Skip to main content
SpringerLink
Log in

Evaluating selection methods on hyper-heuristic multi-objective particle swarm optimization

  • Published:
Journal of Heuristics Aims and scope Submit manuscript

Abstract

Multi-objective particle swarm optimization (MOPSO) is a promising meta-heuristic to solve multi-objective problems (MOPs). Previous works have shown that selecting a proper combination of leader and archiving methods, which is a challenging task, improves the search ability of the algorithm. A previous study has employed a simple hyper-heuristic to select these components, obtaining good results. In this research, an analysis is made to verify if using more advanced heuristic selection methods improves the search ability of the algorithm. Empirical studies are conducted to investigate this hypothesis. In these studies, first, four heuristic selection methods are compared: a choice function, a multi-armed bandit, a random one, and the previously proposed roulette wheel. A second study is made to identify if it is best to adapt only the leader method, the archiving method, or both simultaneously. Moreover, the influence of the interval used to replace the low-level heuristic is analyzed. At last, a final study compares the best variant to a hyper-heuristic framework that combines a Multi-Armed Bandit algorithm into the multi-objective optimization based on decomposition with dynamical resource allocation (MOEA/D-DRA) and a state-of-the-art MOPSO. Our results indicate that the resulting algorithm outperforms the hyper-heuristic framework in most of the problems investigated. Moreover, it achieves competitive results compared to a state-of-the-art MOPSO.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Notes

  1. The results of different parameter configurations are available at: http://www.inf.ufpr.br/gmfritsche/hmopsosupplementary.pdf.

References

  • Bader, J., Deb, K., Zitzler, E.: Faster hypervolume-based search using Monte Carlo sampling. Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems, Lecture Notes in Economics and Mathematical Systems, vol. 634, pp. 313–326. Springer, Berlin (2010)

    Google Scholar 

  • Bilgin, B., Özcan, E., Korkmaz, E.: An experimental study on hyper-heuristics and exam timetabling. Practice and Theory of Automated Timetabling VI, Lecture Notes in Computer Science, vol. 3867, pp. 394–412. Springer, Berlin (2007)

    Chapter  Google Scholar 

  • Blazewicz, J., Burke, E., Kendall, G., Mruczkiewicz, W., Oguz, C., Swiercz, A.: A hyper-heuristic approach to sequencing by hybridization of DNA sequences. Ann. Op. Res. 207(1), 27–41 (2013). https://doi.org/10.1007/s10479-011-0927-y

    Article  MathSciNet  MATH  Google Scholar 

  • Bringmann, K., Friedrich, T.: An efficient algorithm for computing hypervolume contributions. Evol. Comput. 18(3), 383–402 (2010). https://doi.org/10.1162/EVCO_a_00012

    Article  Google Scholar 

  • Britto, A., Pozo, A.: Using archiving methods to control convergence and diversity for many-objective problems in particle swarm optimization. In: IEEE Congress on Evolutionary Computation, pp 1–8, (2012). https://doi.org/10.1109/CEC.2012.6256149

  • Brockhoff, D., Wagner, T., Trautmann, H.: On the properties of the R2 indicator. In: Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation, ACM, New York, NY, USA, GECCO ’12, pp 465–472, (2012). https://doi.org/10.1145/2330163.2330230

  • Burke, E.K., Gendreau, M., Hyde, M., Kendall, G., Ochoa, G., Ozcan, E., Qu, R.: Hyper-heuristics: a survey of the state of the art. J. Oper. Res. Soc. 64(12), 1695–1724 (2013)

    Article  Google Scholar 

  • Castro, Jr. O.R., Pozo, A.: A MOPSO based on hyper-heuristic to optimize many-objective problems. In: IEEE Symposium on Swarm Intelligence (SIS), 2014, pp 1–8, (2014). https://doi.org/10.1109/SIS.2014.7011803

