Skip to main content
SpringerLink
Log in
Book cover

Handbook of Metaheuristics pp 227–263Cite as

Ant Colony Optimization: Overview and Recent Advances

  • Chapter
  • First Online:

  • 13k Accesses

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 146))

Abstract

Ant Colony Optimization (ACO) is a metaheuristic that is inspired by the pheromone trail laying and following behavior of some ant species. Artificial ants in ACO are stochastic solution construction procedures that build candidate solutions for the problem instance under concern by exploiting (artificial) pheromone information that is adapted based on the ants’ search experience and possibly available heuristic information. Since the proposal of the Ant System, the first ACO algorithm, many significant research results have been obtained. These contributions focused on the development of high-performing algorithmic variants, the development of a generic algorithmic framework for ACO algorithms, successful applications of ACO algorithms to a wide range of computationally hard problems, and the theoretical understanding of properties of ACO algorithms. This chapter reviews these developments and gives an overview of recent research trends in ACO.

This is a preview of subscription content, log in via an institution.

Notes

  1. 1.

    Other approximate methods are also conceivable. For example, when stopping exact methods, like Branch & Bound, before completion [10, 95] (for example, after some given time bound, or when some guarantee on the solution quality is obtained through the use of lower and upper bounds), we can convert exact algorithms into approximate ones.

  2. 2.

    The adaptation to maximization problems is straightforward.

  3. 3.

    Static problems are those whose topology and costs do not change while they are being solved. This is the case, for example, for the classic TSP , in which city locations and intercity distances do not change during the algorithm’s runtime. In contrast, in dynamic problems the topology and costs can change while solutions are built. An example of such a problem is routing in telecommunications networks [47], in which traffic patterns change all the time.

  4. 4.

    The experiment described was originally executed using a laboratory colony of Argentine ants (Iridomyrmex humilis). It is known that these ants deposit pheromone both when leaving and when returning to the nest [80].

  5. 5.

    In the ACO literature, this is often called differential path length effect.

  6. 6.

    A process like this, in which a decision taken at time t increases the probability of making the same decision at time \(T>t\) is said to be an autocatalytic process. Autocatalytic processes exploit positive feedback.

  7. 7.

    Note that when applied to symmetric TSPs the edges are considered to be bidirectional and edges \((i,j)\) and \((j,i)\) are both updated. This is different for the ATSP, where edges are directed; in this case an ant crossing edge \((i,j)\) will update only this edge and not edge \((j,i)\).

  8. 8.

    ACS was an offspring of Ant-Q [74], an algorithm intended to create a link between reinforcement learning [149] and Ant Colony Optimization. Computational experiments have shown that some aspects of Ant-Q, in particular the pheromone update rule, could be strongly simplified without affecting performance. It is for this reason that Ant-Q was abandoned in favor of the simpler and equally good ACS.

  9. 9.

    The maximum time for the largest instances was 20 min on a 450 MHz Pentium III PC with 256 MB RAM. Programs were written in C++ and the PC was run under Red Hat Linux 6.1.

  10. 10.

    There have been several proposals of ant-inspired algorithms for continuous optimization [15, 67, 116]. However, these differ strongly from the underlying ideas of ACO (for example, they use direct communication among ants) and therefore cannot be considered as algorithms falling into the framework of the ACO metaheuristic.

References

  1. Acan, A.: An external memory implementation in ant colony optimization. In: Dorigo, M., Birattari, M., Blum, C., Gambardella, L.M., Mondada, F., Stützle, T. (eds.) Ant Colony Optimization and Swarm Intelligence: 4th International Workshop, ANTS 2004. Lecture Notes in Computer Science, vol. 3172, pp. 73–84. Springer, Berlin (2004)

    Google Scholar 

  2. Acan, A.: An external partial permutations memory for ant colony optimization. In: Raidl, G., Gottlieb, J. (eds.) Evolutionary Computation in Combinatorial Optimization. Lecture Notes in Computer Science, vol. 3448, pp. 1–11. Springer, Berlin (2005)

    Google Scholar 

  3. Alaya, I., Solnon, C., Ghédira, K.: Ant colony optimization for multi-objective optimization problems. In: 19th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2007), vol. 1, pp. 450–457. IEEE Computer Society, Los Alamitos, CA (2007)

    Google Scholar 

  4. Alexandrov, D.A., Kochetov, Y.A.: The behavior of the ant colony algorithm for the set covering problem. In: Inderfurth, K., Schwödiauer, G., Domschke, W., Juhnke, F., Kleinschmidt, P., Wäscher, G. (eds.) Operations Research Proceedings 1999, pp. 255–260. Springer, Berlin (2000)

    Google Scholar 

  5. Angus, D., Woodward, C.: Multiple objective ant colony optimization. Swarm Intell. 3(1), 69–85 (2009)

    Google Scholar 

  6. Applegate, D., Bixby, R.E., Chvátal, V., Cook, W.J.: The Traveling Salesman Problem: A Computational Study. Princeton University Press, Princeton, NJ (2006)

    Google Scholar 

  7. Balaprakash, P., Birattari, M., Stützle, T., Yuan, Z., Dorigo, M.: Estimation-based ant colony optimization algorithms for the probabilistic travelling salesman problem. Swarm Intell., 3(3), 223–242 (2009)

    Google Scholar 

  8. Bauer, A., Bullnheimer, B., Hartl, R.F., Strauss, C.: An ant colony optimization approach for the single machine total tardiness problem. In: Proceedings of the 1999 Congress on Evolutionary Computation (CEC’99), pp. 1445–1450. IEEE Press, Piscataway, NJ (1999)

    Google Scholar 

  9. Beckers, R., Deneubourg, J.-L., Goss, S.: Modulation of trail laying in the ant Lasius niger (hymenoptera: Formicidae) and its role in the collective selection of a food source. J. Insect Behav. 6(6), 751–759 (1993)

