Unit commitment problem on an electricity network consists in choosing the production plan of the plants (units) of a company in order to meet demand constraints. It is generally solved using a decomposition approach where demand constraints are relaxed, resulting in one pricing subproblem for each unit. In this paper we focus on the pricing subproblem for thermal units at EDF, a major French electricity producer. Our objective is to determine an optimal two-day production plan that minimizes the overall cost while respecting several non-linear operational constraints. The pricing problem is generally solved by dynamic programming. However, due to the curse of dimensionality, dynamic programming reaches its limits when extra-constraints have to be enforced. We model the subproblem as a resource constrained shortest path (RCSP) problem. Leveraging on RCSP algorithms recently introduced by the second author, we obtain an order of magnitude speed-up with respect to traditional RCSP algorithms.
The Dubins path problem had enormous applications in path planning for autonomous vehicles. In this paper, we consider a generalization of the Dubins path planning problem, which is to find a shortest Dubins path that starts from a given initial position and heading, and ends on a given target circle with the heading in the tangential direction. This problem has direct applications in Dubins neighborhood traveling salesman problem, obstacle avoidance Dubins path planning problem etc. We characterize the length of the four CSC paths as a function of angular position on the target circle, and de…
In this paper we consider shortest path problems in a directed graph where the transitions between nodes are subject to uncertainty. We use a minimax formulation, where the objective is to guarantee that a special destination state is reached with a minimum cost path under the worst possible instance of the uncertainty. Problems of this type arise, among others, in planning and pursuit-evasion contexts, and in model predictive control. Our analysis makes use of the recently developed theory of abstract semicontractive dynamic programming models. We investigate questions of existence and unique…
We consider the stochastic shortest path planning problem in MDPs, i.e., the problem of designing policies that ensure reaching a goal state from a given initial state with minimum accrued cost. In order to account for rare but important realizations of the system, we consider a nested dynamic coherent risk total cost functional rather than the conventional risk-neutral total expected cost. Under some assumptions, we show that optimal, stationary, Markovian policies exist and can be found via a special Bellman's equation. We propose a computational technique based on difference convex programs…
This paper presents a method of finding the shortest path for an unmanned aerial vehicle (UAV) flying from an initial point to a target line at a constant altitude. The length of a Dubins path is derived as a function of the final position on the line and then differentiated to obtain its extreme value. The primary contribution of the study is a simple analytical solution to determine the minimum-length Dubins path from an initial position to a target line with initial and final orientations given. The proposed method is demonstrated with numerical examples.
The paper addresses the problem of providing suitable reference trajectories in motion planning problems for autonomous vehicles. Among the various approaches to compute a reference trajectory, our aim is to find those trajectories which optimize a given performance criterion, for instance fuel consumption, comfort, safety, time, and obey constraints, e.g. collision avoidance, safety regions, control bounds. This task can be approached by geometric shortest path problems or by optimal control problems, which need to be solved efficiently. To this end we use direct discretization schemes and mo…
Norwegian University of Science and Technology (NTNU)（挪威科技大学）
We consider warm-started optimized trajectory planning for autonomous surface vehicles (ASVs) by combining the advantages of two types of planners: an A* implementation that quickly finds the shortest piecewise linear path, and an optimal control-based trajectory planner. A nonlinear 3-degree-of-freedom underactuated model of an ASV is considered, along with an objective functional that promotes energy-efficient and readily observable maneuvers. The A* algorithm is guaranteed to find the shortest piecewise linear path to the goal position based on a uniformly decomposed map. Dynamic informatio…
University of Texas at Austin（德克萨斯大学奥斯汀分校）；Tokyo Institute of Technology（东京工业大学）
