A dynamic programming operator for tour location problems applied to the covering tour problem

This paper presents an evaluation operator for single-trip vehicle routing problems where it is not necessary to visit all the nodes. Such problems are known as Tour Location Problems. The operator, called Selector, is a dynamic programming algorithm that converts a given sequence of nodes into a feasible tour. The operator returns a subsequence of this giant tour which is optimal in terms of length. The procedure is implemented in an adaptive large neighborhood search to solve a specific tour location problem: the Covering Tour Problem. This problem consists in finding a lowest-cost Hamiltonian cycle over a subset of nodes such that nodes outside the tour are within a given distance from a visited node. The metaheuristic proposed is competitive as shown by the quality of results evaluated using the output of a state-of-the-art exact algorithm.

[1]  Duc-Cuong Dang,et al.  A memetic algorithm for the team orienteering problem , 2008, 4OR.

[2]  Leslie Pérez Cáceres,et al.  The irace package: Iterated racing for automatic algorithm configuration , 2016 .

[3]  Nicolas Jozefowiez,et al.  A Selector Operator-Based Adaptive Large Neighborhood Search for the Covering Tour Problem , 2015, LION.

[4]  Philippe Lacomme,et al.  Order-first split-second methods for vehicle routing problems: A review , 2014 .

[5]  Michel Gendreau,et al.  The Covering Tour Problem , 1997, Oper. Res..

[6]  John R. Current,et al.  The Covering Salesman Problem , 1989, Transp. Sci..

[7]  Luiz Satoru Ochi,et al.  GRASP Metaheuristics to the Generalized Covering Tour Problem , 2001 .

[8]  Michel Gendreau,et al.  An exact algorithm for the elementary shortest path problem with resource constraints: Application to some vehicle routing problems , 2004, Networks.

[9]  John E. Beasley,et al.  Route first--Cluster second methods for vehicle routing , 1983 .

[10]  G. Dantzig.  Discrete-Variable Extremum Problems , 1957 .

[11]  Inmaculada Rodríguez Martín,et al.  The Ring Star Problem: Polyhedral analysis and exact algorithm , 2004, Networks.

[12]  T. A. J. Nicholson,et al.  Finding the Shortest Route between Two Points in a Network , 1966, Comput. J..

[13]  David Pisinger,et al.  A general heuristic for vehicle routing problems , 2007, Comput. Oper. Res..

[14]  Gilbert Laporte,et al.  A Covering Tour Model for Planning Mobile Health Care Facilities in SuhumDistrict, Ghama , 1998 .

[15]  Majid Salari,et al.  An integer programming-based local search for the covering salesman problem , 2012, Comput. Oper. Res..

[16]  Roberto Baldacci,et al.  Scatter Search Methods for the Covering Tour Problem , 2005 .

[17]  Gerhard Reinelt,et al.  TSPLIB - A Traveling Salesman Problem Library , 1991, INFORMS J. Comput..

[18]  Majid Salari,et al.  Combining ant colony optimization algorithm and dynamic programming technique for solving the covering salesman problem , 2015, Comput. Ind. Eng..

[19]  Michel Gendreau,et al.  Traveling Salesman Problems with Profits , 2005, Transp. Sci..

[20]  Christian Prins,et al.  A simple and effective evolutionary algorithm for the vehicle routing problem , 2004, Comput. Oper. Res..

[21]  David Pisinger,et al.  An Adaptive Large Neighborhood Search Heuristic for the Pickup and Delivery Problem with Time Windows , 2006, Transp. Sci..