    Google Scholar 

  10. Bellman, R., Esogbue, A.O., Nabeshima, I.: Mathematical Aspects of Scheduling and Applications. Pergamon Press, New York, NY (1982)

    Google Scholar 

  11. Benedettini, S., Roli, A., Di Gaspero, L.: Two-level ACO for haplotype inference under pure parsimony. In: Dorigo, M., Birattari, M., Blum, C., Clerc, M., Stützle, T., Winfield, A. F. T. (eds.) Ant Colony Optimization and Swarm Intelligence, 6th International Workshop, ANTS 2008. Lecture Notes in Computer Science, vol. 5217, pp. 179–190. Springer, Berlin (2008)

    Google Scholar 

  12. Bertsekas, D.: Network Optimization: Continuous and Discrete Models. Athena Scientific, Belmont, MA (1998)

    Google Scholar 

  13. Bianchi, L., Birattari, M., Manfrin, M., Mastrolilli M., Paquete, L., Rossi-Doria, O., Schiavinotto, T.: Hybrid metaheuristics for the vehicle routing problem with stochastic demands. J. Math. Model. Algorithms 5(1), 91–110 (2006)

    Google Scholar 

  14. Bianchi, L., Gambardella, L.M., Dorigo, M.: An ant colony optimization approach to the probabilistic traveling salesman problem. In: Merelo Guervós, J.J., Adamidis, P., Beyer, H.-G., Fernández-Villacanas, J.-L., Schwefel, H.-P. (eds.) Parallel Problem Solving from Nature – PPSN VII: 7th International Conference, Lecture Notes in Computer Science, vol. 2439, pp. 883–892. Springer, Berlin (2002)

    Google Scholar 

  15. Bilchev, G., Parmee, I.C.: The ant colony metaphor for searching continuous design spaces. In: Fogarty, T.C. (ed.) Evolutionary Computing, AISB Workshop, Lecture Notes in Computer Science, vol. 993, pp. 25–39. Springer, Berlin (1995)

    Google Scholar 

  16. Birattari, M., Di Caro, G., Dorigo, M.: Toward the formal foundation of ant programming. In: Dorigo, M., Di Caro, G., Sampels, M. (eds.) Ant Algorithms: Third International Workshop, ANTS 2002, Lecture Notes in Computer Science, vol. 2463, pp. 188–201. Springer, Berlin (2002)

    Google Scholar 

  17. Blum, C.: Theoretical and Practical Aspects of Ant Colony Optimization. PhD Thesis, IRIDIA, Université Libre de Bruxelles, Brussels, Belgium, 2004

    Google Scholar 

  18. Blum, C.: Beam-ACO–-Hybridizing ant colony optimization with beam search: An application to open shop scheduling. Comput. Oper. Res. 32(6), 1565–1591 (2005)

    Google Scholar 

  19. Blum, C.: Beam-ACO for simple assembly line balancing. INFORMS J. Comput. 20(4), 618–627 (2008)

    Google Scholar 

  20. Blum, C., Blesa, M. J.: New metaheuristic approaches for the edge-weighted k-cardinality tree problem. Comput. Oper. Res. 32(6), 1355–1377 (2005)

    Google Scholar 

  21. Blum, C., Dorigo, M.: The hyper-cube framework for ant colony optimization. IEEE Trans. Syst. Man Cybern. – Part B 34(2), 1161–1172 (2004)

    Google Scholar 

  22. Blum, C., Dorigo, M.: Search bias in ant colony optimization: on the role of competition-balanced systems. IEEE Trans. Evol. Comput. 9(2), 159–174 (2005)

    Google Scholar 

  23. Blum, C., Sampels, M.: Ant colony optimization for FOP shop scheduling: a case study on different pheromone representations. In: Proceedings of the 2002 Congress on Evolutionary Computation (CEC’02), pp. 1558–1563. IEEE Press, Piscataway, NJ, 2002

    Google Scholar 

  24. Blum, C., Sampels, M., Zlochin, M.: On a particularity in model-based search. In: Langdon, W.B. et al. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2002), pp. 35–42. Morgan Kaufmann, San Francisco, CA (2002)

    Google Scholar 

  25. Blum, C., Yabar, M., Blesa, M.J.: An ant colony optimization algorithm for DNA sequencing by hybridization. Comput. Oper. Res. 35(11), 3620–3635 (2008)

    Google Scholar 

  26. Boese, K.D., Kahng, A.B., Muddu, S.: A new adaptive multi-start technique for combinatorial global optimization. Oper. Res. Lett. 16, 101–113 (1994)

    Google Scholar 

  27. Bolondi, M., Bondanza, M.: Parallelizzazione di un algoritmo per la risoluzione del problema del commesso viaggiatore. Master’s thesis, Dipartimento di Elettronica, Politecnico di Milano, Italy, 1993

    Google Scholar 

  28. Brailsford, S.C., Gutjahr, W.J., Rauner, M.S., Zeppelzauer, W.: Combined discrete-event simulation and ant colony optimisation approach for selecting optimal screening policies for diabetic retinopathy. Comput. Manage. Sci. 4(1), 59–83 (2006)

    Google Scholar 

  29. Bullnheimer, B., Hartl, R.F., Strauss, C.: A new rank based version of the ant system–-a computational study. Technical Report, Institute of Management Science, University of Vienna, 1997

    Google Scholar 

  30. Bullnheimer, B., Hartl, R.F., Strauss, C.: A new rank-based version of the ant system: A computational study. Cent. Eur. J. Oper. Res. Econ. 7(1), 25–38 (1999)

    Google Scholar 

  31. Bullnheimer, B., Kotsis, G., Strauss, C.: Parallelization strategies for the ant system. In: De Leone, R., Murli, A., Pardalos, P., Toraldo, G. (eds.) High Performance Algorithms and Software in Nonlinear Optimization. Kluwer Series of Applied Optmization, vol. 24 pp. 87–100. Kluwer, The Netherlands (1998)

