An Iterated Local Search Algorithm for the Pollution Traveling Salesman Problem

  • Valentina Cacchiani
  • Carlos Contreras-Bolton
  • John W. Escobar
  • Luis M. Escobar-Falcon
  • Rodrigo Linfati
  • Paolo Toth
Part of the AIRO Springer Series book series (AIROSS, volume 1)


Motivated by recent works on the Pollution Routing Problem (PRP), introduced in Bektas and Laporte (Transp Res Part B: Methodol 45(8):1232–1250, 2011) [1], we study the Pollution Traveling Salesman Problem (PTSP). It is a generalization of the well-known Traveling Salesman Problem, which aims at finding a Hamiltonian tour that minimizes a function of fuel consumption (dependent on distance travelled, vehicle speed and load) and driver costs. We present a Mixed Integer Linear Programming (MILP) model for the PTSP, enhanced with sub-tour elimination constraints, and propose an Iterated Local Search (ILS) algorithm. It first builds a feasible tour, based on the solution of the Linear Programming (LP) relaxation of the MILP model, and then loops between three phases: perturbation, local search and acceptance criterion. The results obtained by the ILS on instances with up to 50 customers are compared with those found by a Cut-and-Branch algorithm based on the enhanced MILP model. The results show the effectiveness of the ILS algorithm, which can find the best solution for about \(99\%\) of the instances within short computing times.


Pollution Traveling Salesman Problem Iterated Local Search MILP model 



This material is based upon work supported by the Air Force Office of Scientific Research under award number FA9550-17-1-0025. We also acknowledge project CONICYT FONDECYT 11150370.


  1. 1.
    Bektaş, T., Laporte, G.: The pollution-routing problem. Transp. Res. Part B: Methodol. 45(8), 1232–1250 (2011)CrossRefGoogle Scholar
  2. 2.
    Dantzig, G.B., Fulkerson, D.R., Johnson, S.M.: Solution of a large-scale traveling salesman problem. Oper. Res. 2, 393–410 (1954)MathSciNetGoogle Scholar
  3. 3.
    Demir, E., Bektaş, T., Laporte, G.: An adaptive large neighborhood search heuristic for the pollution-routing problem. Eur. J. Oper. Res. 223(2), 346–359 (2012)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Demir, E., Bektaş, T., Laporte, G.: A review of recent research on green road freight transportation. Eur. J. Oper. Res. 237(3), 775–793 (2014)CrossRefGoogle Scholar
  5. 5.
    Kramer, R., Subramanian, A., Vidal, T., Lucídio dos Anjos, F.C.: A matheuristic approach for the pollution-routing problem. Eur. J. Oper. Res. 243(2), 523–539 (2015)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Lourenço, H.R., Martin, O.C., Stützle, T.: Iterated local search: framework and applications. In: Handbook of Metaheuristics, pp. 363–397. Springer, Boston, MA (2010)CrossRefGoogle Scholar
  7. 7.
    Lin, C., Choy, K.L., Ho, G.T., Chung, S.H., Lam, H.Y.: Survey of green vehicle routing problem: past and future trends. Expert Syst. Appl. 41(4), 1118–1138 (2014)CrossRefGoogle Scholar
  8. 8.
    Padberg, M., Rinaldi, G.: An efficient algorithm for the minimum capacity cut problem. Math. Program. 47(1), 19–36 (1990)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Valentina Cacchiani
    • 1
  • Carlos Contreras-Bolton
    • 1
  • John W. Escobar
    • 2
  • Luis M. Escobar-Falcon
    • 3
  • Rodrigo Linfati
    • 4
  • Paolo Toth
    • 1
  1. 1.University of BolognaBolognaItaly
  2. 2.Pontificia Universidad JaverianaCaliColombia
  3. 3.Technological University of PereiraPereiraColombia
  4. 4.University of Bío BíoConcepciónChile

Personalised recommendations