  • Castro Jr., O.R., Pozo, A.: Using hyper-heuristic to select leader and archiving methods for many-objective problems. In: Gaspar-Cunha, A., Henggeler Antunes, C., Coello, C.C. (eds.) Evolutionary Multi-Criterion Optimization, Lecture Notes in Computer Science, vol. 9018, pp. 109–123. Springer International Publishing, Berlin (2015). https://doi.org/10.1007/978-3-319-15934-8_8

    Google Scholar 

  • Castro, Jr. O.R., Britto, A., Pozo, A.: A comparison of methods for leader selection in many-objective problems. In: IEEE Congress on Evolutionary Computation, pp 1–8, (2012). https://doi.org/10.1109/CEC.2012.6256415

  • Coello, C.A.C., Cortés, N.C.: Solving multiobjective optimization problems using an artificial immune system. Genet. Progr. Evol. Mach. 6(2), 163–190 (2005). https://doi.org/10.1007/s10710-005-6164-x

    Article  Google Scholar 

  • Coello, C.A.C., Lamont, G.B., Veldhuizen, D.A.V.: Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation). Springer-Verlag, Secaucus, NJ, USA (2006)

    MATH  Google Scholar 

  • Cowling, P., Kendall, G., Soubeiga, E.: A Hyperheuristic Approach to Scheduling a Sales Summit. In: Burke, E., Erben, W. (eds.) Practice and Theory of Automated Timetabling III, Lecture Notes in Computer Science, vol. 2079, pp. 176–190. Springer, Berlin Heidelberg (2001)

    Chapter  Google Scholar 

  • Deb, K., Jain, H.: An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part i: solving problems with box constraints. IEEE Trans. Evolut. Comput. 18(4), 577–601 (2014). https://doi.org/10.1109/TEVC.2013.2281535

    Article  Google Scholar 

  • Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimisation: NSGA-II. In: Proceedings of the 6th International Conference on Parallel Problem Solving from Nature, Springer-Verlag, London, UK, PPSN VI, pp 849–858 (2000)

  • Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. IEEE Congr. Evolut. Comput. 1, 825–830 (2002)

    MATH  Google Scholar 

  • do Nascimento Ferreira, T., Kuk, J.N., Pozo, A., Vergilio, S.R.: Product selection based on upper confidence bound moea/d-dra for testing software product lines. In: 2016 IEEE Congress on Evolutionary Computation (CEC), pp 4135–4142, (2016) https://doi.org/10.1109/CEC.2016.7744315

  • Drake, J., Ozcan, E., Burke, E.: An improved choice function heuristic selection for cross domain heuristic search. In: Coello, C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds.) Parallel Problem Solving from Nature—PPSN XII, Lecture Notes in Computer Science, pp. 307–316. Springer, Berlin Heidelberg (2012). https://doi.org/10.1007/978-3-642-32964-7_31

    Chapter  Google Scholar 

  • Durillo, J.J., García-Nieto, J., Nebro, A.J., Coello, C.A.C., Luna, F., Alba, E.: Multi-objective particle swarm optimizers: An experimental comparison. In: Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization, Springer-Verlag, Berlin, Heidelberg, EMO ’09, pp 495–509 (2009)

  • Eberhart, R.C., Shi, Y.: Particle swarm optimization: developments, applications and resources. In: Proceedings of the 2001 Congress on Evolutionary Computation, vol 1, pp 81–86, (2001) https://doi.org/10.1109/CEC.2001.934374

  • Elarbi, M., Bechikh, S., Gupta, A., Said, L.B., Ong, Y.s.: A New Decomposition-Based NSGA-II for Many-Objective Optimization. IEEE Transactions on Systems, Man, and Cybernetics - Systems pp 1–20, (2017). https://doi.org/10.1109/TSMC.2017.2654301