    Google Scholar 

  32. Cantú-Paz, E.: Efficient and Accurate Parallel Genetic Algorithms. Kluwer, Boston, MA (2000)

    Google Scholar 

  33. Chen, L., Zhang, C.: Adaptive parallel ant colony algorithm. In: Advances in Natural Computation, First International Conference, ICNC 2005. Lecture Notes in Computer Science, vol. 3611, pp. 1239–1249. Springer, Berlin (2005)

    Google Scholar 

  34. Colorni, A., Dorigo, M., Maniezzo, V.: Distributed optimization by ant colonies. In: Varela, F.J., Bourgine, P. (eds.) Proceedings of the First European Conference on Artificial Life, pp. 134–142. MIT Press, Cambridge, MA (1992)

    Google Scholar 

  35. Colorni, A., Dorigo, M., Maniezzo, V.: An investigation of some properties of an ant algorithm. In: Männer, R., Manderick, B. (eds.) Parallel Problem Solving from Nature – PPSN II, pp. 509–520. North-Holland, Amsterdam, The Netherlands (1992)

    Google Scholar 

  36. Cordón, O., Fernández de Viana, I., Herrera, F.: Analysis of the best-worst Ant System and its variants on the TSP. Math. Soft Comput. 9(2–3), 177–192 (2002)

    Google Scholar 

  37. Cordón, O., Fernández de Viana, I., Herrera, F., Moreno, L.: A new ACO model integrating evolutionary computation concepts: The best-worst Ant System. In: Dorigo, M., Middendorf, M., Stützle, T. (eds.) Abstract proceedings of ANTS 2000 – From Ant Colonies to Artificial Ants: Second International Workshop on Ant Algorithms, pp. 22–29. IRIDIA, Université Libre de Bruxelles, Brussels, Belgium (2000)

    Google Scholar 

  38. Cordón, O., Herrera, F., Stützle, T.: Special issue on ant colony optimization: models and applications. Mathw. Soft Comput. 9(2–3), 137–268 (2003)

    Google Scholar 

  39. Costa, D., Hertz, A.: Ants can colour graphs. J. Oper. Res. Soc. 48, 295–305 (1997)

    Google Scholar 

  40. de Campos, L.M., Fernández-Luna, J.M., Gámez, J.A., Puerta, J.M.: Ant colony optimization for learning Bayesian networks. Int. J. Approx. Reasoning 31(3), 291–311 (2002)

    Google Scholar 

  41. de Campos, L.M., Gamez, J.A., Puerta, J.M.: Learning Bayesian networks by ant colony optimisation: searching in the space of orderings. Mathw. Soft Comput. 9(2–3), 251–268 (2002)

    Google Scholar 

  42. den Besten, M.L., Stützle, T., Dorigo, M.: Ant colony optimization for the total weighted tardiness problem. In: Schoenauer, M., Deb, K., Rudolph, G., Yao, X., Lutton, E., Merelo, J.J., Schwefel, H.-P. (eds.) Proceedings of PPSN-VI, Sixth International Conference on Parallel Problem Solving from Nature. Lecture Notes in Computer Science, vol. 1917, pp. 611–620. Springer, Berlin (2000)

    Google Scholar 

  43. Deneubourg, J.-L., Aron, S., Goss, S., Pasteels, J.-M.: The self-organizing exploratory pattern of the Argentine ant. J. Insect Behav. 3, 159–168 (1990)

    Google Scholar 

  44. Di Caro, G.: Ant Colony Optimization and its application to adaptive routing in telecommunication networks. PhD thesis, IRIDIA, Université Libre de Bruxelles, Brussels, Belgium, 2004

    Google Scholar 

  45. Di Caro, G., Dorigo, M.: AntNet: a mobile agents approach to adaptive routing. Technical Report IRIDIA/97-12, IRIDIA, Université Libre de Bruxelles, Brussels, Belgium, 1997

    Google Scholar 

  46. Di Caro, G., Dorigo, M.: Ant colonies for adaptive routing in packet-switched communications networks. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) Proceedings of PPSN-V, Fifth International Conference on Parallel Problem Solving from Nature. Lecture Notes in Computer Science, vol. 1498, pp. 673–682. Springer, Berlin (1998)

    Google Scholar 

  47. Di Caro, G., Dorigo, M.: AntNet: distributed stigmergetic control for communications networks. J. Artif. Intell. Res. 9, 317–365 (1998)

    Google Scholar 

  48. Di Caro, G., Dorigo, M.: Mobile agents for adaptive routing. In: El-Rewini, H. (ed.) Proceedings of the 31st International Conference on System Sciences (HICSS-31), pp. 74–83. IEEE Computer Society Press, Los Alamitos, CA (1998)

    Google Scholar 

  49. Di Caro, G., Ducatelle, F., Gambardella, L.M.: AntHocNet: an adaptive nature-inspired algorithm for routing in mobile ad hoc networks. Eur. Trans. Telecomm. 16(5), 443–455 (2005)

    Google Scholar 

  50. Doerner, K.F., Hartl, R.F., Benkner, S., Lucka, M.: Parallel cooperative saving based ant colony optimization - multiple search and decomposition approaches. Parallel Process. Lett. 16(3), 351–369 (2006)

    Google Scholar 

  51. Doerner, K.F., Hartl, R.F., Reimann, M.: Are CompetAnts more competent for problem solving? The case of a multiple objective transportation problem. Cent. Eur. J. Oper. Res. Econ. 11(2), 115–141 (2003)

    Google Scholar 

  52. Doerner, K.F., Merkle, D., Stützle, T.: Special issue on ant colony optimization. Swarm Intell. 3(1), 1–85 (2009)

    Google Scholar 

  53. Doerr, B., Neumann, F., Sudholt, D., Witt, C.: On the runtime analysis of the 1-ANT ACO algorithm. In: Genetic and Evolutionary Computation Conference, GECCO 2007, Proceedings, pp. 33–40. ACM press, New York, NY (2007)

