A variable neighborhood search method for the orienteering problem with hotel selection

In this paper, we present the orienteering problem with hotel selection (OPHS), an extension of the orienteering problem (OP). In the OPHS, a set of vertices with a score and a set of hotels are given. The goal is to determine a fixed number of connected trips that visits some vertices and maximizes the sum of the collected scores. Each trip is limited in length and should start and end in one of the hotels. We formulate the problem mathematically, explain the differences with related optimization problems and indicate what makes this problem inherently more difficult.

[1]  Tom M. Cavalier,et al.  A heuristic for the multiple tour maximum collection problem , 1994, Comput. Oper. Res..

[2]  Alain Hertz,et al.  Metaheuristics for the team orienteering problem , 2005, J. Heuristics.

[3]  Bruce L. Golden,et al.  A fast and effective heuristic for the orienteering problem , 1996 .

[4]  Nacima Labadie,et al.  The Team Orienteering Problem with Time Windows: An LP-based Granular Variable Neighborhood Search , 2012, Eur. J. Oper. Res..

[5]  Giri Narasimhan,et al.  Resource-constrained geometric network optimization , 1998, SCG '98.

[6]  Richard F. Hartl,et al.  Metaheuristics for the bi-objective orienteering problem , 2009, Swarm Intelligence.

[7]  T. Tsiligirides,et al.  Heuristic Methods Applied to Orienteering , 1984 .

[8]  R. A. Zemlin,et al.  Integer Programming Formulation of Traveling Salesman Problems , 1960, JACM.

[9]  Bruce L. Golden,et al.  The team orienteering problem , 1996 .

[10]  G. Laporte,et al.  A Branch-and-Cut Algorithm for the Undirected Selective Traveling Salesman Problem , 1998 .

[11]  G. V. Berghe,et al.  Metaheuristics for Tourist Trip Planning , 2009 .

[12]  Aise Zülal Sevkli,et al.  Variable Neighborhood Search for the Orienteering Problem , 2006, ISCIS.

[13]  Richard F. Hartl,et al.  Heuristics for the multi-period orienteering problem with multiple time windows , 2010, Comput. Oper. Res..

[14]  Dirk Van Oudheusden,et al.  The orienteering problem: A survey , 2011, Eur. J. Oper. Res..

[15]  Kenneth Sörensen,et al.  The travelling salesperson problem with hotel selection , 2012, J. Oper. Res. Soc..

[16]  Dirk Van Oudheusden,et al.  A guided local search metaheuristic for the team orienteering problem , 2009, Eur. J. Oper. Res..

[17]  Pierre Hansen,et al.  Variable neighborhood search: Principles and applications , 1998, Eur. J. Oper. Res..