Optimal Routing Schedules for Robots Operating in Aisle-Structures

TL;DR

This paper addresses the Constant-cost Orienteering Problem for robots in aisle-structured graphs, providing polynomial-time solutions for special cases and a heuristic that outperforms existing algorithms in complex scenarios.

Contribution

It introduces polynomial-time algorithms for two special cases of COP and a new heuristic for the general case, improving solution quality in aisle-structured robot routing.

Findings

Optimal solutions for special cases are computationally efficient.

The heuristic outperforms state-of-the-art algorithms in complex scenarios.

Solutions are competitive even in real and synthetic environments.

Abstract

In this paper, we consider the Constant-cost Orienteering Problem (COP) where a robot, constrained by a limited travel budget, aims at selecting a path with the largest reward in an aisle-graph. The aisle-graph consists of a set of loosely connected rows where the robot can change lane only at either end, but not in the middle. Even when considering this special type of graphs, the orienteering problem is known to be NP-hard. We optimally solve in polynomial time two special cases, COP-FR where the robot can only traverse full rows, and COP-SC where the robot can access the rows only from one side. To solve the general COP, we then apply our special case algorithms as well as a new heuristic that suitably combines them. Despite its light computational complexity and being confined into a very limited class of paths, the optimal solutions for COP-FR turn out to be competitive even for COP in both real and synthetic scenarios. Furthermore, our new heuristic for the general case outperforms state-of-art algorithms, especially for input with highly unbalanced rewards.