Skip to main content
SpringerLink
Log in

DMEA: a direction-based multiobjective evolutionary algorithm

  • Regular Research Paper
  • Published:
Memetic Computing Aims and scope Submit manuscript

Abstract

A novel direction-based multi-objective evolutionary algorithm (DMEA) is proposed, in which a population evolves over time along some directions of improvement. We distinguish two types of direction: (1) the convergence direction between a non-dominated solution (stored in an archive) and a dominated solution from the current population; and, (2) the spread direction between two non-dominated solutions in the archive. At each generation, these directions are used to perturb the current parental population from which offspring are produced. The combined population of offspring and archived solutions forms the basis for the creation of both the next-generation archive and parental pools. The rule governing the formation of the next-generation parental pool is as follows: the first half is populated by non-dominated solutions whose spread is aided by a niching criterion applied in the decision space. The second half is filled with both non-dominated and dominated solutions from the sorted remainder of the combined population. The selection of non-dominated solutions for the next-generation archive is also assisted by a mechanism, in which neighborhoods of rays in objective space serve as niches. These rays originate from the current estimate of the Pareto optimal front’s (POF’s) ideal point and emit randomly into the hyperquadrant that contains the current POF estimate. Experiments on two well-known benchmark sets, namely ZDT and DTLZ have been carried out to investigate the performance and the behavior of the DMEA. We validated its performance by comparing it with four well-known existing algorithms. With respect to convergence and spread performance, DMEA turns out to be very competitive.

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. Abbass HA (2006) An economical cognitive approach for bi-objective optimization using bliss points, visualization, and interaction. Soft Comput 10(8): 687–698

    Article  Google Scholar 

  2. Abbass HA, Sarker R, Newton C (2001) PDE: a Pareto frontier differential evolution approach for multiobjective optimization problems. In: Proceedings of the congress on evolutionary computation, IEEE Service Center, Seoul, Korea, vol 2, pp 971–978

  3. Bleuler S, Laumanns M, Thiele L, Zitzler E (2003) Pisa: a platform and programming language independent interface for search algorithms. In: Evolutionary multi-criterion optimization. Lecture notes in computer science, vol 2632. Springer, Berlin, pp 494–508

  4. Bui LT, Alam S (2008) Multi-objective optimization in computational intelligence: theory and practice. Information Science Reference Series: IGI Global, Hershey, USA

    Google Scholar 

  5. Bui LT, Abbass HA, Essam D (2009) Local models—an approach to distributed multi-objective optimization. Comput Optim Appl 42(1): 105–139

    Article  MathSciNet  MATH  Google Scholar 

  6. Caponio A, Neri F (2009) Integrating cross-dominance adaptation in multi-objective memetic algorithms. In: Goh C-K, Ong Y-S, Tan KC (eds) Multi-objective memetic algorithms. Studies in computational intelligence, vol 171. Springer, Berlin, pp 325–351

    Chapter  Google Scholar 

  7. Coello CAC (2006) Evolutionary multi-objective optimization: a historical view of the field. IEEE Comput Intell Mag 1(1): 28–36

    Article  Google Scholar 

  8. Coello CAC, Veldhuizen DAV, Lamont GB (2002) Evolutionary algorithms for solving multi-objective problems. Kluwer, New York

    MATH  Google Scholar 

  9. Coello CAC, Pulido GT, Lechuga MS (2004) Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput 8(3): 256–279

    Article  Google Scholar 

  10. Coello CAC, Lamont GB, Veldhuizen DAV (2007) Evolutionary algorithms for solving multi-objective problems. Springer, New York

    MATH  Google Scholar 

  11. Deb K (2001) Multiobjective optimization using evolutionary algorithms. Wiley, New York

    Google Scholar 

  12. Deb K, Thiele L, Laumanns M, Zitzler E (2001) Scalable test problems for evolutionary multi-objective optimization. TIK-Report no. 112. Tech. rep., Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH), Zurich

  13. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2): 182–197

    Article  Google Scholar 

  14. DeJong KA (1975) An analysis of the behavior of a class of genetic adaptive systems. PhD thesis, University of Michigan, Ann Arbor

  15. Díaz-Madron̈ero M, Peidro D, Mula J, Ferriols FJ (2009) Fuzzy multiobjective mathematical programming approaches for operational transport planning in an automobile supply chain. J Quant Methods Econ Bus Adm 9: 44–68

    Google Scholar 

  16. Goh CK, Teoh EJ, Tan KC (2008) Hybrid multiobjective evolutionary design for artificial neural networks. IEEE Trans Neural Netw 19(9): 1531–1548

