The Bounded Acceleration Shortest Path problem: complexity and solution algorithms

TL;DR

This paper introduces the Bounded Acceleration Shortest Path (BASP) problem, a complex vehicle routing challenge considering acceleration and speed constraints, proving its NP-hardness and proposing solution algorithms with polynomial complexity under certain conditions.

Contribution

It formalizes the BASP problem, proves its NP-hardness, and develops solution algorithms that are polynomial-time solvable under specific assumptions.

Findings

BASP is NP-hard.

Polynomial-time algorithms are possible under certain conditions.

The problem generalizes the classical shortest path problem.

Abstract

The purpose of this work is to introduce and characterize the Bounded Acceleration Shortest Path (BASP) problem, a generalization of the Shortest Path (SP) problem. This problem is associated to a graph: the nodes represent positions of a mobile vehicle and the arcs are associated to pre-assigned geometric paths that connect these positions. BASP consists in finding the minimum-time path between two nodes. Differently from SP, we require that the vehicle satisfy bounds on maximum and minimum acceleration and speed, that depend on the vehicle position on the currently traveled arc. We prove that BASP is NP-hard and define solution algorithm that achieves polynomial time-complexity under some additional hypotheses on problem data.