  • Ferreira, A.S., Gonçalves, R.A., Pozo, A.T.R.: A multi-armed bandit hyper-heuristic. In: 2015 Brazilian Conference on Intelligent Systems (BRACIS), pp 13–18, (2015). https://doi.org/10.1109/BRACIS.2015.31

  • Fialho, A., Da Costa, L., Schoenauer, M., Sebag, M.: Analyzing bandit-based adaptive operator selection mechanisms. Ann. Math. Artif. Intell. 60(1–2), 25–64 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • Friedman, M.: The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J. Am. Stat. Assoc. 32(200), 675–701 (1937)

    Article  MATH  Google Scholar 

  • Gonçalves, R., Kuk, J., Almeida, C., Venske, S.: MOEA/D-HH: a hyper-heuristic for multi-objective problems. In: Gaspar-Cunha, A., Henggeler Antunes, C., Coello, C.C. (eds.) Evolutionary Multi-Criterion Optimization, Lecture Notes in Computer Science, vol. 9018, pp. 94–108. Springer International Publishing, Berlin (2015a). https://doi.org/10.1007/978-3-319-15934-8_7

    Google Scholar 

  • Gonçalves, R.A., Almeida, C.P., Kuk, J.N., Pozo, A.: Moea/d with adaptive operator selection for the environmental/economic dispatch problem. In: 2015 Latin America Congress on Computational Intelligence (LA-CCI), pp 1–6, (2015b) https://doi.org/10.1109/LA-CCI.2015.7435971

  • Gonçalves, R.A., Almeida, C.P., Pozo, A.: Upper confidence bound (UCB) algorithms for adaptive operator selection in moea/d. In: Gaspar-Cunha, A., Henggeler Antunes, C., Coello, C.C. (eds.) Evolutionary Multi-Criterion Optimization, Lecture Notes in Computer Science, vol. 9018, pp. 411–425. Springer International Publishing, Berlin (2015c). https://doi.org/10.1007/978-3-319-15934-8_28

    Google Scholar 

  • Gonçalves, R.A., Almeida, C.P., Pozo, A.: Upper Confidence Bound (UCB) Algorithms for Adaptive Operator Selection in MOEA/D, Springer International Publishing, Cham, pp 411–425. (2015). https://doi.org/10.1007/978-3-319-15934-8_28

  • Guizzo, G., Fritsche, G.M., Vergilio, S.R., Pozo, A.T.R.: A hyper-heuristic for the multi-objective integration and test order problem. In: Proceedings of the 2015 on Genetic and Evolutionary Computation Conference, ACM, New York, NY, USA, GECCO ’15, pp 1343–1350, (2015). https://doi.org/10.1145/2739480.2754725

  • Hansen, M.P., Jaszkiewicz, A.: Evaluating the quality of approximations to the non-dominated set. Tech. Rep. IMM-REP-1998-7, Technical University of Denmark (1998)

  • Helbig, M., Engelbrecht, A.P.: Heterogeneous dynamic vector evaluated particle swarm optimisation for dynamic multi-objective optimisation. In: 2014 IEEE Congress on Evolutionary Computation (CEC), pp 3151–3159, (2014). https://doi.org/10.1109/CEC.2014.6900303

  • Hitomi, N., Selva, D.: A classification and comparison of credit assignment strategies in multiobjective adaptive operator selection. IEEE Trans. Evol. Comput. 21(2), 294–314 (2017). https://doi.org/10.1109/TEVC.2016.2602348

    Article  Google Scholar 

  • Huband, S., Hingston, P., Barone, L., While, L.: A review of multiobjective test problems and a scalable test problem toolkit. IEEE Trans. Evol. Comput. 10(5), 477–506 (2006). https://doi.org/10.1109/TEVC.2005.861417

    Article  MATH  Google Scholar 

  • Jiang, S., Ong, Y.S., Zhang, J., Feng, L.: Consistencies and contradictions of performance metrics in multiobjective optimization. IEEE Trans. Cybern. 44(12), 2391–2404 (2014). https://doi.org/10.1109/TCYB.2014.2307319

