Swarm Intelligence

, Volume 3, Issue 1, pp 69–85 | Cite as

Multiple objective ant colony optimisation

  • Daniel Angus
  • Clinton Woodward


Multiple Objective Optimisation is a fast growing area of research, and consequently several Ant Colony Optimisation approaches have been proposed for a variety of these problems. In this paper, a taxonomy for Multiple Objective Ant Colony Optimisation algorithms is proposed and many existing approaches are reviewed and described using the taxonomy. The taxonomy offers guidelines for the development and use of Multiple Objective Ant Colony Optimisation algorithms.


Multiple Objective Optimisation Pareto Optimisation Ant Colony Optimisation Taxonomy 


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  1. Angus, D. (2007). Crowding population-based ant colony optimisation for the multi-objective travelling salesman problem. In 2007 IEEE symposium on computational intelligence in multi-criteria decision-making (MCDM 2007) (pp. 333–340). New York: IEEE Press. CrossRefGoogle Scholar
  2. Barán, B., & Schaerer, M. (2003). A multiobjective ant colony system for vehicle routing problem with time windows. In Proceedings of the 21st IASTED international conference on applied informatics (pp. 97–102). Calgary: ACTA Press. Google Scholar
  3. Bilchev, G., & Parmee, I. C. (1995). The ant colony metaphor for searching continuous design spaces. In T. C. Fogarty (Ed.), LNCS : Vol. 993. Proceedings of the AISB workshop on evolutionary computation (pp. 25–39). Berlin: Springer. Google Scholar
  4. Cardoso, P., Jesus, M., & Márquez, A. (2003). MONACO—multi-objective network optimisation based on ACO. In F. S. Leal & D. Orden (Eds.), Encuentros de geometría computacional. Santander: Universidad de Cantabria. Google Scholar
  5. Corne, D. W., Jerram, N. R., Knowles, J. D., & Oates, M. J. (2001). PESA-II: Region-based selection in evolutionary multiobjective optimization. In L. Spector, E. D. Goodman, A. Wu, W. Langdon, H. M. Voigt, M. Gen, S. Sen, M. Dorigo, S. Pezeshk, M. H. Garzon, & E. Burke (Eds.), Proceedings of the genetic and evolutionary computation conference (GECCO’2001) (pp. 283–290). San Mateo: Morgan Kaufmann. Google Scholar
  6. Das, I., & Dennis, J. (1996). A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems (Technical Report 96–36). Houston: Rice University, Dept. Of Computational and Applied Mathematics. Google Scholar
  7. Deb, K. (2002). Wiley-Interscience series in systems and optimization. Multi-objective optimization using evolutionary algorithms (2nd ed.). New York: Wiley. Google Scholar
  8. Deb, K., Agrawal, S., Pratap, A., & Meyarivan, T. (2000). A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In M. Schoenauer, K. Deb, G. Rudolph, X. Yao, E. Lutton, J. J. Merelo, & H. P. Schwefel (Eds.), LNCS : Vol. 1917. Parallel problem solving from nature (PPSN VI) (pp. 849–858). Berlin: Springer. CrossRefGoogle Scholar
  9. Doerner, K., Hartl, R., & Teimann, M. (2003). Are COMPETants more competent for problem solving? The case of full truckload transportation. Central European Journal of Operations Research (CEJOR), 11(2), 115–141. zbMATHMathSciNetGoogle Scholar
  10. Doerner, K., Gutjahr, W. J., Hartl, R. F., Strauss, C., & Stummer, C. (2004). Pareto ant colony optimization: A metaheuristic approach to multiobjective portfolio selection. Annals of Operations Research, 131(14), 79–99. zbMATHCrossRefMathSciNetGoogle Scholar
  11. Dorigo, M., & Di Caro, G. (1999). The ant colony optimization meta-heuristic. In D. Corne, M. Dorigo, & F. Glover (Eds.), New ideas in optimisation (pp. 11–32). London: McGraw-Hill. Google Scholar
  12. Dorigo, M., & Gambardella, L. (1997). Ant colonies for the traveling salesman problem. Biosystems, 43, 73–81. CrossRefGoogle Scholar
  13. Dorigo, M., & Stützle, T. (2004). Ant colony optimization. Cambridge: MIT Press. zbMATHGoogle Scholar
