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Soft Computing

, Volume 15, Issue 1, pp 149–182 | Cite as

\(\epsilon\)- DANTE : an ant colony oriented depth search procedure

  • Pedro CardosoEmail author
  • Mário Jesus
  • Alberto Márquez
Original Paper

Abstract

The \(\epsilon\)-Depth ANT Explorer (\(\epsilon\)- DANTE ) algorithm applied to a multiple objective optimization problem is presented in this paper. This method is a hybridization of the ant colony optimization algorithm with a depth search procedure, putting together an oriented/limited depth search. A particular design of the pheromone set of rules is suggested for these kinds of optimization problems, which are an adaptation of the single objective case. Six versions with incremental features are presented as an evolutive path, beginning in a single colony approach, where no depth search is applied, to the final \(\epsilon\)- DANTE . Versions are compared among themselves in a set of instances of the multiple objective Traveling Salesman Problem. Finally, our best version of \(\epsilon\)- DANTE is compared with several established heuristics in the field showing some promising results.

Keywords

Swarm intelligence optimization Ant colony optimization Hybrid algorithms Multiple objective optimization Depth local search 

Notes

Acknowledgments

We thank the Engineering Institute of the University of Algarve, in particular to the Department of Electrical Engineering, the Department of Civil Engineering, and the Centro de Simulação e Cálculo (CsC) for the resources, the projects Optimización de redes de interconexión (MTM2008-05866-C03-01) and Matemática Discreta en Andalucia (MaDiscA) (P06-FQM-01649), and the help for the consolidation of the research group FQM-164 (2008/FQM-164). A special thanks to the reviewers who significantly helped to improve this contribution and to the authors of García-Martínez et al. (2007) for providing us the base codes for some of the methods presented in Sect. 6.

