Calculus of Variations and Geometric Measure Theory
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F. Bagagiolo - A. Festa - L. Marzufero

The orienteering problem: a hybrid control formulation

created by marzufero on 22 Dec 2020
modified on 12 Jan 2022

[BibTeX]

Published Paper

Inserted: 22 dec 2020
Last Updated: 12 jan 2022

Journal: IFAC-PapersOnLine
Volume: 54
Number: 5
Pages: 175-180
Year: 2021
Doi: 10.1016/j.ifacol.2021.08.494

ArXiv: 2012.07712 PDF

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.

Keywords: optimal control of hybrid systems, modeling of human performance, application of nonlinear analysis and design, generalized solutions of Hamilton-Jacobi equations

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