Variable neighborhood search to solve the generalized orienteering problem

Abstract

This paper presents a variable neighborhood search (VNS) algorithm to solve the extension of the orienteering problem known as the generalized orienteering problem (GOP). Our algorithm aims to use a reduced number of neighborhoods without compromising the quality of the results. This reduced number of neighborhoods, together with the precalculation of scores associated with points of interest, allows us, in most cases, to outperformall previous metaheuristics proposed for this problem. This is the first time a VNS is being applied to theGOP, and it provides promising computational results. In particular, in the case studies considered in the paper, we were able to find 35 new best solutions, all of which were found using a shorter computational time. Furthermore, the information regarding other best-known solutions provided in the literature has also been improved, with corrections to some previously published errors regarding scores and distances. In addition, the benchmark has been extended with the incorporation of new case studies based on real data from three of the most popular tourist cities in Spain.