    Google Scholar 

  54. Donati, A.V., Montemanni, R., Casagrande, N., Rizzoli, A.E., Gambardella, L.M.: Time dependent vehicle routing problem with a multi ant colony system. Euro. J. Oper. Res. 185(3), 1174–1191 (2008)

    Google Scholar 

  55. Dorigo, M.: Optimization, learning and natural algorithms (in Italian). PhD thesis, Dipartimento di Elettronica, Politecnico di Milano, Italy, 1992

    Google Scholar 

  56. Dorigo, M., Blum, C.: Ant colony optimization theory: a survey. Theor. Comput. Sci. 344(2–3), 243–278 (2005)

    Google Scholar 

  57. Dorigo, M., Di Caro, G.: The ant colony optimization meta-heuristic. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, pp. 11–32. McGraw Hill, London, UK (1999)

    Google Scholar 

  58. Dorigo, M., Di Caro, G., Stützle T. (eds.): Special issue on “Ant Algorithms”. Future Gen. Comput. Syst. 16(8), 851–946 (2000)

    Google Scholar 

  59. Dorigo, M., Di Caro, G., Gambardella, L. M. Ant algorithms for discrete optimization. Artif. Life 5(2), 137–172 (1999)

    Google Scholar 

  60. Dorigo, M., Gambardella, L.M.: Ant colonies for the traveling salesman problem. BioSystems 43, 73–81 (1997)

    Google Scholar 

  61. Dorigo, M., Gambardella, L.M.: Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans. Evol. Comput. 1(1), 53–66 (1997)

    Google Scholar 

  62. Dorigo, M., Gambardella, L.M., Middendorf, M., Stützle, T. (eds.): Special section on “Ant Colony Optimization”. IEEE Trans. Evol. Comput. 6(4), 317–365 (2002)

    Google Scholar 

  63. Dorigo, M., Maniezzo, V., Colorni, A.: The ant system: an autocatalytic optimizing process. Technical Report 91-016 Revised, Dipartimento di Elettronica, Politecnico di Milano, Italy, 1991

    Google Scholar 

  64. Dorigo, M., Maniezzo, V., Colorni, A.: Positive feedback as a search strategy. Technical Report 91-016, Dipartimento di Elettronica, Politecnico di Milano, Italy, 1991

    Google Scholar 

  65. Dorigo, M., Maniezzo, V., Colorni, A.: Ant system: optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. – Part B 26(1), 29–41 (1996)

    Google Scholar 

  66. Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Cambridge, MA (2004)

    Google Scholar 

  67. Dréo, J., Siarry, P.: Continuous interacting ant colony algorithm based on dense heterarchy. Future Gen. Comput. Syst. 20(5), 841–856 (2004)

    Google Scholar 

  68. Ducatelle, F., Di Caro, G., Gambardella, L.M.: Using ant agents to combine reactive and proactive strategies for routing in mobile ad hoc networks. Int. J. Comput. Intell. Appl. 5(2), 169–184 (2005)

    Google Scholar 

  69. Ducatelle, F., Di Caro, G., Gambardella, L.M.: Principles and applications of swarm intelligence for adaptive routing in telecommunications networks. Swarm Intell. (2009)

    Google Scholar 

  70. Eyckelhof, C.J., Snoek, M.: Ant systems for a dynamic TSP: ants caught in a traffic jam. In: Dorigo, M., Di Caro, G., Sampels, M. (eds.) Ant Algorithms: Third International Workshop, ANTS 2002. Lecture Notes in Computer Science, vol. 2463 pp. 88–99. Springer, Berlin (2002)

    Google Scholar 

  71. Farooq, M., Di Caro, G.: Routing protocols for next-generation intelligent networks inspired by collective behaviors of insect societies. In: Blum, C., Merkle, D. (eds.) Swarm Intelligence: Introduction and Applications, Natural Computing Series, pp. 101–160. Springer, Berlin (2008)

    Google Scholar 

  72. Favaretto, D., Moretti, E., Pellegrini, P.: Ant colony system for a VRP with multiple time windows and multiple visits. J. Interdiscip. Math. 10(2), 263–284 (2007)

    Google Scholar 

  73. Fuellerer, G., Doerner, K.F., Hartl, R.F., Iori, M.: Ant colony optimization for the two-dimensional loading vehicle routing problem. Comput. Oper. Res. 36(3), 655–673 (2009)

    Google Scholar 

  74. Gambardella, L.M., Dorigo, M.: Ant-Q: a reinforcement learning approach to the traveling salesman problem. In: Prieditis, A., Russell, S. (eds.) Proceedings of the Twelfth International Conference on Machine Learning (ML-95), pp. 252–260. Morgan Kaufmann Publishers, Palo Alto, CA (1995)

    Google Scholar 

  75. Gambardella, L.M., Dorigo, M.: Solving symmetric and asymmetric TSPs by ant colonies. In: Proceedings of the 1996 IEEE International Conference on Evolutionary Computation (ICEC’96), pp. 622–627. IEEE Press, Piscataway, NJ (1996)

    Google Scholar 

  76. Gambardella, L.M., Dorigo, M.: Ant colony system hybridized with a new local search for the sequential ordering problem. INFORMS J. Comput. 12(3), 237–255 (2000)

    Google Scholar 

  77. Gambardella, L.M., Taillard, é.D., Agazzi, G. MACS-VRPTW: a multiple ant colony system for vehicle routing problems with time windows. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, pp. 63–76. McGraw Hill, London, UK (1999)

    Google Scholar 

  78. García-Martínez, C., Cordón, O., Herrera, F.: A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP. Euro. J. Oper. Res. 180(1), 116–148 (2007)

    Google Scholar 

  79. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of \({\cal N\!\!\!P}\)-Completeness. Freeman, San Francisco, CA (1979)

    Google Scholar 

  80. Goss, S., Aron, S., Deneubourg, J.L., Pasteels, J.M.: Self-organized shortcuts in the Argentine ant. Naturwissenschaften 76, 579–581 (1989)