References

  1. Aarts E, Lenstra J (1997) Local search in combinatorial optimization. Wiley-Interscience Series in discrete mathematics and optimization. Wiley, LondonGoogle Scholar
  2. Barán B, Schaerer M (2003) A multiobjective ant colony system for vehicle routing problem with time windows. In: 21st IASTED International Multi-Conference on Applied Informatics, Innsbruck, Austria, pp 97–102Google Scholar
  3. Blum C (2005a) Ant colony optimization: introduction and recent trends. Phys Life Rev 2(4):353–373CrossRefGoogle Scholar
  4. Blum C (2005b) Beam–ACO—hybridizing ant colony optimization with beam search: an application to open shop scheduling. Comput Oper Res 32(6):1565–1591CrossRefGoogle Scholar
  5. Blum C, Roli A (2003) Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Comput Surv (CSUR) 35(3):268–308CrossRefGoogle Scholar
  6. Blum C, Bautista J, Pereira J (2006) Beam–ACO applied to assembly line balancing. LNCS 4150:96–107. doi: 10.1007/11839088 Google Scholar
  7. Bui L, Essam D, Abbass H, Green D (2001) Performance analysis of evolutionary multiobjective optimization methods in noisy environments. Tech. Rep. TR-ALAR-200504006, University of New South Wales, AustraliaGoogle Scholar
  8. Camerini P, Galbiati G, Maffioli F (1980) Complexity of spanning tree problems: part I. Eur J Oper Res 5:346–352zbMATHCrossRefMathSciNetGoogle Scholar
  9. Camerini P, Galbiati G, Maffioli F (1983) On the complexity of finding multi-constrained spanning trees. Discret Appl Math 5:39–50zbMATHCrossRefMathSciNetGoogle Scholar
  10. Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, LondonGoogle Scholar
  11. Deb K, Pratap A, Agarwal S, Meyarivan T (2000) A fast elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197CrossRefGoogle Scholar
  12. Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30MathSciNetGoogle Scholar
  13. Dorigo M, Stützle T (2004) Ant colony optimization. MIT Press, CambridgeGoogle Scholar
  14. Dorigo M, Bonabeau E, Theraulaz G (1999) Swarm intelligence: from natural to artificial systems. Oxford University Press, OxfordGoogle Scholar
  15. Ehrgott M, Gandibleux X (2004) Approximative solution methods for multiobjective combinatorial optimization. TOP 12(1):1–63zbMATHCrossRefMathSciNetGoogle Scholar
  16. Gambardella L, Dorigo M (2000) An ant colony system hybridized with a new local search for the sequential ordering problem. INFORMS J Comput 12(3)Google Scholar
  17. Gambardella LM, Taillard E, Agazzi G (1999) Macs-vrptw: a multiple ant colony system for vehicle routing problems with time windows. New ideas in optimization, pp 63–76Google Scholar
  18. García S, Herrera F (2008) Design of experiments in computational intelligence: on the use of statistical inference. In: HAIS ’08: Proceedings of the 3rd international workshop on hybrid artificial intelligence systems. Springer, Berlin, pp 4–14. doi: 10.1007/978-3-540-87656-4_3
  19. García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms behaviour: a case study on the CEC2005 special session on real parameter optimization. J Heuristics 15(6):617–644zbMATHCrossRefGoogle Scholar
  20. García S, Fernandez A, Luengo J, Herrera F (2009) A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability. Soft Comput 13(10):959–977CrossRefGoogle Scholar
  21. García-Martínez C, Cordón O, Herrera F (2004) An empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP. ANTS Workshop, Lecture Notes in Computer Science 3172:61–72Google Scholar
  22. García-Martínez C, Cordón O, Herrera F (2007) A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP. Eur J Oper Res 127(1):116–148CrossRefGoogle Scholar
  23. Garey M, Johnson D (1990) Computers and intractability; a guide to the theory of NP-Completeness. W. Freeman & Co., New YorkGoogle Scholar
  24. Glover F, Laguna M (1997) Tabu search. Kluwer, DordrechtGoogle Scholar
  25. Hamacher H, Ruhe G (1994) On spanning tree problems with multiple objective. Ann Oper Res 52:209–230zbMATHCrossRefMathSciNetGoogle Scholar
  26. Ishibuchi H, Murata T (1998) Multi-objective genetic local search algorithm and its application to flowshop scheduling. IEEE Trans Syst Man Cybern 3(28):392–403Google Scholar
  27. Jaszkiewicz A (2001) Multiple objective metaheuristic algorithms for combinatorial optimization. PhD thesis, Poznan University of TechnologyGoogle Scholar
  28. Jaszkiewicz A (2002) Genetic local search for multiple objective combinatorial optimization. Eur J Oper Res 137:50–71zbMATHCrossRefMathSciNetGoogle Scholar
  29. Jaszkiewicz A (2006) A comparative experiment with multiple objective genetic local search algorithm on multi-objective travelling salesperson problem. http://www-idss.cs.put.poznan.pl/∼jaszkiewicz/motsp