    Article  Google Scholar 

  • Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, pp 1942–1948 (1995)

  • Krempser, E., Fialho, Á., Barbosa, H.: Adaptive operator selection at the hyper-level. Parallel Problem Solving from Nature-PPSN XII pp 378–387 (2012)

  • Kruskal, W.H., Wallis, W.A.: Use of ranks in one-criterion variance analysis. J. Am. Stat. Assoc. 47(260), 583–621 (1952)

    Article  MATH  Google Scholar 

  • Laumanns, M., Zenklusen, R.: Stochastic convergence of random search methods to fixed size Pareto front approximations. Eur. J. Oper. Res. 213(2), 414–421 (2011). https://doi.org/10.1016/j.ejor.2011.03.039

    Article  MathSciNet  MATH  Google Scholar 

  • Li, K., Fialho, Á., Kwong, S.: Multi-objective differential evolution with adaptive control of parameters and operators. Learning and Intelligent Optimization, pp. 473–487. Springer, Berlin Heidelberg (2011)

    Chapter  Google Scholar 

  • Li, K., Fialho, A., Kwong, S., Zhang, Q.: Adaptive operator selection with bandits for a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 18(1), 114–130 (2014a). https://doi.org/10.1109/tevc.2013.2239648

    Article  Google Scholar 

  • Li, K., Deb, K., Zhang, Q., Kwong, S.: An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans. Evol. Comput. 19(5), 694–716 (2015). https://doi.org/10.1109/TEVC.2014.2373386

    Article  Google Scholar 

  • Li, M., Yang, S., Liu, X.: Diversity comparison of pareto front approximations in many-objective optimization. IEEE Trans. Cybern. 44(12), 2568–2584 (2014b). https://doi.org/10.1109/TCYB.2014.2310651

    Article  Google Scholar 

  • Luke, S.: Essentials of Metaheuristics, 2nd edn. Lulu, available for free at (2013). http://cs.gmu.edu/~sean/book/metaheuristics/

  • Maashi, M., Özcan, E., Kendall, G.: A multi-objective hyper-heuristic based on choice function. Expert Syst. Appl. 41(9), 4475–4493 (2014)

    Article  Google Scholar 

  • Maturana, J., Fialho, Á., Saubion, F., Schoenauer, M., Lardeux, F., Sebag, M.: Adaptive operator selection and management in evolutionary algorithms. Autonomous Search, pp. 161–189. Springer, Berlin, Heidelberg (2012)

    Google Scholar 

  • Mostaghim, S., Teich, J.: Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO). In: Proceedings of the 2003 IEEE Swarm Intelligence Symposium., pp 26–33 (2003)

  • Nebro, A.J., Durillo, J.J., Garcia-Nieto, J., Coello, C.A.C., Luna, F., Alba, E.: SMPSO: A new PSO-based metaheuristic for multi-objective optimization. In: Computational intelligence in multi-criteria decision-making., IEEE, pp 66–73 (2009)

  • Ozcan, E., Bykov, Y., Birben, M., Burke, E.: Examination timetabling using late acceptance hyper-heuristics. In: IEEE Congress on Evolutionary Computation, 2009. CEC ’09. pp 997–1004, (2009). https://doi.org/10.1109/CEC.2009.4983054

  • Padhye, N., Branke, J., Mostaghim, S.: Empirical comparison of MOPSO methods: guide selection and diversity preservation. In: Proceedings of the Eleventh Congress on Evolutionary Computation, IEEE Press, Piscataway, NJ, USA, CEC’09, pp 2516–2523 (2009)

  • Parsopoulos, K.E., Vrahatis, M.N.: Multi-Objective Particles Swarm Optimization Approaches. In: Multi-Objective Optimization in Computational Intelligence, IGI Global, pp 20–42, 10.4018/978-1-59904-498-9.ch002, (2008). URL http://services.igi-global.com/resolvedoi/resolve.aspx?doi=10.4018/978-1-59904-498-9.ch002