We propose a path planning methodology for a mobile robot navigating through an obstacle-filled environment to generate a reference path that is traceable with moderate sensing efforts. The desired reference path is characterized as the shortest path in an obstacle-filled Gaussian belief manifold equipped with a novel information-geometric distance function. The distance function we introduce is shown to be an asymmetric quasi-pseudometric and can be interpreted as the minimum information gain required to steer the Gaussian belief. An RRT*-based numerical solution algorithm is presented to sol…
Ground staff agents of airlines operate many jobs at airports such as passengers check-in, planes cleaning, etc. Shift planning aims at building the sequences of jobs operated by ground staff agents, and have been widely studied given its impact on operating costs. As these jobs are closely related to flights arrivals and departures, flights delays disrupt ground staff schedules, which leads to high additional costs. Our goal is to provide a solution for shift planning at Air France that takes into account these additional costs. We therefore introduce a stochastic version of the shift plannin…
Dijkstra as an Oracle for Online Stochastic Shortest Path Navigation with Provable Guarantees
King Fahd University of Petroleum and Minerals (KFUPM)（法赫德国王石油与矿产大学）；Islamic University of Madinah（麦地那伊斯兰大学）；Universitas Muhammadiyah Yogyakarta（日惹穆罕默迪亚大学）
IBM Watson Research Center（IBM沃森研究中心）；Laboratoire d’Analyse et d’Architecture des Systèmes (LAAS), Institute of Mathematics, University of Toulouse（图卢兹大学数学研究所系统分析与架构实验室）；Robotics at Google（谷歌机器人部门）
We propose a novel method for planning shortest length piecewise-linear motions through complex environments punctured with static, moving, or even morphing obstacles. Using a moment optimization approach, we formulate a hierarchy of semidefinite programs that yield increasingly refined lower bounds converging monotonically to the optimal path length. For computational tractability, our global moment optimization approach motivates an iterative motion planner that outperforms competing sampling-based and nonlinear optimization baselines. Our method natively handles continuous time constraints …
An Efficient Method for Extracting the Shortest Path from the Dubins Set for Short Distances Between Initial and Final Positions
State Key Laboratory for Manufacturing Systems Engineering（制造系统工程国家重点实验室）；School of Automation Science and Engineering（自动化科学与工程学院）；Faculty of Electronic and Information Engineering（电子与信息工程学院）
Two-stage methods addressing continuous shortest path problems start local minimization from discrete shortest paths in a spatial graph. The convergence of such hybrid methods to global minimizers hinges on the discretization error induced by restricting the discrete global optimization to the graph, with corresponding implications on choosing an appropriate graph density. A prime example is flight planning, i.e., the computation of optimal routes in view of flight time and fuel consumption under given weather conditions. Highly efficient discrete shortest path algorithms exist and can be used…
Multiple Shooting Approach for Finding Approximately Shortest Paths for Autonomous Robots in Unknown Environments in 2D
Institute of Mathematical and Computational Sciences, Ho Chi Minh City University of Technology (HCMUT)（胡志明市理工大学数学与计算科学研究所）；Vietnam National University Ho Chi Minh City（越南国家大学胡志明市分校）；Institute of Mathematics, Vietnam Academy of Science and Technology (VAST)（越南科学技术翰林院数学研究所）
A Dubins path is a shortest path with bounded curvature. The seminal result in non-holonomic motion planning is that (in the absence of obstacles) a Dubins path consists either from a circular arc followed by a segment followed by another arc, or from three circular arcs [Dubins, 1957]. Dubins original proof uses advanced calculus; later, Dubins result was reproved using control theory techniques [Reeds and Shepp, 1990], [Sussmann and Tang, 1991], [Boissonnat, Cérézo, and Leblond, 1994]. We introduce and study a discrete analogue of curvature-constrained motion. We show that shortest "bounded-…
The ubiquitous expansion and transformation of the energy supply system involves large-scale power infrastructure construction projects. In the view of investments of more than a million dollars per kilometre, planning authorities aim to minimise the resistances posed by multiple stakeholders. Mathematical optimisation research offers efficient algorithms to compute globally optimal routes based on geographic input data. We propose a framework that utilizes a graph model where vertices represent possible locations of transmission towers, and edges are placed according to the feasible distance …
