Artificial Intelligence Review

, Volume 45, Issue 1, pp 97–130 | Cite as

Metaheuristic algorithms and probabilistic behaviour: a comprehensive analysis of Ant Colony Optimization and its variants

  • Anandkumar Prakasam
  • Nickolas Savarimuthu


The application of metaheuristic algorithms to combinatorial optimization problems is on the rise and is growing rapidly now than ever before. In this paper the historical context and the conducive environment that accelerated this particular trend of inspiring analogies or metaphors from various natural phenomena are analysed. We have implemented the Ant System Model and the other variants of ACO including the 3-Opt, Max–Min, Elitist and the Rank Based Systems as mentioned in their original works and we converse the missing pieces of Dorigo’s Ant System Model. Extensive analysis of the variants on Travelling Salesman Problem and Job Shop Scheduling Problem shows how much they really contribute towards obtaining better solutions. The stochastic nature of these algorithms has been preserved to the maximum extent to keep the implementations as generic as possible. We observe that stochastic implementations show greater resistance to changes in parameter values, still obtaining near optimal solutions. We report how Polynomial Turing Reduction helps us to solve Job Shop Scheduling Problem without making considerable changes in the implementation of Travelling Salesman Problem, which could be extended to solve other NP-Hard problems. We elaborate on the various parallelization options based on the constraints enforced by strong scaling (fixed size problem) and weak scaling (fixed time problem). Also we elaborate on how probabilistic behaviour helps us to strike a balance between intensification and diversification of the search space.


Ant Colony Optimization Metaheuristics Ant System ACO variants Travelling Salesman Problem Job Shop Scheduling Problem 



The authors would like to acknowledge the infrastructure support provided by the Massively Parallel Programming Laboratory (CUDA Teaching Centre), Department of Computer Applications, National Institute of Technology, Trichy. The authors would like to thank Dr. Hemalatha Thiagarajan, Professor, Department of Mathematics, National Institute of Technology, Trichy for providing valuable insights on the simulation of various probability distribution functions. The authors would also like to thank their fellow researchers Mr.S.Thiruselvan, Mr.P.Arish and Ms.R.Eswari for their valuable suggestions and support.