    Article  Google Scholar 

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

    Article  Google Scholar 

  18. Kwan CM, Chang CS (2008) Timetable synchronization of mass rapid transit system using multiobjective evolutionary approach. IEEE Trans Syst Man Cybern Part C 38(5): 636–648

    Article  Google Scholar 

  19. Lara A, Coello CAC, Schuetze O (2010) Using gradient information for multi-objective problems in the evolutionary context. In: GECCO’10, pp 2011–2014

  20. Ong, YS, Tan, KC, Goh, C-K (eds) (2009) Multi-objective memetic algorithms. Studies in computational intelligence, vol 171. Springer, Berlin

    Google Scholar 

  21. Osman, IH, Kelly, JP (eds) (1996) Meta-heuristics: theory and applications. Kluwer, New York

    MATH  Google Scholar 

  22. Price K, Storn R, Lampinen J (2005) Differential evolution—a practical approach to global optimization. Springer, Berlin

    MATH  Google Scholar 

  23. Rudolph G, Agapie A (2000) Convergence properties of some multi-objective evolutionary algorithms. In: Proceedings of the congress on evolutionary computation. IEEE Press, New York, pp 1010–1016

  24. Schaffer JD (1985) Multiple objective optimization with vector evaluated genetic algorithms. In: Genetic algorithms and their applications: proceedings of the first international conference on genettic algorithms, Hillsdale, New Jersey, pp 93–100

  25. Shir OM, Bäck T (2009) Niching with derandomized evolution strategies in artificial and real-world landscapes. Nat Comput 8(1): 171–196

    Article  MathSciNet  MATH  Google Scholar 

  26. Shir OM, Preuss M, Naujoks B, Emmerich M (2009) Enhancing decision space diversity in evolutionary multiobjective algorithms. In: Matthias E et al (eds) Proceedings of the 5th international conference on evolutionary multi-criterion optimization, France, pp 95–109

  27. Snyman JA (2005) Practical mathematical optimization: an introduction to basic optimization theory and classical and new gradient-based algorithms. Springer, Berlin

    MATH  Google Scholar 

  28. Storn R, Price K (1995) Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical report tr-95-012. Tech. rep., ICSI

  29. Tan KC, Khor EF, Lee TH (2005) Multiobjective evolutionary algorithms and applications. Springer, Berlin

    MATH  Google Scholar 

  30. Tan KC, Chiam SC, Mamun AA, Goh CK (2009) Balancing exploration and exploitation with adaptive variation for evolutionary multi-objective optimization. Eur J Oper Res 197(2): 701–713

    Article  MATH  Google Scholar 

  31. Veldhuizen DAV (1999) Multiobjective evolutionary algorithms: Classifications, analyses, and new innovation. PhD thesis, Department of Electrical Engineering and Computer Engineering, Air Force Institute of Technology, Ohio, USA

  32. Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications. PhD thesis, Ph.D. dissertation, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland

  33. Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2): 173–195

    Article  Google Scholar 

  34. Zitzler E, Thiele L, Deb K (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(1): 173–195

    Article  Google Scholar 

  35. Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: Giannakoglou KC, Tsahalis DT, Periaux J, Papailiou KD, Fogarty T (eds) Evolutionary methods for design optimization and control with applications to industrial problems. International Center for Numerical Methods in Engineering (Cmine), pp 95–100

Download references

Author information

Authors and Affiliations

  1. Department of Software Engineering, Faculty of Information Technology Organization, The Le Quy Don Technical University, Hanoi, Vietnam

    Lam T. Bui

  2. School of Engineering and Information Technology, The University of New South Wales at the Australian Defence Force Academy, Canberra, 2600, Australia

    Jing Liu, Michael Barlow & Hussein A. Abbass

  3. Defence Science and Technology Organisation, Edinburgh SA 5111, Adelaide, Australia

    Axel Bender

  4. DRDC Centre for Operational Research and Analysis, Ottawa, Canada

    Slawomir Wesolkowski

Authors
  1. Lam T. Bui
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jing Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Axel Bender
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Michael Barlow
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Slawomir Wesolkowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Hussein A. Abbass
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jing Liu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bui, L.T., Liu, J., Bender, A. et al. DMEA: a direction-based multiobjective evolutionary algorithm. Memetic Comp. 3, 271–285 (2011). https://doi.org/10.1007/s12293-011-0072-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12293-011-0072-9

Keywords

Search

Navigation