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The non-smooth and bi-objective team orienteering problem with soft constraints

- Estrada-Moreno, Alejandro, Ferrer, Albert, Juan, Angel, Panadero, Javier, Bagirov, Adil

  • Authors: Estrada-Moreno, Alejandro , Ferrer, Albert , Juan, Angel , Panadero, Javier , Bagirov, Adil
  • Date: 2020
  • Type: Text , Journal article
  • Relation: Mathematics Vol. 8, no. 9 (2020), p.
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  • Description: 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. © 2020 by the authors.
  • Description: This work has been partially supported by the Spanish Ministry of Economy and Competitiveness & FEDER (SEV-2015-0563), the Spanish Ministry of Science (PID2019-111100RB-C21, RED2018-102642-T), and the Erasmus+ Program (2019-I-ES01-KA103-062602).

Comparative study of RPSALG algorithm for convex semi-infinite programming

- Auslender, Alfred, Ferrer, Albert, Goberna, Miguel, López, Marco

  • Authors: Auslender, Alfred , Ferrer, Albert , Goberna, Miguel , López, Marco
  • Date: 2014
  • Type: Text , Journal article
  • Relation: Computational Optimization and Applications Vol. 60, no. 1 (2014), p. 59-87
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  • Description: The Remez penalty and smoothing algorithm (RPSALG) is a unified framework for penalty and smoothing methods for solving min-max convex semi-infinite programing problems, whose convergence was analyzed in a previous paper of three of the authors. In this paper we consider a partial implementation of RPSALG for solving ordinary convex semi-infinite programming problems. Each iteration of RPSALG involves two types of auxiliary optimization problems: the first one consists of obtaining an approximate solution of some discretized convex problem, while the second one requires to solve a non-convex optimization problem involving the parametric constraints as objective function with the parameter as variable. In this paper we tackle the latter problem with a variant of the cutting angle method called ECAM, a global optimization procedure for solving Lipschitz programming problems. We implement different variants of RPSALG which are compared with the unique publicly available SIP solver, NSIPS, on a battery of test problems.

Solving DC programs using the cutting angle method

- Ferrer, Albert, Bagirov, Adil, Beliakov, Gleb

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