solution that minimizes the total time, subject to the discretization of battery levels. If the UGVs are slower than the UAVs, then the algorithm also finds the minimum number of UGVs required to support the UAV mission such that the UAV is not required to wait for the UGV. Our simulation results show that the running time is acceptable for reasonably sized instances in practice. We evaluate the performance of our algorithm through simulations and proof‐of‐concept field experiments with a fully autonomous system of one UAV and UGV.
An Efficient Algorithm for Routing and Recharging of Electric Vehicles
In this paper, we address the routing and recharging problem for electric vehicles, where charging nodes have heterogeneous prices and waiting times, and the objective is to minimize the total recharging cost. We prove that the problem is NP-hard and propose two algorithms to solve it. The first, is an algorithm which obtains the optimal solution in pseudo-polynomial time. The second, is a polynomial time algorithm that obtains a solution with the total cost of recharging not greater than the optimal cost for a more constrained instance of the problem with the maximum waiting time of (1−ϵ)⋅W , where W is the maximum allowable waiting time.
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- Award ID(s):
- 1724227
- NSF-PAR ID:
- 10288206
- Date Published:
- Journal Name:
- COCOA 2020: Combinatorial Optimization and Applications
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We study the problem of maximizing a non-monotone submodular function subject to a cardinality constraint in the streaming model. Our main contribution is a single-pass (semi-)streaming algorithm that uses roughly $O(k / \varepsilon^2)$ memory, where $k$ is the size constraint. At the end of the stream, our algorithm post-processes its data structure using any offline algorithm for submodular maximization, and obtains a solution whose approximation guarantee is $\frac{\alpha}{1+\alpha}-\varepsilon$, where $\alpha$ is the approximation of the offline algorithm. If we use an exact (exponential time) post-processing algorithm, this leads to $\frac{1}{2}-\varepsilon$ approximation (which is nearly optimal). If we post-process with the algorithm of \cite{buchbinder2019constrained}, that achieves the state-of-the-art offline approximation guarantee of $\alpha=0.385$, we obtain $0.2779$-approximation in polynomial time, improving over the previously best polynomial-time approximation of $0.1715$ due to \cite{feldman2018less}. It is also worth mentioning that our algorithm is combinatorial and deterministic, which is rare for an algorithm for non-monotone submodular maximization, and enjoys a fast update time of $O(\frac{\log k + \log (1/\alpha {\varepsilon^2})$ per element.more » « less
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null (Ed.)Waiting at the right location at the right time can be critically important in certain variants of time-dependent shortest path problems. We investigate the computational complexity of time-dependent shortest path problems in which there is either a penalty on waiting or a limit on the total time spent waiting at a given subset of the nodes. We show that some cases are nondeterministic polynomial-time hard, and others can be solved in polynomial time, depending on the choice of the subset of nodes, on whether waiting is penalized or constrained, and on the magnitude of the penalty/waiting limit parameter. Summary of Contributions: This paper addresses simple yet relevant extensions of a fundamental problem in Operations Research: the Shortest Path Problem (SPP). It considers time-dependent variants of SPP, which can account for changing traffic and/or weather conditions. The first variant that is tackled allows for waiting at certain nodes but at a cost. The second variant instead places a limit on the total waiting. Both variants have applications in transportation, e.g., when it is possible to wait at certain locations if the benefits outweigh the costs. The paper investigates these problems using complexity analysis and algorithm design, both tools from the field of computing. Different cases are considered depending on which of the nodes contribute to the waiting cost or waiting limit (all nodes, all nodes except the origin, a subset of nodes…). The computational complexity of all cases is determined, providing complexity proofs for the variants that are NP-Hard and polynomial time algorithms for the variants that are in P.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1007/978-3-030-64843-5_48
