Skip to main content
SpringerLink
Log in

A Hybrid Meta-Heuristic for Multi-Objective Optimization: MOSATS

  • Published:
Journal of Mathematical Modelling and Algorithms

Abstract

Real optimization problems often involve not one, but multiple objectives, usually in conflict. In single-objective optimization there exists a global optimum, while in the multi-objective case no optimal solution is clearly defined but rather a set of solutions, called the Pareto-optimal front. Thus, the goal of multi-objective strategies is to generate a set of non-dominated solutions as an approximation to this front. However, the majority of problems of this kind cannot be solved exactly because they have very large and highly complex search spaces. In recent years, meta-heuristics have become important tools for solving multi-objective problems encountered in industry as well as in the theoretical field. This paper presents a novel approach based on hybridizing Simulated Annealing and Tabu Search. Experiments on the Graph Partitioning Problem show that this new method is a better tool for approximating the efficient set than other strategies also based on these meta-heuristics.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aleta, A., Codina, J.M., Sanchez, J., Gonzalez, A.: Graph-partitioning based instruction scheduling for clustered processors. In: Proceedings of 34th Annual ACM/IEEE International Symposium on Microarchitecture, pp. 150–159, 2001

  2. Baños, R., Gil, C., Ortega, J., Montoya, F.G.: Parallel multilevel metaheuristic for graph partitioning. Journal of Heuristics 10(3), 315–336 (2004)

    Article  Google Scholar 

  3. Burke, E.K., Cowling, P., Landa Silva, J.D., Petrovic, S.: Combining hybrid metaheuristics and populations for the multiobjective optimisation of space allocation problems. In: Proceedings of the 2001 Genetic and Evolutionary Computation Conference, San Francisco, pp. 1252–1259, 2001

  4. Corne, D.W., Knowles, J.D., Oates, M.J.: The pareto-envelope based selection algorithm for multiobjective optimization. In: Proceedings of the Sixt International Conference on Parallel Problem Solving from Nature, Lecture Notes in Computer Science 1917, pp. 839–848. Springer, Berlin Heidelberg New York (2000)

  5. Czyzak, P., Jaszkiewicz, A.: Pareto simulated annealing – A metaheuristic technique for multiple-objective combinatorial optimization. J. Multi-Criteria Decis. Anal. 7(1), 34–47 (1998)

    Article  MATH  Google Scholar 

  6. Deb, K., Agrawal, S., Pratabm, A., Meyarivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Proceedings of the Sixt International Conference on Parallel Problem Solving from Nature, Lecture Notes in Computer Science 1917, pp. 849–858. Springer, Berlin Heidelberg New York (2000)

  7. Erickson, M., Mayer, A., Horn, J.: The niched pareto genetic algorithm 2 applied to the design of groundwater remediation systems. In: Proceedings of First International Conference on Evolutionary Multi-Criterion Optimization, pp. 681–695. Springer, Berlin Heidelberg New York (2001)

  8. Fonseca, C.M., Fleming, P.J.: Genetic algorithms for multiobjective optimization: Formulation, discussion and generalizatio. In: Proceedings of the Fifth International Conference on Genetic Algorithms, pp. 416–423, 1993

  9. Gandibleux, X., Freville, A.: Tabu search based procedure for solving the 0–1 multiobjective knapsack problem: The two objectives case. Journal of Heuristics 6(3), 361–383 (2000)

    Article  MATH  Google Scholar 

  10. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)

    MATH  Google Scholar 

  11. Gil, C., Ortega, J., Montoya, M.G.: Parallel VLSI test in a shared memory multiprocessor. Concurrency: Practice and Experience 12(5), 311–326 (2000)

    Article  MATH  Google Scholar 

  12. Gil, C., Ortega, J., Montoya, M.G., Baños, R.: A mixed heuristic for circuit partitioning. Comput Optim. Appl. 23(3), 321–340 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  13. Glover, F., Laguna, M., Dowsland, K.A.: In: Reeves, C.R. (eds.) Modern Heuristic Techniques for Combinatorial Problems. Blackwell, London, (1993)

    Google Scholar 

  14. Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley (1989)

  15. GPA, (Walshaw's Graph Partitioning Archive), http://staffweb.cms.gre.ac.uk/~c.walshaw/partition/ URL time: October 12th, 2005, 1650

  16. Hajela, P., Y-Lin, C.: Genetic search strategies in multi-criterion optimal design. Struct. Optim. 4, 99–107 (1992)

    Article  Google Scholar 

  17. Hansen, P.H.: Tabu Search for Multiobjective Optimization: MOTS. In: Proceedings of the 13th International Conference on Multiple Criteria Decision Making, 1997

