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Article

The Non-Smooth and Bi-Objective Team Orienteering Problem with Soft Constraints

1
Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain
2
Internet Interdisciplinary Institute (IN3), Computer Science Department, Universitat Oberta de Catalunya, 08018 Barcelona, Spain
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Department of Mathematics, Universitat Politècnica de Catalunya, 08028 Barcelona, Spain
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Department of Data Science, Euncet Business School, 08225 Terrassa, Spain
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School of Engineering, Information Technology and Physical Sciences, Federation University, Ballarat 3350, Australia
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(9), 1461; https://doi.org/10.3390/math8091461
Received: 8 August 2020 / Revised: 21 August 2020 / Accepted: 25 August 2020 / Published: 1 September 2020
(This article belongs to the Special Issue Multi-Criteria Optimization Models and Applications)
In the classical team orienteering problem (TOP), a fixed fleet of vehicles is employed, each of them with a limited driving range. The manager has to decide about the subset of customers to visit, as well as the visiting order (routes). Each customer offers a different reward, which is gathered the first time that it is visited. The goal is then to maximize the total reward collected without exceeding the driving range constraint. This paper analyzes a more realistic version of the TOP in which the driving range limitation is considered as a soft constraint: every time that this range is exceeded, a penalty cost is triggered. This cost is modeled as a piece-wise function, which depends on factors such as the distance of the vehicle to the destination depot. As a result, the traditional reward-maximization objective becomes a non-smooth function. In addition, a second objective, regarding the design of balanced routing plans, is considered as well. A mathematical model for this non-smooth and bi-objective TOP is provided, and a biased-randomized algorithm is proposed as a solving approach. View Full-Text
Keywords: team orienteering problem; soft constraints; non-smooth optimization; multi-objective optimization; biased-randomized algorithms team orienteering problem; soft constraints; non-smooth optimization; multi-objective optimization; biased-randomized algorithms
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MDPI and ACS Style

Estrada-Moreno, A.; Ferrer, A.; Juan, A.A.; Panadero, J.; Bagirov, A. The Non-Smooth and Bi-Objective Team Orienteering Problem with Soft Constraints. Mathematics 2020, 8, 1461. https://doi.org/10.3390/math8091461

AMA Style

Estrada-Moreno A, Ferrer A, Juan AA, Panadero J, Bagirov A. The Non-Smooth and Bi-Objective Team Orienteering Problem with Soft Constraints. Mathematics. 2020; 8(9):1461. https://doi.org/10.3390/math8091461

Chicago/Turabian Style

Estrada-Moreno, Alejandro, Albert Ferrer, Angel A. Juan, Javier Panadero, and Adil Bagirov. 2020. "The Non-Smooth and Bi-Objective Team Orienteering Problem with Soft Constraints" Mathematics 8, no. 9: 1461. https://doi.org/10.3390/math8091461

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