    Google Scholar 

  81. Guntsch, M., Middendorf, M.: Pheromone modification strategies for ant algorithms applied to dynamic TSP. In: Boers, E.J.W., Gottlieb, J., Lanzi, P.L., Smith, R.E., Cagnoni, S., Hart, E., Raidl, G.R., Tijink, H. (eds.) Applications of Evolutionary Computing: Proceedings of EvoWorkshops 2001, Lecture Notes in Computer Science, vol. 2037, pp. 213–222. Springer, Berlin (2001)

    Google Scholar 

  82. Guntsch, M., Middendorf, M.: A population based approach for ACO. In: Cagnoni, S., Gottlieb, J., Hart, E., Middendorf, M., Raidl, G. R. editors, Applications of Evolutionary Computing, Proceedings of EvoWorkshops2002: EvoCOP, EvoIASP, EvoSTim. Lecture Notes in Computer Science, vol. 2279, pp. 71–80. Springer, Berlin (2002)

    Google Scholar 

  83. Gutjahr, W.J.: A graph-based ant system and its convergence. Future Gen. Comput. Syst. 16(8), 873–888 (2000)

    Google Scholar 

  84. Gutjahr, W.J.: ACO algorithms with guaranteed convergence to the optimal solution. Inf. Process. Lett. 82(3), 145–153 (2002)

    Google Scholar 

  85. Gutjahr, W.J.: S-ACO: an ant-based approach to combinatorial optimization under uncertainty. In: Dorigo, M., Gambardella, L., Mondada, F., Stützle, T., Birratari, M., Blum, C. (eds.) Ant Colony Optimization and Swarm Intelligence: 4th International Workshop, ANTS 2004. Lecture Notes in Computer Science, vol. 3172, pp. 238–249. Springer, Berlin (2004)

    Google Scholar 

  86. Gutjahr, W.J.: On the finite-time dynamics of ant colony optimization. Methodol. Comput. Appl. Probability 8(1), 105–133 (2006)

    Google Scholar 

  87. Gutjahr, W.J.: Mathematical runtime analysis of ACO algorithms: survey on an emerging issue. Swarm Intell. 1(1), 59–79 (2007)

    Google Scholar 

  88. Gutjahr, W.J.: First steps to the runtime complexity analysis of ant colony optimization. Comput. OR 35(9), 2711–2727 (2008)

    Google Scholar 

  89. Gutjahr, W.J., Sebastiani, G.: Runtime analysis of ant colony optimization with best-so-far reinforcement. Methodol. Comput. Appl. Probability 10, 409–433 (2008)

    Google Scholar 

  90. Hadji, R., Rahoual, M., Talbi, E., Bachelet, V.: Ant colonies for the set covering problem. In: Dorigo, M., Middendorf, M., Stützle, T. (eds.) Abstract proceedings of ANTS 2000 – From Ant Colonies to Artificial Ants: Second International Workshop on Ant Algorithms, pp. 63–66. Université Libre de Bruxelles, Brussels, Belgium (2000)

    Google Scholar 

  91. Hernández, H., Blum, C.: Ant colony optimization for multicasting in static wireless ad-hoc networks. Swarm Intell. 3(2), 125–148 (2009)

    Google Scholar 

  92. López Ibáñez, M., Paquete, L., Stützle, T.: On the design of ACO for the biobjective quadratic assignment problem. In: Dorigo, M., Gambardella, L., Mondada, F., Stützle, T., Birratari, M., Blum, C. (eds.) ANTS’2004, Fourth International Workshop on Ant Algorithms and Swarm Intelligence, Lecture Notes in Computer Science, vol. 3172, pp. 214–225. Springer, Berlin (2004)

    Google Scholar 

  93. Iredi, S., Merkle, D., Middendorf, M.: Bi-criterion optimization with multi colony ant algorithms. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D. (eds.) First International Conference on Evolutionary Multi-Criterion Optimization, (EMO’01). Lecture Notes in Computer Science, vol. 1993, pp. 359–372. Springer, Berlin (2001)

    Google Scholar 

  94. Johnson, D.S., McGeoch, L.A.: The travelling salesman problem: a case study in local optimization. In: Aarts, E.H.L., Lenstra, J.K. (eds.) Local Search in Combinatorial Optimization, pp. 215–310. Wiley, Chichester, UK (1997)

    Google Scholar 

  95. Jünger, M., Reinelt, G., Thienel, S.: Provably good solutions for the traveling salesman problem. Zeitschrift für Oper. Res. 40, 183–217 (1994)

    Google Scholar 

  96. Khichane, M., Albert, P., Solnon, C.: Integration of ACO in a constraint programming language. In: Dorigo, M., Birattari, M., Blum, C., Clerc, M., Stützle, T., Winfield, A.F.T. (eds.) Ant Colony Optimization and Swarm Intelligence, 6th International Conference, ANTS 2008. Lecture Notes in Computer Science, vol. 5217, pp. 84–95. Springer, Berlin (2008)

    Google Scholar 

  97. Korb, O., Stützle, T., Exner, T.E.: Application of ant colony optimization to structure-based drug design. In: Dorigo, M., Birattari, M., Blum, C., Clerc, M., Stützle, T., Winfield, A.F.T. (eds.) Ant Colony Optimization and Swarm Intelligence, 5th International Workshop, ANTS 2006. Lecture Notes in Computer Science, vol. 4150, pp. 247–258. Springer, Berlin (2006)

    Google Scholar 

  98. Korb, O., Stützle, T., Exner, T.E.: An ant colony optimization approach to flexible protein-ligand docking. Swarm Intelli. 1(2), 115–134 (2007)

    Google Scholar 

  99. Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B.: The Travelling Salesman Problem. Wiley, Chichester, UK (1985)

    Google Scholar 

  100. Leguizamón, G., Michalewicz, Z.: A new version of ant system for subset problems. In: Proceedings of the 1999 Congress on Evolutionary Computation (CEC’99), pp. 1459–1464. IEEE Press, Piscataway, NJ (1999)

