Bi-Criterion Optimization with Multi Colony Ant Algorithms

  • Steffen Iredi
  • Daniel Merkle
  • Martin Middendorf
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1993)


In this paper we propose a new approach to solve bi-criterion optimization problems with ant algorithms where several colonies of ants cooperate in finding good solutions. We introduce two methods for cooperation between the colonies and compare them with a multistart ant algorithm that corresponds to the case of no cooperation. Heterogeneous colonies are used in the algorithm, i.e. the ants differ in their preferences between the two criteria. Every colony uses two pheromone matrices — each suitable for one optimization criterion. As a test problem we use the Single Machine Total Tardiness problem with changeover costs.


Pareto Front Total Tardiness Global Good Solution Changeover Cost Pheromone Matrice 
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  1. [1]
    A. Bauer, B. Bullnheimer, R. Hartl, and C. Strauss. An ant colony optimization approach for the single machine total tardiness problem. In Proceedings of the 1999 Congress on Evolutionary Computation (CEC99), 6-9 July Washington D.C., USA, pages 1445–1450, 1999.Google Scholar
  2. [2]
    H. Crauwels, C. Potts, and L. V. Wassenhove. Local search heuristics for the single machine total weighted tardiness scheduling problem. Informs Journal on Computing, 10:341–350, 1998.zbMATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    M. den Besten, T. Stützle, and M. Dorigo. Scheduling single machines by ants. Technical Report IRIDIA/99–16, IRIDIA, Université Libre de Bruxelles, Belgium, 1999.Google Scholar
  4. [4]
    M. Dorigo and G. Di Caro. The ant colony optimization meta-heuristic. In D. Corne, M. Dorigo, and F. Glover, editors, New Ideas in Optimization, pages 11–32, London, 1999. McGraw-Hill.Google Scholar
  5. [5]
    J. Du and J.-T. Leung. Minimizing total tardiness on one machine is NP-hard. MOR: Mathematics of Operations Research, 15:483–496, 1990.zbMATHMathSciNetGoogle Scholar
  6. [6]
    C. Gagné, M. Gravel, and W. Price. Scheduling a single machine where setup times are sequence dependent using an ant-colony heuristic. In Abstract Proceedings of ANTS’2000, 7.-9. September Brussels, Belgium, pages 157–160, 2000.Google Scholar
  7. [7]
    L. M. Gambardella, É. Taillard, and G. Agazzi. MACS-VRPTW: A multiple ant colony system for vehicle routing problems with time windows. In D. Corne, M. Dorigo, and F. Glover, editors, New Ideas in Optimization, pages 63–76. McGraw-Hill, London, 1999.Google Scholar
  8. [8]
    E. Lawler. A ‘pseudopolynomial’ algorithm for sequencing jobs to minimize total tardiness. Annals of Discrete Mathematics, pages 331–342, 1977.Google Scholar
  9. [9]
    C. E. Mariano and E. Morales. 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, and R. E. Smith, editors, Proceedings of the Genetic and Evolutionary Computation Conference, volume 1, pages 894–901, Orlando, Florida, USA, 13-17 July 1999. Morgan Kaufmann.Google Scholar
  10. [10]
    D. Merkle and M. Middendorf. An ant algorithm with a new pheromone evaluation rule for total tardiness problems. In Proceeding of the EvoWorkshops 2000, number 1803 in Lecture Notes in Computer Science, pages 287–296. Springer Verlag, 2000.Google Scholar
  11. [11]
    D. Merkle, M. Middendorf, and H. Schmeck. Pheromone evaluation in ant colony optimization. IEEE Press, 2000. to appear in: Proceeding of the Third AsiaPacific Conference on Simulated Evolution and Learning (SEAL2000), Nagoya, Japan, 25-27 Oct. 2000.Google Scholar
  12. [12]
    M. Middendorf, F. Reischle, and H. Schmeck. Information exchange in multi colony ant algorithms. In SPDP: IEEE Symposium on Parallel and Distributed Processing. ACM Special Interest Group on Computer Architecture (SIGARCH), and IEEE Computer Society, 2000.Google Scholar
  13. [13]
    D. A. V. Veldhuizen and G. B. Lamont. Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art. Evolutionary Computation, 8(2):125–147, 2000.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Steffen Iredi
    • 1
  • Daniel Merkle
    • 1
  • Martin Middendorf
    • 1
  1. 1.Institute AIFBUniversity of KarlsruheKarlsruheGermany

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