Memetic Computing

, Volume 6, Issue 1, pp 19–29 | Cite as

A bare-bones ant colony optimization algorithm that performs competitively on the sequential ordering problem

  • Ahmed Ezzat
  • Ashraf M. Abdelbar
  • Donald C. WunschII
Regular research paper
First Online:
Received:
Accepted:

Abstract

EigenAnt is a bare-bones ant colony optimization algorithm that has been proven to converge to the optimal solution under certain conditions. In this paper, we extend EigenAnt to the sequential ordering problem (SOP), comparing its performance to Gambardella et al.’s enhanced ant colony system (EACS), a model that has been found to have state-of-the-art performance on the SOP. Our experimental results, using the SOPLIB2006 instance library, indicate that there is no statistically significant difference in performance between our proposed method and the state-of-the-art EACS method.

Keywords

Ant colony optimization Sequential ordering problem  Swarm intelligence EigenAnt algorithm Ant colony system Metaheuristic Traveling salesman problem 
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Notes

Acknowledgments

The partial support of the National Science Foundation, the Missouri University of Science and Technology Center for Infrastructure Engineering Studies and Intelligent Systems Center, and the Mary K. Finley Missouri Endowment are gratefully acknowledged. We would like to thank Jayadeva for providing the Matlab source code for the EigenAnt algorithm. Although our implementation, in C, did not directly incorporate this code, having access to it was useful in validating our implementation.