  30. Johnson S (2001) Emergence. The connected lives of ants, brains, cities, and software. ScribnerGoogle Scholar
  31. Kampstra P (2008) Beanplot: a boxplot alternative for visual comparison of distributions. J Stat Softw Code Snippets 28(1):1–9Google Scholar
  32. Kirkpatrick S, Gelatt C, Vecchi M (1983) Optimization by simulated annealing. Science 220(4598):671–680Google Scholar
  33. Knowles J (2002) Local-search and hybrid evolutionary algorithms for pareto optimization. PhD thesis, University of Reading, UKGoogle Scholar
  34. Knowles J, Corne D (2000a) Approximating the nondominated front using the pareto archived evolution strategy. Evol Comput MIT Press 8(22):149–172CrossRefGoogle Scholar
  35. Knowles J, Corne D (2000b) M-PAES: a memetic algorithm for multiobjective optimization. In: Proceedings of the 2000 Congress on evolutionary computation, vol 1. IEEE Press, La Jolla, pp 325–332Google Scholar
  36. Knowles J, Corne D (2001) A comparative assessment of memetic, evolutionary, and constructive algorithms for the multiobjective d-MST problem. In: 2nd Workshop on memetic algorithms, WOMA2001, pp 162–167Google Scholar
  37. Knowles J, Corne D (2002) On metrics for comparing non-dominated sets. In: Congress on evolutionary computation (CEC 2002), vol 1. pp 711–716. doi: 10.1109/CEC.2002.1007013
  38. Levine J, Ducatelle F (2004) Ant colony optimisation and local search for bin packing and cutting stock problems. J Oper Res Soc Special Issue on Local Search 55(7):705–716zbMATHGoogle Scholar
  39. Mann H, Whitney D (1947) On a test of whether one of two random variables is stochastically larger than the other. Ann Math Stat 18:50–60zbMATHCrossRefMathSciNetGoogle Scholar
  40. Middendorf M, Reischle F, Schmeck H (2002) Multi colony ant algorithms. J Heuristics 8:305–320zbMATHCrossRefGoogle Scholar
  41. Miettinen K (1999) Nonlinear multiobjective optimization. Kluwer, DordrechtGoogle Scholar
  42. Murata T (1997) Genetic algortithms for multi-objective optimization. PhD thesis, Osaka Prefecture UniversityGoogle Scholar
  43. Paquete L, Stützle T (2003) A two-phase local search for the biobjective traveling salesman problem. In: Fonseca C, Fleming P, Zitzler E, Deb K, Thiele L (eds) Second International Conference on evolutionary multi-Criterion optimization, EMO 2003, vol 2632. Faro, Portugal, pp 479–493Google Scholar
  44. Paquete L, Stützle T (2006) A study of stochastic local search algorithms for the biobjective QAP with correlated flow matrices. Eur J Oper Res 169(3):943–959zbMATHCrossRefGoogle Scholar
  45. Parmee I (2001) Evolutionary and adaptive computing in engineering design. Springer, London, iSNB:1-85233-029-5Google Scholar
  46. Reimann M, Laumanns M (2004) A hybrid aco algorithm for the capacitated minimum spanning tree problem. In: Blum C, Roli A, Sampels M (eds) First International Workshop on hybrid metaheuristics (HM 2004). Valencia, Spain, pp 1–10Google Scholar
  47. Reimann M, Doerner K, Hartl R (2004) D-ants: savings based ants divide and conquer the vehicle routing problem. Comput Oper Res 31(4):563–591zbMATHCrossRefGoogle Scholar
  48. Romero C (1993) Teorí a de la decisión multicritério: conceptos, técnicas y aplicaciones (in spanish). Alianza Universidad TextosGoogle Scholar
  49. Talbi EG (2002) A taxonomy of hybrid metaheuristics. J Heuristics 8(5):541–564CrossRefGoogle Scholar
  50. Ulungu E, Teghem J, Fortemps P, Tuyttens D (1999) MOSA method: a tool for solving multiobjective combinatorial optimization problems. J Multi-Criteria Decis Anal 8(4):221 – 236zbMATHCrossRefGoogle Scholar
  51. Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications. PhD thesis, Swiss Federal Institute of Technology (ETH), Zurich, SwitzerlandGoogle Scholar
  52. Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans Evol Comput 3(4):257–271CrossRefGoogle Scholar
  53. Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8:173–195CrossRefGoogle Scholar
  54. Zitzler E, Thiele L, Laumanns M, Fonseca C, Fonseca V (2002) Why quality assessment of multiobjective optimizers is difficult. In: Proceedings of the genetic and evolutionary computation conference (GECCO 2002), pp 666–674Google Scholar
  55. Zitzler E, Thiele L, Laumanns M, Fonseca C, Fonseca V (2003) Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans Evol Comput 7(2):117–132CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.University of Algarve, ISEFaroPortugal
  2. 2.University of SevillaSevillaSpain

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