Shortest path with acceleration constraints: complexity and approximation algorithms

作     者：Ardizzoni, S. Consolini, L. Laurini, M. Locatelli, M. 

作者机构：Univ Parma Dipartimento Ingn & Architettura Parco Area Sci181-A Parma Italy 

出 版 物：《COMPUTATIONAL OPTIMIZATION AND APPLICATIONS》 (计算优化及其应用)

年 卷 期：2022年第83卷第2期

页      面：555-592页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Universita degli Studi di Parma within the CRUI-CARE Agreement 

主　　题：Shortest path Speed planning Complexity Approximation algorithms 

摘      要：We introduce a variant of the Shortest Path Problem (SPP), in which we impose additional constraints on the acceleration over the arcs, and call it Bounded Acceleration SPP (BASP). This variant is inspired by an industrial application: a vehicle needs to travel from its current position to a target one in minimum-time, following pre-defined geometric paths connecting positions within a facility, while satisfying some speed and acceleration constraints depending on the vehicle position along the currently traveled path. We characterize the complexity of BASP, proving its NP-hardness. We also show that, under additional hypotheses on problem data, the problem admits a pseudo-polynomial time-complexity algorithm. Moreover, we present an approximation algorithm with polynomial time-complexity with respect to the data of the original problem and the inverse of the approximation factor e. Finally, we present some computational experiments to evaluate the performance of the proposed approximation algorithm.