References

  1. 1.
    Abdelbar AM (2008) Stubborn ants. In: Proceedings SIS-08, St. Louis, pp 1–5Google Scholar
  2. 2.
    Abdelbar AM (2012) Is there a computational advantage to representing evaporation rate in ant colony optimization as a Gaussian random variable?. In: Proceedings GECCO-12, Philadelphia, pp 1–8Google Scholar
  3. 3.
    Abdelbar AM, Wunsch DC (2012) Improving the performance of MAX-MIN ant system on the TSP using stubborn ants. In: Proceedings GECCO-12, Philadelphia, pp 1395–1396Google Scholar
  4. 4.
    Anghinolfi D, Montemanni R, Paolucci M, Gambardella LM (2009) A particle swarm optimization approach for the sequential ordering problem. In: Proceedings MIC-09. Hamburg, GermanyGoogle Scholar
  5. 5.
    Anghinolfi D, Montemanni R, Paolucci M, Gambardella LM (2011) A hybrid particle swarm optimization approach for the sequential ordering problem. Comput Operat Res 38(7):1076–1085CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Ascheuer N (1995) Hamiltonian path problems in the on-line optimization of flexible manufacturing systems, PhD Thesis, Technische Universität BerlinGoogle Scholar
  7. 7.
    Bentley JJ (1992) Fast algorithms for geometric traveling salesman problems. ORSA J Comput 4(4):387–411CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Bullnheimer B, Hartl RF, Strauss C (1999) An improved ant system algorithm for the vehicle routing problem. Ann Operat Res 89:25–38CrossRefMathSciNetGoogle Scholar
  9. 9.
    Chen S, Smith S (1996) Commonality and genetic algorithms, Technical Report CMURI-TR-96-27, Robotic Institute, Carnegie Mellon UniversityGoogle Scholar
  10. 10.
    Chica M, Cordón O, Damas S, Bautista J (2011) A new diversity induction mechanism for a multi-objective ant colony algorithm to solve a real-world time and space assembly line balancing problem. Memet Comput 3:15–24CrossRefGoogle Scholar
  11. 11.
    Cordón O, de Viana IF, Herrera F (2002) Analysis of the best-worst ant system and its variants on the TSP. Mathw Soft Comput 9(2–3):177–192MATHGoogle Scholar
  12. 12.
    Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. Mach Learn Res 7:1–30MATHMathSciNetGoogle Scholar
  13. 13.
    Dorigo M, Gambardella LM (1997) Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans Evolut Comput 1(1):35–66CrossRefGoogle Scholar
  14. 14.
    Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperative agents. IEEE Trans Syst Man Cybern 26(1):29–41CrossRefGoogle Scholar
  15. 15.
    Dorigo M, Stützle T (2004) Ant colony optimization. MIT Press, CambridgeCrossRefMATHGoogle Scholar
  16. 16.
    Dorigo M, Stützle T (2010) Ant colony optimization: overview and recent advances. In: Gendreau M, Potvin Y (eds) Handbook of metaheuristics, 2nd edn. Springer, New York, pp 227–263CrossRefGoogle Scholar
  17. 17.
    Escudero LF (1988) An inexact algorithm for the sequential ordering problem. Eur J Operat Res 37:232–253CrossRefMathSciNetGoogle Scholar
  18. 18.
    Ezzat A, Abdelbar AM (2013) A less-exploitative variation of the enhanced ant colony system applied to SOP. In: Proceedings CEC-2013, Canćun, Mexico, pp 1917–1924Google Scholar
  19. 19.
    Gambardella LM, Dorigo M (2000) An ant colony system hybridized with a new local search for the sequential ordering problem. INFORMS J Comput 12(3):237–255CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    Gambardella LM, Montemanni R, Weyland D (2012) Coupling ant colony systems with strong local searches. Eur J Operat Res 220(3):831–843 Google Scholar
  21. 21.
    Guerriero F, Mancini M (2003) A cooperative parallel rollout algorithm for the sequential ordering problem. Parallel Comput 29(5):663–677CrossRefGoogle Scholar
  22. 22.
    Jackson DE, Bicak M, Holcombe M (2011) Decentralized communication, trail connectivity and emergent benefits of ant pheromone trail networks. Memet Comput 3:25–32CrossRefGoogle Scholar
  23. 23.
    Jayadeva, Shah S, Bhaya A, Kothari R, Chandra S (2013) Ants find the shortest path: a mathematical proof. Swarm Intell 7(1):43–62CrossRefGoogle Scholar
  24. 24.
    Kindervater G, Savelsbergh M (1997) Vehicle routing: handling edge exchanges. In: Aarts EHL, Lenstra JK (eds) Local search in combinatorial optimization. Wiley, Chichester, pp 337–360Google Scholar
  25. 25.
    Lin S (1965) Computer solutions of the traveling salesman problem. Bell Syst Tech J 44:2245–2269CrossRefMATHGoogle Scholar
  26. 26.
    Lin S, Kernighan BW (1973) An effective heuristic algorithm for the traveling-salesman problem. Operat Res 21:498–516CrossRefMATHMathSciNetGoogle Scholar
  27. 27.
    Montemanni R. SOPLIB2006 Problem Instance Library. http://www.idsia.ch/~roberto/SOPLIB06.zip
  28. 28.
    Montemanni R, Smith DH, Gambardella LM (2007) Ant colony systems for large sequential ordering problems. In: Proceedings SIS-07, Honolulu, pp 60–67Google Scholar
  29. 29.
    Montemanni R, Smith DH, Gambardella LM (2008) A heuristic manipulation technique for the sequential ordering problem. Comput Operat Res 35(12):3931–3944CrossRefMATHGoogle Scholar
  30. 30.
    Montemanni R, Smith DH, Rizzoli AE, Gambardella LM (2009) Sequential ordering problems for crane scheduling in port terminals. Int J Simul Process Model 5(4):348–361CrossRefGoogle Scholar
  31. 31.
    Or I (1976) Traveling salesman-type combinatorial problems and their relation to the logistics of regional blood banking, PhD Thesis, Dept. of Industrial Engineering and Management Sciences, Northwestern UniversityGoogle Scholar
  32. 32.
    Otero FEB, Freitas AA, Johnson CG (2010) A hierarchical multi-label classification ant colony algorithm for protein function prediction. Memet Comput 2:165–181CrossRefGoogle Scholar
  33. 33.
    Pullyblank W, Timlin M (1991) Precedence constrained routing and helicopter scheduling: heuristic design, Technical Report RC17154 (#76032). IBM T.J. Watson Research CenterGoogle Scholar
  34. 34.
    Savelsbergh MWP (1990) An efficient implementation of local search algorithms for constrained routing problems. Eur J Operat Res 47:75–85CrossRefMATHMathSciNetGoogle Scholar
  35. 35.
    Seo DI, Moon BR (2003) A hybrid genetic algorithm based on complete graph representation for the sequential ordering problem. In: Proceedings GECCO-03, Chicago, pp 669–680Google Scholar
  36. 36.
    Stützle T. ACOTSP: a software package for various ant colony optimization algorithms applied to the symmetric traveling salesman problem. http://www.aco-metaheuristic.org/aco-code/
  37. 37.
    Stützle T, Hoos H (2000) MAX-MIN ant system. Future Gener Comput Syst 16(8):889–914CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Ahmed Ezzat
    • 1
  • Ashraf M. Abdelbar
    • 2
  • Donald C. WunschII
    • 3
  1. 1.Department of Computer Science and EngineeringAmerican University in CairoCairoEgypt
  2. 2.Department of Mathematics and Computer ScienceBrandon UniversityBrandonCanada
  3. 3.Department of Electrical and Computer EngineeringMissouri University of Science and TechnologyRollaUSA

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