    Google Scholar 

  101. Lessing, L., Dumitrescu, I., Stützle, T.: A comparison between ACO algorithms for the set covering problem. In: Dorigo, M., Gambardella, L., Mondada, F., Stützle, T., Birratari, M., Blum, C. (eds.) Ant Colony Optimization and Swarm Intelligence: 4th International Workshop, ANTS 2004. Lecture Notes in Computer Science, vol. 3172, pp. 1–12. Springer, Berlin (2004)

    Google Scholar 

  102. López-Ibáñez, M., Blum, C., Thiruvady, D., Ernst, A.T., Meyer, B.: Beam-ACO based on stochastic sampling for makespan optimization concerning the TSP with time windows. In: Cotta, C., Cowling, P. (eds.) Evolutionary Computation in Combinatorial Optimization. Lecture Notes in Computer Science, vol. 5482 pp. 97–108. Springer, Berlin (2009)

    Google Scholar 

  103. Manfrin, M., Birattari, M., Stützle, T., Dorigo, M.: Parallel ant colony optimization for the traveling salesman problem. In: Dorigo, M., Gambardella, L.M., Birattari, M., Martinoli, A., Poli, R., Stützle, T. (eds.) Ant Colony Optimization and Swarm Intelligence: 5th International Workshop, ANTS 2006. Lecture Notes in Computer Science, vol. 4150, pp. 224–234. Springer, Berlin (2006)

    Google Scholar 

  104. Maniezzo, V.: Exact and approximate nondeterministic tree-search procedures for the quadratic assignment problem. Technical Report CSR 98-1, Scienze dell’Informazione, Universitá di Bologna, Sede di Cesena, Italy, 1998

    Google Scholar 

  105. Maniezzo, V.: Exact and approximate nondeterministic tree-search procedures for the quadratic assignment problem. INFORMS J. Comput. 11(4), 358–369 (1999)

    Google Scholar 

  106. Maniezzo, V., Carbonaro, A.: An ANTS heuristic for the frequency assignment problem. Future Gen. Comput. Syst. 16(8), 927–935 (2000)

    Google Scholar 

  107. Martens, D., De Backer, M., Haesen, R., Vanthienen, J., Snoeck, M., Baesens, B.: Classification with ant colony optimization. IEEE Trans. Evol. Comput. 11(5), 651–665 (2007)

    Google Scholar 

  108. Merkle, D., Middendorf, M.: Modeling the dynamics of ant colony optimization. Evol. Comput. 10(3), 235–262 (2002)

    Google Scholar 

  109. Merkle, D., Middendorf, M.: Ant colony optimization with global pheromone evaluation for scheduling a single machine. Appl. Intell. 18(1), 105–111 (2003)

    Google Scholar 

  110. Merkle, D., Middendorf, M., Schmeck, H.: Ant colony optimization for resource-constrained project scheduling. In: Whitley, D., Goldberg, D., Cantu-Paz, E., Spector, L., Parmee, I., Beyer, H.-G. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2000), pp. 893–900. Morgan Kaufmann, San Francisco, CA (2000)

    Google Scholar 

  111. Merkle, D., Middendorf, M., Schmeck, H.: Ant colony optimization for resource-constrained project scheduling. IEEE Trans. Evol. Comput. 6(4), 333–346 (2002)

    Google Scholar 

  112. Meuleau, N., Dorigo, M.: Ant colony optimization and stochastic gradient descent. Artif. Life 8(2), 103–121 (2002)

    Google Scholar 

  113. Meyer, B., Ernst, A.: Integrating ACO and constraint propagation. In: Dorigo, M., Birattari, M., Blum, C., Gambardella, L.M., Mondada, F., Stützle, T. (eds.) Ant Colony Optimization and Swarm Intelligence, 4th International Workshop, ANTS 2004. Lecture Notes in Computer Science, vol. 3172, pp. 166–177. Springer, Berlin (2004)

    Google Scholar 

  114. Michel, R., Middendorf, M.: An ACO algorithm for the shortest supersequence problem. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, pp. 51–61. McGraw Hill, London, UK (1999)

    Google Scholar 

  115. Middendorf, M., Reischle, F., Schmeck, H.: Multi colony ant algorithms. J. Heuristics 8(3), 305–320 (2002)

    Google Scholar 

  116. Monmarché, N., Venturini, G.: On how Pachycondyla apicalis ants suggest a new search algorithm. Future Gen. Comput. Syst. 16(8), 937–946 (2000)

    Google Scholar 

  117. Montemanni, R., Gambardella, L.M., Rizzoli, A.E., Donati, A.V.: Ant colony system for a dynamic vehicle routing problem. J. Comb. Optimization 10, 327–343 (2005)

    Google Scholar 

  118. Morton, T.E., Rachamadugu, R.M., Vepsalainen, A.: Accurate myopic heuristics for tardiness scheduling. GSIA Working Paper 36-83-84, Carnegie Mellon University, Pittsburgh, PA, 1984

    Google Scholar 

  119. Neumann, F., Sudholt, D., Witt, C.: Analysis of different MMAS ACO algorithms on unimodal functions and plateaus. Swarm Intell. 3(1), 35–68 (2009)

    Google Scholar 

  120. Neumann, F., Witt, C.: Runtime analysis of a simple ant colony optimization algorithm. Electron. Colloq. Comput. Complexity (ECCC) 13(084) (2006)

    Google Scholar 

  121. Otero, F.E.B., Freitas, A.A., Johnson, C.G.: cAnt-Miner: an ant colony classification algorithm to cope with continuous attributes. In: Dorigo, M., Birattari, M., Blum, C., Clerc, M., Stützle, T., Winfield, A.F.T. (eds.) Ant Colony Optimization and Swarm Intelligence, 6th International Workshop, ANTS 2008. Lecture Notes in Computer Science, vol. 5217, pp. 48–59. Springer, Berlin (2008)

