Improving ACO Convergence with Parallel Tempering

  • Rafał Skinderowicz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10449)


Parallel Tempering (PT) is an efficient Monte Carlo simulation method known from statistical physics. We present a novel PT-based Ant Colony Optimization algorithm (PTACO) in which multiple replicas of the Ant Colony System enhanced with a temperature parameter (ACST) are executed in parallel. Based on computational experiments on a set of TSP and ATSP instances we show that the PTACO converges (in terms of solutions quality) significantly faster than the ACS and is competitive to the state-of-the-art Ant Colony Extended algorithm.


Ant Colony System Parallel Tempering Simulated Annealing Travelling salesman problem 



This research was supported in part by PL-Grid Infrastructure.


  1. 1.
    Ayob, M.B., Jaradat, G.M.: Hybrid ant colony systems for course timetabling problems. In: Proceedings of the 2nd Conference on Data Mining and Optimization, DMO 2009, Universiti Kebangsaan Malaysia, 27–28 October 2009, pp. 120–126. IEEE (2009)Google Scholar
  2. 2.
    Behnamian, J., Zandieh, M., Ghomi, S.F.: Parallel-machine scheduling problems with sequence-dependent setup times using an aco, SA and VNS hybrid algorithm. Expert Syst. Appl. 36(6), 9637–9644 (2009)CrossRefGoogle Scholar
  3. 3.
    Chen, C.-H., Ting, C.-J.: A hybrid ant colony system for vehicle routing problem with time windows. J. East. Asia Soc. Transp. Stud. 6, 2822–2836 (2005)Google Scholar
  4. 4.
    Citrolo, A.G., Mauri, G.: A hybrid Monte Carlo ant colony optimization approach for protein structure prediction in the HP model. In: Graudenzi, A., Caravagna, G., Mauri, G., Antoniotti, M. (eds.) Proceedings of Wivace 2013 - Italian Workshop on Artificial Life and Evolutionary Computation, EPTCS, Milan, Italy, 1–2 July 2013, vol. 130, pp. 61–69 (2013)CrossRefGoogle Scholar
  5. 5.
    Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)zbMATHGoogle Scholar
  6. 6.
    Dorigo, M., Stützle, T.: Ant colony optimization: overview and recent advances. In: Gendreau, M., Potvin, J.Y. (eds.) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol. 146, pp. 227–263. Springer, Boston (2010). doi: 10.1007/978-1-4419-1665-5_8CrossRefGoogle Scholar
  7. 7.
    Earl, D.J., Deem, M.W.: Parallel tempering: theory, applications, and new perspectives. Phys. Chem. Chem. Phys. 7(23), 3910–3916 (2005)CrossRefGoogle Scholar
  8. 8.
    Escario, J.B., Jimenez, J.F., Giron-Sierra, J.M.: Ant colony extended: experiments on the travelling salesman problem. Expert Syst. Appl. 42(1), 390–410 (2015)CrossRefGoogle Scholar
  9. 9.
    Katzgraber, H.G., Trebst, S., Huse, D.A., Troyer, M.: Feedback-optimized parallel tempering Monte Carlo. J. Stat. Mech.: Theory Exp. 2006(03), P03018 (2006)CrossRefGoogle Scholar
  10. 10.
    Kone, A., Kofke, D.A.: Selection of temperature intervals for parallel-tempering simulations. J. Chem. Phys. 122(20), 206101 (2005)CrossRefGoogle Scholar
  11. 11.
    Li, Y., Protopopescu, V.A., Arnold, N., Zhang, X., Gorin, A.: Hybrid parallel tempering and simulated annealing method. Appl. Math. Comput. 212(1), 216–228 (2009)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Skinderowicz, R.: Ant colony system with a restart procedure for TSP. In: Nguyen, N.-T., Manolopoulos, Y., Iliadis, L., Trawiński, B. (eds.) ICCCI 2016. LNCS, vol. 9876, pp. 91–101. Springer, Cham (2016). doi: 10.1007/978-3-319-45246-3_9CrossRefGoogle Scholar
  13. 13.
    Skinderowicz, R.: The GPU-based parallel ant colony system. J. Parallel Distrib. Comput. 98, 48–60 (2016)CrossRefGoogle Scholar
  14. 14.
    Skinderowicz, R.: An improved ant colony system for the sequential ordering problem. Comput. Oper. Res. 86, 1–17 (2017)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Wang, C., Hyman, J.D., Percus, A., Caflisch, R.: Parallel tempering for the traveling salesman problem. Int. J. Mod. Phys. C 20(04), 539–556 (2009)CrossRefGoogle Scholar
  16. 16.
    Zhu, J., Rui, T., Liao, M., Zhang, J.: Simulated annealing ant colony algorithm based on backfire method for QAP. In: Yu, X., Lienhart, R., Zha, Z., Liu, Y., Satoh, S. (eds.) The 4th International Conference on Internet Multimedia Computing and Service, ICIMCS 2012, Wuhan, China, 9–11 September 2012, pp. 100–105. ACM (2012)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Computer ScienceSilesia UniversitySosnowiecPoland

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