  14. Dorigo, M., Di Caro, G., & Gambardella, L. M. (1999). Ant algorithms for discrete optimization. Artificial Life, 5, 137–172. CrossRefGoogle Scholar
  15. Fonseca, C. M., & Fleming, P. J. (1996). On the performance assessment and comparison of stochastic multiobjective optimizers. In H. M. Voigt, W. Ebeling, I. Rechenberg, & H. P. Schwefel (Eds.), LNCS : Vol. 1141. Proceedings of the 4th international conference on parallel problem solving from nature (PPSN IV) (pp. 584–593). Berlin: Springer. CrossRefGoogle Scholar
  16. Gambardella, L. M., Taillard, E., & Agazzi, G. (1999). MACS-VRPTW: A multiple ant colony system for vehicle routing problems with time windows. In D. Corne, M. Dorigo, & F. Glover (Eds.), New ideas in optimisation (pp. 63–76). London: McGraw-Hill. Google Scholar
  17. Garcìa-Martínez, C., Cordón, O., & Herrera, F. (2007). A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for bi-criteria TSP. European Journal of Operational Research, 180(1), 116–148. zbMATHCrossRefGoogle Scholar
  18. Gravel, M., Price, W. L., & Gagné, C. (2002). Scheduling continuous casting of aluminum using a multiple-objective ant colony optimization metaheuristic. European Journal of Operations Research, 143(1), 218–229. zbMATHCrossRefGoogle Scholar
  19. Guntsch, M. (2004). Ant algorithms in stochastic and multi-criteria environments. Ph.D. thesis, Universität Fridericiana zu Karlsruhe, Germany. Google Scholar
  20. Guntsch, M., & Middendorf, M. (2003). Solving multi-criteria optimization problems with population-based ACO. In G. Goos, J. Hartmanis, & J. van Leeuwen (Eds.), LNCS : Vol. 2632. Proceedings of the second international conference on evolutionary multi-criterion optimization (EMO 2003) (pp. 464–478). Berlin: Springer. CrossRefGoogle Scholar
  21. Horn, J., Nafpliotis, N., & Goldberg, D. E. (1994). A niched Pareto genetic algorithm for multiobjective optimization. In IEEE world congress on computational intelligence : Vol. 1. Proceedings of the first IEEE conference on evolutionary computation (pp. 82–87). New York: IEEE Press. CrossRefGoogle Scholar
  22. Hwang, C. L., & Masud, A. S. M. (1979). Lecture notes in economics and mathematical systems: Vol. 164. Multiple objective decision making, methods and applications: a state-of-the-art survey. Heidelberg: Springer. zbMATHGoogle Scholar
  23. Iredi, S., Merkle, D., & Middendorf, M. (2001). Bi-criterion optimization with multi colony ant algorithms. In E. Zitzler, K. Deb, L. Thiele, C. C. Coello, & D. Corne (Eds.), LNCS : Vol. 1993. First international conference on evolutionary multi-criterion optimization (pp. 359–372). Berlin: Springer. Google Scholar
  24. Knowles, J. (2005). A summary-attainment-surface plotting method for visualizing the performance of stochastic multiobjective optimizers. In H. Kwasnicka & M. Paprzycki (Eds.), ISDA ’05: Proceedings of the 5th international conference on intelligent systems design and applications (pp. 552–557). Los Alamitos: IEEE Computer Society. CrossRefGoogle Scholar
  25. Knowles, J. D., & Corne, D. W. (2000). Approximating the nondominated front using the Pareto archived evolution strategy. Evolutionary Computation, 8(2), 149–172. CrossRefGoogle Scholar
  26. Knowles, J. D., Thiele, L., & Zitzler, E. (2006) A tutorial on the performance assessment of stochastic multiobjective optimizers (Technical Report TIK Report No. 214). Switzerland: Computer Engineering and Networks Laboratory, ETH Zurich. Google Scholar
  27. López-Ibáñez, M., Paquete, L., & Stützle, T. (2004). On the design of ACO for the biobjective quadratic assignment problem. In M. Dorigo, M. Birattari, C. Blum, L. M. Gambardella, F. Mondada, & T. Stützle (Eds.), LNCS : Vol. 3172. ANTS’2004, Fourth international workshop on ant algorithms and swarm intelligence (pp. 214–225). Berlin: Springer. Google Scholar
  28. Maniezzo, V., & Carbonaro, A. (1999). Ant colony optimization: an overview. In P. Hansen & C. Ribeiro (Eds.), Proceedings of the third metaheuristics international conference (MIC’99) (pp. 21–44). Dordrecht: Kluwer Academic. Google Scholar