    Google Scholar 

  122. Ow, P.S., Morton, T.E.: Filtered beam search in scheduling. Int. J. Prod. Res., 26, 297–307 (1988)

    Google Scholar 

  123. Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading, MA (1994)

    Google Scholar 

  124. Parpinelli, R.S., Lopes, H.S., Freitas, A.A.: Data mining with an ant colony optimization algorithm. IEEE Trans. Evol. Comput. 6(4), 321–332 (2002)

    Google Scholar 

  125. Rajendran, C., Ziegler, H.: Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs. Eur. J. Oper. Res. 155(2), 426–438 (2004)

    Google Scholar 

  126. Randall, M., Lewis, A.: A parallel implementation of ant colony optimization. J. Parallel Distr. Comput. 62(9), 1421–1432 (2002)

    Google Scholar 

  127. Reimann, M., Doerner, K., Hartl, R.F.: D-ants: savings based ants divide and conquer the vehicle routing problems. Comput. Oper. Res. 31(4), 563–591 (2004)

    Google Scholar 

  128. Reinelt, G.: The Traveling Salesman: Computational Solutions for TSP Applications. Lecture Notes in Computer Science, vol. 840, Springer, Berlin (1994)

    Google Scholar 

  129. Rizzoli, A.E., Montemanni, R., Lucibello, E., Gambardella, L.M.: Ant colony optimization for real-world vehicle routing problems. From theory to applications. Swarm Intell. 1(2), 135–151 (2007)

    Google Scholar 

  130. Ruiz, R., Stützle, T.: A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem. Euro. J. Oper. Res. 177(3), 2033–2049 (2007)

    Google Scholar 

  131. Schoonderwoerd, R., Holland, O., Bruten, J., Rothkrantz, L.: Ant-based load balancing in telecommunications networks. Adaptive Behav. 5(2), 169–207 (1996)

    Google Scholar 

  132. Shmygelska, A., Hoos, H.H.: An ant colony optimisation algorithm for the 2D and 3D hydrophobic polar protein folding problem. BMC Bioinformat. 6, 30 (2005)

    Google Scholar 

  133. Sim, K.M., Sun, W.H.: Ant colony optimization for routing and load-balancing: survey and new directions. IEEE Trans. Syst. Man Cyber.-Part A: Syst. Hum. 33(5), 560–572 (2003)

    Google Scholar 

  134. Socha, K.: ACO for continuous and mixed-variable optimization. In: Dorigo, M., Gambardella, L., Mondada, F., Stützle, T., Birratari, M., Blum, C. (eds.) Ant Colony Optimization and Swarm Intelligence: 4th International Workshop, ANTS 2004. Lecture Notes in Computer Science, vol. 3172, pp. 25–36. Springer, Berlin (2004)

    Google Scholar 

  135. Socha, K., Blum, C.: An ant colony optimization algorithm for continuous optimization: An application to feed-forward neural network training. Neural Comput. Appl. 16(3), 235–248 (2007)

    Google Scholar 

  136. Socha, K., Dorigo, M.: Ant colony optimization for mixed-variable optimization problems. Technical Report TR/IRIDIA/2007-019, IRIDIA, Université Libre de Bruxelles, Brussels, Belgium, October 2007

    Google Scholar 

  137. Socha, K., Dorigo, M.: Ant colony optimization for continuous domains. Eur. J. Oper. Res. 185(3), 1155–1173 (2008)

    Google Scholar 

  138. Socha, K., Knowles, J., Sampels, M.: A \(\mathcal MAX-MIN\) ant system for the university course timetabling problem. In: Dorigo, M., Di Caro, G., Sampels, M. (eds.) Ant Algorithms: Third International Workshop, ANTS 2002. Lecture Notes in Computer Science, vol. 2463, pp. 1–13. Springer, Berlin (2002)

    Google Scholar 

  139. Socha, K., Sampels, M., Manfrin, M.: Ant algorithms for the university course timetabling problem with regard to the state-of-the-art. In: Raidl, G.R., Meyer, J.-A., Middendorf, M., Cagnoni, S., Cardalda, J.J.R., Corne, D.W., Gottlieb, J., Guillot, A., Hart, E., Johnson, C.G., Marchiori, E. (eds.) Applications of Evolutionary Computing, Proceedings of EvoWorkshops 2003. Lecture Notes in Computer Science, vol. 2611, pp. 334–345. Springer, Berlin (2003)

    Google Scholar 

  140. Solnon, C.: Combining two pheromone structures for solving the car sequencing problem with ant colony optimization. Eur. J. Oper. Res. 191(3), 1043–1055 (2008)

    Google Scholar 

  141. Solnon, C., Fenet, S.: A study of ACO capabilities for solving the maximum clique problem. J. Heuristics 12(3), 155–180 (2006)

    Google Scholar 

  142. Stützle, T.: An ant approach to the flow shop problem. In: Proceedings of the Sixth European Congress on Intelligent Techniques & Soft Computing (EUFIT’98), vol. 3, pp. 1560–1564. Verlag Mainz, Wissenschaftsverlag, Aachen, Germany, 1998

    Google Scholar 

  143. Stützle, T.: Parallelization strategies for ant colony optimization. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) Proceedings of PPSN-V, Fifth International Conference on Parallel Problem Solving from Nature. Lecture Notes in Computer Science, vol. 1498, pp. 722–731. Springer, Berlin (1998)

    Google Scholar 

  144. Stützle, T.: Local Search Algorithms for Combinatorial Problems: Analysis, Improvements, and New Applications, DISKI, vol. 220, Infix, Sankt Augustin, Germany, 1999

    Google Scholar 

  145. Stützle, T., Dorigo, M.: A short convergence proof for a class of ACO algorithms. IEEE Trans. Evol. Comput. 6(4), 358–365 (2002)

    Google Scholar 

  146. Stützle, T., Hoos, H.H.: Improving the ant system: a detailed report on the \(\cal MAX\)–\(\cal MIN\) Ant System. Technical Report AIDA–96–12, FG Intellektik, FB Informatik, TU Darmstadt, Germany, August 1996