  18. Hendrickson, B., Leland, R.: A Multilevel Algorithm for Partitioning Graphs. Technical Report SAND93-1301, Sandia National Laboratories, USA, 1993

  19. Horn, J., Nafpliotis, N., Goldberg, D.: A niched pareto genetic algorithm for multiobjective optimization. In: Proceedings of the First IEEE Conference on Evolutionary Computation, Piscataway, New Jersey, USA, pp. 82–87, 1994

  20. Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20(1), 359–392 (1998)

    Article  MathSciNet  Google Scholar 

  21. Knowles, J.D., Corne, D.: Approximating the nondominated front using the pareto archived evolution strategy. Evol. Comput. 8(2), 149–172 (2000)

    Article  Google Scholar 

  22. Knowles, J.D., Corne, D.: Bounded Pareto archiving: Theory and practice.In: Gandibleux et al. (eds.) Metaheuristics for Multiobjective Optimisation, Springer Lecture Notes in Economics and Math. Systems, vol. 535, pp. 39–64. (2004)

  23. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)

    Article  MathSciNet  Google Scholar 

  24. Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., Teller, E.: Equation of state calculations by fast computing machines. J. Chem. Phys. 21(6), 1087–1092 (1953)

    Article  Google Scholar 

  25. Rudolph, G., Agapie, A.: Convergence properties of some multi-objective evolutionary algorithms. In: Proceedings of the 2000 Conference on Evolutionary Computation, Piscataway, New Jersey, vol. 2, pp. 1010–1016, 2000

  26. Rummler, A., Apetrei, A.: Graph partitioning revised – A multiobjective perspective. In: Proceedings of the 6th World Conf. On Systemics, Cybernetics and Informatics, Orlando, Florida, USA, 2002

  27. Schaffer, J.D.: Multiple objective optimization with vector evaluated genetic algorithms. In: Proceedings of the First International Conference on Genetic Algorithms, Pittsburgh, Pennsylvania, USA, pp. 93–100, 1985

  28. Selvakkumaran, N., Karypis, G.: Multi-objective hypergraph partitioning algorithms for cut and maximum subdomain degree minimization. In: Proceedings of International Conference on Computer Aided Design, San Jose, California, USA, pp. 726–733, 2003

  29. Serafini, P.: In: Tzeng, G.H. et al. (eds.) Simulated Annealing for Multi-objective Optimization Problems. Multiple Criteria Decision Making: Expand and Enrich the Domains of Thinking and Application. Springer, Berlin Heidelberg New York (1993)

    Google Scholar 

  30. Srinivas, N., Deb, K.: Multiobjective optimization using nondominated sorting in genetic algorithms. Evol. Comput. 2(3), 221–248 (1994)

    Google Scholar 

  31. Talbi, E.: A taxonomy of hybrid metaheuristics. Journal of Heuristics 8(5), 541–564 (2002)

    Google Scholar 

  32. Ulungu, E.L., Teghem, J., Fortemps, P.H., Tuyytens, D.: MOSA method: A tool for solving multiobjective combinatorial optimization problems. J. Multi-Criteria Decis. Anal. 8(4), 221–236 (1999)

    Article  MATH  Google Scholar 

  33. Walshaw, C., Cross, M., Everett, M.G.: In: Topping, B.H.V. (ed.) Mesh Partitioning and Load-balancing for Distributed Memory Parallel Systems. Parallel & Distributed Processing for Computational Mechanics: Systems and Tools, pp. 110–123. Saxe-Coburg, Edinburgh (1999)

    Google Scholar 

  34. Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach. IEEE Trans. Evol. Comput. 3(4), 257–271 (1999)

    Article  Google Scholar 

  35. Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization. In: Proceedings of Evolutionary Methods for Design, Optimisation, and Control, Barcelona, Spain, pp. 95–100, 2001

Download references

Author information

Authors and Affiliations

  1. Departamento de Arquitectura de Computadores y Electrónica, Universidad de Almería, La Cañada de San Urbano s/n, 04120, Almería, Spain

    R. Baños & C. Gil

  2. Centre for Emergent Computing, Napier University, Edinburgh, Scotland

    B. Paechter

  3. Departamento de Arquitectura y Tecnologia de Computadores, Universidad de Granada, C/ Daniel Saucedo Aranda, Granada, Spain

    J. Ortega

Authors
  1. R. Baños
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Gil
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. Paechter
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. Ortega
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Baños.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baños, R., Gil, C., Paechter, B. et al. A Hybrid Meta-Heuristic for Multi-Objective Optimization: MOSATS. J Math Model Algor 6, 213–230 (2007). https://doi.org/10.1007/s10852-006-9041-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10852-006-9041-6

Key words

Mathematics Subject Classifications (2000)

Search

Navigation