Supplementary material

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  1. Abidin ZZ, Ngah UK, Arshad MR, Ping OB (2010) A novel y optimization algorithm for swarming application. In: IEEE conference on robotics, automation and mechatronics (RAM), pp 425–428Google Scholar
  2. Amdahl Gene M (1967) Validity of the single processor approach to achieving Large-Scale Computing Capabilities (PDF). AFIPS Conference Proceedings 30: 483–485. doi: 10.1145/1465482.1465560
  3. Apostolopoulos T, Vlachos A (2011) Application of the firefly algorithm for solving the economic emissions load dispatch problem. Int J Comb 2011: Article ID 523806Google Scholar
  4. Barricelli NA (1954) Esempi numerici di processi di evoluzione. Methodos 6:45–68MathSciNetGoogle Scholar
  5. Barricelli NA (1957) Symbiognetic evolution processes realized by artificial methods. Methodos 9:143–182Google Scholar
  6. Beni G, Wang J (1989) Swarm intelligence in cellular robotic systems. In: Proceedings of NATO advanced workshop on robots and biological systems. Tuscany, ItalyGoogle Scholar
  7. Bottou Lon (1998) Online algorithms and stochastic approximations. Online Learning and Neural Networks. Cambridge University Press. ISBN 978-0-521-65263-6Google Scholar
  8. Bullnheimer B, Richard F, Hartl, Strau C (1997) A new rank based version of the ant system: a computational study. Working Paper No. 1Google Scholar
  9. Coelho L, Bernert DL, Mariani VC (2011) A chaotic firefly algorithm applied to reliability-redundancy optimization. In: 2011 IEEE congress on evolutionary computation (CEC’11), pp 517–521Google Scholar
  10. Colorni A, Dorigo M, Maniezzo V (1991) Distributed optimization by ant colonies. In: ECAL91—European conference on artificial life, pp 134–142Google Scholar
  11. Denebourg JL, Goss S (1989) Collective patterns and decision-making. Ethol Ecol Evol 1(4):295–311CrossRefGoogle Scholar
  12. Deneubourg J-L, Pasteels JM, Verhaeghe JC (1983) Probabilistic behaviour in ants: a strategy of errors. J Theoret Biol 105(2):259–271CrossRefGoogle Scholar
  13. Dorigo M, Gambardella LM (1997b) Ant colonies for the traveling salesman problem. BioSystems 43(2):73–81CrossRefGoogle Scholar
  14. Dorigo M, Gambardella LM (1997a) Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans Evol Comput 1(1):53–66CrossRefGoogle Scholar
  15. Dorigo M, Maniezzo V, Colorni A (1991) The ant system: an autocatalytic optimizing process. In: No. 91-016. Technical reportGoogle Scholar
  16. Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on 26(1):29–41CrossRefGoogle Scholar
  17. Finilla AB, Gomez MA, Sebenik C, Doll DJ (1994) Quantum annealing: a new method for minimizing multidimensional functions. Chem Phys Lett 219:343CrossRefGoogle Scholar
  18. Fraser AS (1960) Simulation of genetic systems by automatic digital computers vi. epistasis. Aust J Biol Sci 13(2):150–162Google Scholar
  19. Glover F (1977) Heuristics for integer programming, using surrogate constraints. Decis Sci 8(1):156–166CrossRefGoogle Scholar
  20. Glover F (1986) Future paths for integer programming and links to artificial intelligence. Comput Operat Res 13(5):533549. doi: 10.1016/0305-0548(86)90048-1 MathSciNetGoogle Scholar
  21. Glover F (1989) Tabu search-part I. ORSA J Comput 1(3):190zbMATHCrossRefGoogle Scholar
  22. Goldberg DE (1991) The theory of virtual alphabets-parallel problem solving from nature. Springer, BerlinGoogle Scholar
  23. Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Mach Learn 32:95–99CrossRefGoogle Scholar
  24. Green DG, Liu J, Abbass H (2014) Dual phase evolution: from theory to practice. Springer, Berlin ISBN 978-1441984227CrossRefGoogle Scholar
  25. Gupta DK, Arora Y, Singh UK, Gupta JP (2012) Recursive Ant Colony Optimization for estimation of parameters of a function. In: Recent advances in Information Technology (RAIT), International conference. doi: 10.1109/RAIT.2012.6194620, pp 448–454
  26. Gustafson JL (1988) Reevaluating Amdahl’s Law. Commun ACM 31(5):532–533CrossRefGoogle Scholar
  27. Gutjahr WJ (2000) A graph-based Ant System and its convergence. Future Gener Comput Syst 16:873–888CrossRefGoogle Scholar
  28. Haddad OB, Afshar A, Marino AB (2006) Honey-bees mating optimization (HBMO) algorithm: a new heuristic approach for water resources optimization. Water Resour Manag 20(5):661–680CrossRefGoogle Scholar
  29. Hedayatzadeh R, Salmassi F, Keshtgari M, Akbari R, Ziarati K (2010) Termite colony optimization: a novel approach for optimizing continuous problems. In: 18th Iranian conference on electrical engineering (ICEE), pp 553–558Google Scholar
  30. Heppner F, Grenander U, Krasner S (1990) A stochastic nonlinear model for coordinated bird flocks. In: The Ubiquity of Chaos. AAAS Publications, Washington, DCGoogle Scholar
  31. Holland JH (1975) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. University of Michigan Press, MichiganGoogle Scholar