    Google Scholar 

  147. Stützle, T., Hoos, H.H.: The \(\cal MAX\)–\(\cal MIN\) Ant System and local search for the traveling salesman problem. In: Bäck, T., Michalewicz, Z., Yao, X. (eds.) Proceedings of the 1997 IEEE International Conference on Evolutionary Computation (ICEC’97), pp. 309–314. IEEE Press, Piscataway, NJ (1997)

    Google Scholar 

  148. Stützle, T., Hoos, H.H.: \(\cal MAX\)–\(\cal MIN\) ant system. Future Gen. Comput. Syst. 16(8), 889–914 (2000)

    Google Scholar 

  149. Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. MIT Press, Cambridge, MA (1998)

    Google Scholar 

  150. Talbi, E.-G., Roux, O.H., Fonlupt, C., Robillard, D.: Parallel ant colonies for the quadratic assignment problem. Future Gen. Comput. Syst. 17(4), 441–449 (2001)

    Google Scholar 

  151. Tsutsui, S.: Ant colony optimisation for continuous domains with aggregation pheromones metaphor. In: Proceedings of the The 5th International Conference on Recent Advances in Soft Computing (RASC-04), pp. 207–212, Nottingham, UK (2004)

    Google Scholar 

  152. Tsutsui, S.: cAS: Ant colony optimization with cunning ants. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo Guervós, J.J., Whitley, L.D., Yao, X. (eds.) Parallel Problem Solving from Nature–PPSN IX, 9th International Conference. Lecture Notes in Computer Science, vol. 4193, pp. 162–171. Springer, Berlin (2006)

    Google Scholar 

  153. Tsutsui, S.: An enhanced aggregation pheromone system for real-parameter optimization in the ACO metaphor. In: Dorigo, M., Gambardella, L.M., Birattari, M., Martinoli, A., Poli, R., Stützle, T. (eds.) Ant Colony Optimization and Swarm Intelligence: 5th International Workshop, ANTS 2006. Lecture Notes in Computer Science, vol. 4150, pp. 60–71. Springer, Berlin (2006)

    Google Scholar 

  154. Twomey, C., Stützle, T., Dorigo, M., Manfrin, M., Birattari, M.: An analysis of communication policies for homogeneous multi-colony ACO algorithms. Technical Report TR/IRIDIA/2009-012, IRIDIA, Université Libre de Bruxelles, Brussels, Belgium, May 2009

    Google Scholar 

  155. Wiesemann, W., Stützle, T.: Iterated ants: an experimental study for the quadratic assignment problem. In: Dorigo, M., Gambardella, L.M., Birattari, M., Martinoli, A., Poli, R., Stützle, T. (eds.) Ant Colony Optimization and Swarm Intelligence: 5th International Workshop, ANTS 2006. Lecture Notes in Computer Science, vol. 4150, pp. 179–190. Springer, Berlin (2006)

    Google Scholar 

  156. Yagiura, M., Kishida, M., Ibaraki, T.: A 3-flip neighborhood local search for the set covering problem. Eur. J. Oper. Res. 172, 472–499 (2006)

    Google Scholar 

  157. Yannakakis, M.: Computational complexity. In: Aarts, E.H.L., Lenstra, J.K. (eds.) Local Search in Combinatorial Optimization, pp. 19–55. Wiley, Chichester, UK (1997)

    Google Scholar 

  158. Yuan, Z., Fügenschuh, A., Homfeld, H., Balaprakash, P., Stützle, T., Schoch, M.: Iterated greedy algorithms for a real-world cyclic train scheduling problem. In: Blesa, M.J., Blum, C., Cotta, C., Fernández, A.J., Gallardo, J.E., Roli, A., Sampels, M. (eds.) Hybrid Metaheuristics, 5th International Workshop, HM 2008. Lecture Notes in Computer Science, vol. 5296, pp. 102–116. Springer, Berlin (2008)

    Google Scholar 

  159. Zhang, Y., Kuhn, L.D., Fromherz, M.P.J.: Improvements on ant routing for sensor networks. In: Dorigo, M., Gambardella, L.M., Mondada, F., Stützle, T., Birattari, M., Blum, C. (eds.) Ant Colony Optimization and Swarm Intelligence: 4th International Workshop, ANTS 2004. Lecture Notes in Computer Science, vol. 3172, pp. 154–165. Springer, Berlin (2004)

    Google Scholar 

  160. Zlochin, M., Birattari, M., Meuleau, N., Dorigo, M.: Model-based search for combinatorial optimization: a critical survey. Ann. Oper. Res. 131(1–4), 373–395 (2004)

    Google Scholar 

Download references

Acknowledgments

This work was supported by the META-X project, an Action de Recherche Concertée funded by the Scientific Research Directorate of the French Community of Belgium. Marco Dorigo and Thomas Stützle acknowledge support from the Belgian F.R.S.-FNRS, of which they are a Research Director and a Research Associate, respectively.

Author information

Authors and Affiliations

  1. IRIDIA, Université Libre de Bruxelles (ULB), Brussels, Belgium

    Marco Dorigo & Thomas Stützle

Authors
  1. Marco Dorigo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thomas Stützle
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marco Dorigo .

Editor information

Editors and Affiliations

  1. , Département de mathématiques et génie in, École Polytechnique Montréal, Montreal, H3C 3A7, Québec, Canada

    Michel Gendreau

  2. Dépt. Informatique et Recherche, Opérationnelle, Université de Montreal, Pavillon André-Aisenstadt, Montreal, H3C 3J7, Québec, Canada

    Jean-Yves Potvin

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Dorigo, M., Stützle, T. (2010). Ant Colony Optimization: Overview and Recent Advances. In: Gendreau, M., Potvin, JY. (eds) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol 146. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1665-5_8

Download citation

Publish with us

Policies and ethics

Search

Navigation