  29. McMullen, P. R. (2001). An ant colony optimization approach to addressing a JIT sequencing problem with multiple objectives. Artificial Intelligence in Engineering, 15(3), 309–317. CrossRefGoogle Scholar
  30. Purshouse, R. C., & Fleming, P. J. (2003). Conflict, harmony, and independence: Relationships in evolutionary multi-criterion optimisation. In C. M. Fonseca, P. J. Fleming, E. Zitzler, K. Deb, & L. Thiele (Eds.), LNCS : Vol. 2632. Proceedings of the second international evolutionary multi-criterion optimization conference (EMO 2003) (pp. 16–30). Berlin: Springer. CrossRefGoogle Scholar
  31. Romero, C. E. M., & Manzanares, E. M. (1999). MOAQ an Ant-Q algorithm for multiple objective optimization problems. In W. Banzhaf, J. Daida, A. E. Eiben, M. H. Garzon, V. Honavar, M. Jakiela, & R. E. Smith (Eds.), Genetic and evolutionary computing conference (GECCO 99) (Vol. 1, pp. 894–901). San Mateo: Morgan Kaufmann. Google Scholar
  32. Shelokar, P. S., Jayaraman, V. K., & Kulkarni, B. D. (2002). Ant algorithm for single and multiobjective reliability optimization problems. Quality and Reliability Engineering International, 18(6), 497–514. CrossRefGoogle Scholar
  33. Socha, K., & Dorigo, M. (2008). Ant colony optimization for continuous domains. European Journal of Operations Research, 185(3), 1155–1173. zbMATHCrossRefMathSciNetGoogle Scholar
  34. Srinivas, N., & Deb, K. (1994). Multiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary Computation, 2(3), 221–248. CrossRefGoogle Scholar
  35. Stützle, T., & Hoos, H. (2000). \(\mathcal{MAX}\)\(\mathcal{MIN}\) ant system. Future Generation Computer Systems, 16(8), 889–914. CrossRefGoogle Scholar
  36. T’kindt, V., Monmarché, N., Tercinet, F., & Laügt, D. (2002). An ant colony optimization algorithm to solve a 2-machine bicriteria flowshop scheduling problem. European Journal of Operational Research, 142(2), 250–257. zbMATHCrossRefMathSciNetGoogle Scholar
  37. Van Veldhuizen, D. A. (1999) Multiobjective evolutionary algorithms: classifications, analyses, and new innovations. Ph.D. thesis, Department of Electrical and Computer Engineering. Graduate School of Engineering, Air Force Institute of Technology, Wright-Patterson AFB, OH. Google Scholar
  38. Zitzler, E., & Künzli, S. (2004). Indicator-based selection in multiobjective search. In X. Yao, E. Burke, J. A. Lozano, J. Smith, & J. J. Merelo-Guervos (Eds.), LNCS : Vol. 3242. Proceedings of the 8th international conference on parallel problem solving from nature (PPSN VIII) (pp. 832–842). Berlin: Springer. Google Scholar
  39. Zitzler, E., Laumanns, M., & Thiele, L. (2002) SPEA2: Improving the strength Pareto evolutionary algorithm. In: K. Giannakoglou, D. Tsahalis, J. Periaux, P. Papailou, T. Fogarty (Eds.), EUROGEN 2001, evolutionary methods for design, optimization and control with applications to industrial problems, international center for numerical methods in engineering (CIMNE), Barcelona, Spain (pp. 95–100). Google Scholar
  40. Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C., & Fonseca, V. (2003). Performance assessment of multiobjective optimizers: an analysis and review. IEEE Transactions on Evolutionary Computation, 7(2), 117–132. CrossRefGoogle Scholar
  41. Zitzler, E., Brockhoff, D., & Thiele, L. (2007). The hypervolume indicator revisited: On the design of Pareto-compliant indicators via weighted integration. In S. Obayashi, K. Deb, C. Poloni, T. Hiroyasu, & T. Murata (Eds.), LNCS : Vol. 4403. Proceedings of the forth international evolutionary multi-criterion optimization conference (EMO 2007) (pp. 862–876). Berlin: Springer. CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, LLC 2008

Authors and Affiliations

  1. 1.The University of QueenslandBrisbaneAustralia
  2. 2.Swinburne University of TechnologyMelbourneAustralia

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