  • Phan, D., Suzuki, J.: R2-IBEA: R2 indicator based evolutionary algorithm for multiobjective optimization. In: IEEE Congress on Evolutionary Computation, pp 1836–1845, (2013). https://doi.org/10.1109/CEC.2013.6557783

  • Reyes-Sierra, M., Coello, C.A.C.: Multi-objective particle swarm optimizers: a survey of the state-of-the-art. Int. J. Comput. Intell. Res. 2(3), 287–308 (2006)

    MathSciNet  Google Scholar 

  • Sabar, N., Ayob, M., Kendall, G., Qu, R.: A dynamic multiarmed bandit-gene expression programming hyper-heuristic for combinatorial optimization problems. IEEE Trans. Cybern. 45(2), 217–228 (2015). https://doi.org/10.1109/TCYB.2014.2323936

    Article  Google Scholar 

  • Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: IEEE International Conference on Evolutionary Computation, pp 69–73, (1998). https://doi.org/10.1109/ICEC.1998.699146

  • Trivedi, A., Srinivasan, D., Sanyal, K., Ghosh, A.: A survey of multiobjective evolutionary algorithms based on decomposition. IEEE Transactions on Evolutionary Computation PP(99): 1–1, (2016). https://doi.org/10.1109/TEVC.2016.2608507

  • While, L., Bradstreet, L., Barone, L.: A fast way of calculating exact hypervolumes. IEEE Trans. Evol. Comput. 16(1), 86–95 (2012)

    Article  Google Scholar 

  • Yuan, Y., Xu, H., Wang, B., Yao, X.: A new dominance relation-based evolutionary algorithm for many-objective optimization. IEEE Trans. Evol. Comput. 20(1), 16–37 (2016). https://doi.org/10.1109/TEVC.2015.2420112

    Article  Google Scholar 

  • Zhang, Q., Liu, W., Li, H.: The performance of a new version of MOEA/D on CEC09 unconstrained MOP test instances. In: IEEE Congress on Evolutionary Computation, pp. 203–208, (2009). https://doi.org/10.1109/CEC.2009.4982949

  • Zhu, Q., Lin, Q., Chen, W., Wong, K.C., Coello, C.A.C., Li, J., Chen, J., Zhang, J.: An external archive-guided multiobjective particle swarm optimization algorithm. IEEE Trans. Cybern. 47(9), 2794–2808 (2017). https://doi.org/10.1109/TCYB.2017.2710133

    Article  Google Scholar 

  • 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 

Download references

Acknowledgements

The authors would like to thank the Academic Publishing Advisory Center (Centro de Assessoria de Publicação Acadêmica, CAPA - www.capa.ufpr.br) of the Federal University of Paraná for assistance with English language editing. Also, the authors would like to thank CNPq (National Council for Scientific and Technological Development) and CAPES (Coordination for the Improvement of Higher Education Personnel) for the financial support.

Author information

Authors and Affiliations

  1. Computer Science’s Department, Federal University of Paraná, Curitiba, Paraná, Brazil

    Olacir R. Castro Jr., Gian Mauricio Fritsche & Aurora Pozo

Authors
  1. Olacir R. Castro Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gian Mauricio Fritsche
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aurora Pozo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Olacir R. Castro Jr..

Additional information

This work was supported by CNPq, National Council for Scientific and Technological Development—Brazil (Productivity Grant Nos. 305986/2012-0 and Program Science Without Borders Nos. 200040/2015-4).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Castro, O.R., Fritsche, G.M. & Pozo, A. Evaluating selection methods on hyper-heuristic multi-objective particle swarm optimization. J Heuristics 24, 581–616 (2018). https://doi.org/10.1007/s10732-018-9369-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10732-018-9369-x

Keywords

Search

Navigation