  32., 2000. Visited in (January 2003)
  33. James K, Eberhart R (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, vol 4(2)Google Scholar
  34. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. In: Technical Report TR06, Erciyes University Press, ErciyesGoogle Scholar
  35. Karaboga D (2010) Artificial bee colony algorithm. Scholarpedia 5(3):6915. doi: 10.4249/scholarpedia.6915 CrossRefGoogle Scholar
  36. Kennedy J, Eberhart R (1995) Particle Swarm Optimization. Proceedings of IEEE International Conference on Neural Networks IV. doi: 10.1109/ICNN.1995.488968
  37. Kirkpatrick S, Gelattr SD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671zbMATHMathSciNetCrossRefGoogle Scholar
  38. Krishnanand KN, Ghose D (2005) Detection of multiple source locations using a glowworm metaphor with applications to collective robotics. In: IEEE Swarm intelligence symposium, pp 84–91Google Scholar
  39. Laarhoven PJM, Aarts EHL (1987) Simulated annealing: theory and applications. Springer, BerlinzbMATHCrossRefGoogle Scholar
  40. Lukasik S, Zak S (2009) Firefly algorithm for continuous constrained optimization tasks. Computational collective intelligence. In: Semantic Web, Social networks and multi-agent systems, pp 97–106Google Scholar
  41. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21(6):1087CrossRefGoogle Scholar
  42. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey Wolf Optimizer. Adv Eng Softw 69:46–61CrossRefGoogle Scholar
  43. Mirjalili S (2015) The Ant Lion optimizer. Adv Eng Softw 83:8098CrossRefGoogle Scholar
  44. Nakrani S, Tovey C (2004) On honey bees and dynamic server allocation in internet hosting centers. Adapt Behav 12(3–4):223240Google Scholar
  45. Niu B (2012) Bacterial colony optimization. Dis Dyn Nat Soc. Article ID 698057Google Scholar
  46. Osman IH, Laporte G (1996) Metaheuristics: a bibliography. Ann Operat Res 63(513):623MathSciNetGoogle Scholar
  47. Pan WT (2011) A new fruitfly optimization algorithm: taking the financial distress model as an example. Knowl Based Syst 26:69–74CrossRefGoogle Scholar
  48. Rampriya B, Mahadevan K, Kannan S (2010) Unit commitment in deregulated power system using Lagrangian firefly algorithm. In: Proceedings of IEEE international conference on communication control and computing technologies (ICCCCT), pp 389–393Google Scholar
  49. Reynolds CW (1987) Flocks, herds and schools: a distributed behavioral model. Comput Graph 21(4):25–34CrossRefGoogle Scholar
  50. Rosengren R (1971) Route fidelity, visual memory and recruitment behaviour in foraging wood ants of the genus Formica (Hymenoptera, Formicidae). Acta Zool Fenn 133:1–106Google Scholar
  51. Sayadi MK, Ramezanian R, Ghaffari-Nasab N (2010) A discrete firefly meta-heuristic with local search for makespan minimization in permutation flow shop scheduling problems. Int J Ind Eng Comput 1:110Google Scholar
  52. Schmidt G (2000) Scheduling with limited machine availability. Eur J Oper Res 121(1):1–15zbMATHCrossRefGoogle Scholar
  53. Shi Y, Eberhart R (1998) A modified particle swarm optimizer. Evolutionary computation proceedings. In: IEEE World congress on computational intelligence, the 1998 IEEE international conference on IEEEGoogle Scholar
  54. Snyder L (1986) Type architectures, shared memory, and the corollary of modest potential. Ann Rev Comput Sci 1:289–317CrossRefGoogle Scholar
  55. Sorensen K (2012) Metaheuristics the metaphor exposed. In: International transactions of operations research. Pub Online: Feb 08, 2013. doi: 10.1111/itor.12001 (p)
  56. Sorin CN, Oprean C, Kifor CV, Carabulea I (2008) Elitist ant system for route allocation problem. In: World scientific and engineering academy and society (WSEAS) Stevens Point, Wisconsin, USAGoogle Scholar
  57. Sttzle T, Hoos HH (2000) Max Min Ant System. Future Gener Comput Syst 16:889–914CrossRefGoogle Scholar
  58. Talreja S (2013) A heuristic proposal in the dimension of Ant colony Optimization. Appl Math Sci 7(41):2017–2026MathSciNetGoogle Scholar
  59. Whitley D (1994) A genetic algorithm tutorial. Stat Comput 4(2):6585. doi: 10.1007/BF00175354
  60. Xiao-Min H, Zhang J, Li Y (2008) Orthogonal methods based Ant Colony search for solving continuous optimization problems. J Comput Sci Technol 23(1):2–18CrossRefGoogle Scholar
  61. Yang XS (2008) Nature-inspired metaheuristic algorithms. Frome. In: Luniver Press. ISBN 1-905986-10-6Google Scholar
  62. Yang XS (2010) A new metaheuristic bat-inspired algorithm. In: Gonzalez JR et al (eds) Nature inspired cooperative strategies for optimization (NISCO 2010), Studies in computational intelligence, vol 284. Springer, Berlin, pp 65–74CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Computer ApplicationsNational Institute of TechnologyTiruchirappalliIndia

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