The orienteering problem: a hybrid control formulation

TL;DR

This paper introduces a novel hybrid control approach to solve the orienteering problem, integrating continuous navigation and discrete visit tracking, using advanced dynamical programming methods for improved solution efficiency.

Contribution

It presents an original hybrid control formulation for the orienteering problem, combining continuous and discrete states with non-standard dynamical programming techniques.

Findings

Effective hybrid control model for orienteering problems

Demonstrated improved solution approach over traditional methods

Applicable to navigation, logistics, and tourism scenarios

Abstract

In the last years, a growing number of challenging applications in navigation, logistics, and tourism were modeled as orienteering problems. This problem has been proposed in relation to a sport race where certain control points must be visited in a minimal time. In a certain kind of these competitions, the choice of the number and the order for the control points are left to the competitor. We propose an original approach to solve the orienteering problem based on hybrid control. The continuous state of the system contains information about the navigation toward the next control point. In contrast, the discrete state keeps track of the already visited ones. The control problem is solved using non-standard dynamical programming techniques.