The Correlated Arc Orienteering Problem

TL;DR

This paper defines the correlated arc orienteering problem (CAOP), a complex route optimization challenge for robots that maximizes environmental feature rewards considering spatial correlations and resource constraints.

Contribution

It introduces CAOP as a generalization of existing problems, formulates it as a MIQP for optimal solutions, and develops a greedy algorithm for NP-hard instances.

Findings

Formulated CAOP as a mixed integer quadratic program.

Developed an efficient greedy constructive algorithm.

Demonstrated applications in gas leak detection and road network coverage.

Abstract

This paper introduces the correlated arc orienteering problem (CAOP), where the task is to find routes for a team of robots to maximize the collection of rewards associated with features in the environment. These features can be one-dimensional or points in the environment, and can have spatial correlation, i.e., visiting a feature in the environment may provide a portion of the reward associated with a correlated feature. A robot incurs costs as it traverses the environment, and the total cost for its route is limited by a resource constraint such as battery life or operation time. As environments are often large, we permit multiple depots where the robots must start and end their routes. The CAOP generalizes the correlated orienteering problem (COP), where the rewards are only associated with point features, and the arc orienteering problem (AOP), where the rewards are not spatially correlated. We formulate a mixed integer quadratic program (MIQP) that formalizes the problem and gives optimal solutions. However, the problem is NP-hard, and therefore we develop an efficient greedy constructive algorithm. We illustrate the problem with two different applications: informative path planning for methane gas leak detection and coverage of road networks.