Skip to main content

Advertisement

SpringerLink
Log in

A reference point-based evolutionary algorithm for approximating regions of interest in multiobjective problems

  • Original Paper
  • Published:
TOP Aims and scope Submit manuscript

Abstract

Most evolutionary multiobjective optimization algorithms are designed to approximate the entire Pareto front. During the last decade, a series of preference-based evolutionary algorithms have been developed, where a part of the Pareto front is approximated by incorporating the preferences of a Decision Maker. However, only a few such algorithms are able to obtain well-distributed solutions covering the complete “region of interest” that is determined by a reference point. In this paper, a preference-based evolutionary algorithm for approximating the region of interest is proposed. It is based on the state-of-the-art genetic algorithm NSGA-II and the CHIM approach introduced in the NBI method which is used to obtain uniformly distributed solutions in the region of interest. The efficiency of the proposed algorithm has been experimentally evaluated and compared to other state-of-the-art multiobjective preference-based evolutionary algorithms by solving a set of multiobjective optimization benchmark problems. It has been shown that the incorporation of the Decision Maker’s preferences and the CHIM approach into the NSGA-II algorithm allows approximating the whole region of interest accurately while maintaining a good distribution of the obtained solutions.

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

Similar content being viewed by others

References

  • Agrawal RB, Deb K, Agrawal R (1995) Simulated binary crossover for continuous search space. Complex Syst 9(2):115–148

    Google Scholar 

  • Bechikh S, Kessentini M, Said LB, Ghédira K (2015) Chapter Four—Preference incorporation in evolutionary multiobjective optimization: a survey of the state-of-the-art. Adv Comput 98:141–207

    Google Scholar 

  • Benson HP, Sayin S (1997) Towards finding global representations of the efficient set in multiple objective mathematical programming. Nav Res Logist 44(1):47–67

    Google Scholar 

  • Branke J (2016) MCDA and multiobjective evolutionary algorithms. Multiple criteria decision analysis. Springer, New York, pp 977–1008

    Google Scholar 

  • Cabello J, Luque M, Miguel F, Ruiz A, Ruiz F (2014) A multiobjective interactive approach to determine the optimal electricity mix in Andalucía (Spain). Top 22(1):109–127

    Google Scholar 

  • Coello CAC, Van Veldhuizen DA, Lamont GB (2002) Evolutionary algorithms for solving multi-objective problems, vol 242. Springer, New York

    Google Scholar 

  • Das I, Dennis JE (1998) Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM J Optim 8(3):631–657

    Google Scholar 

  • Deb K (1999) Multi-objective genetic algorithms: problem difficulties and construction of test problems. Evol Comput 7:205–230

    Google Scholar 

  • Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, New York

    Google Scholar 

  • Deb K, Jain H (2014) An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans Evol Comput 18(4):577–601

    Google Scholar 

  • Deb K, Kumar A (2007) Interactive evolutionary multi-objective optimization and decision-making using reference direction method. In: Proceedings of the 9th annual conference on genetic and evolutionary computation, ACM, pp 781–788

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

  • Deb K, Thiele L, Laumanns M, Zitzler E (2002b) Scalable multi-objective optimization test problems. In: Proceedings of the 2002 congress on evolutionary computation, CEC’02, pp 825–830, IEEE

  • Deb K, Sundar J, Udaya Bhaskara Rao N, Chaudhuri S (2006) Reference point based multi-objective optimization using evolutionary algorithms. Int J Comput Intell Res 2(3):273–286

    Google Scholar 

  • Deb K, Siegmund F, Ng AH (2014) R-HV: a metric for computing hyper-volume for reference point based EMOs. In: International conference on swarm, evolutionary, and memetic computing, Springer, pp 98–110

  • Figueira JR, Liefooghe A, Talbi EG, Wierzbicki AP (2010) A parallel multiple reference point approach for multi-objective optimization. Eur J Oper Res 205(2):390–400

    Google Scholar 

  • Filatovas E, Kurasova O, Sindhya K (2015) Synchronous R-NSGA-II: an extended preference-based evolutionary algorithm for multi-objective optimization. Informatica 26(1):33–50

    Google Scholar 

  • Filatovas E, Kurasova O, Redondo JL, Fernández J (2016) A preference-based multi-objective evolutionary algorithm for approximating a region of interest. In: XIII Globall optimizatin workshop, GOW’16, pp 21–24

  • Filatovas E, Lančinskas A, Kurasova O, Žilinskas J (2017) A preference-based multi-objective evolutionary algorithm R-NSGA-II with stochastic local search. Cent Eur J Oper Res 25(4):859–878

    Google Scholar 

  • Fonseca CM, Fleming PJ et al (1993) Genetic algorithms for multiobjective optimization: formulation, discussion and generalization. In: ICGA, vol 93, Morgan Kaufmann Publishers Inc., pp 416–423

  • Hong W, Tang K (2016) Convex hull-based multi-objective evolutionary computation for maximizing receiver operating characteristics performance. Memet Comput 8(1):35–44

    Google Scholar 

  • Hong W, Lu G, Yang P, Wang Y, Tang K (2015) A new evolutionary multi-objective algorithm for convex hull maximization. In: IEEE Congress on evolutionary computation, CEC’15, pp 931–938, IEEE

  • Karasakal E, Silav A (2016) A multi-objective genetic algorithm for a bi-objective facility location problem with partial coverage. Top 24(1):206–232

    Google Scholar 

  • Korhonen PJ, Laakso J (1986) A visual interactive method for solving the multiple criteria problem. Eur J Oper Res 24(2):277–287

    Google Scholar 

  • Kurasova O, Petkus T, Filatovas E (2013) Visualization of Pareto front points when solving multi-objective optimization problems. Inf Technol Control 42(4):353–361

    Google Scholar 

  • Lam JSL (2010) An integrated approach for port selection, ship scheduling and financial analysis. Netnomics Econ Res Electron Netw 11(1):33–46

    Google Scholar 

  • Li K, Deb K (2016) Performance assessment for preference-based evolutionary multi-objective optimization using reference points. COIN Rep 1(1):1–23

    Google Scholar 

  • Li L, Yevseyeva I, Basto-Fernandes V, Trautmann H, Jing N, Emmerich M (2017) Building and using an ontology of preference-based multiobjective evolutionary algorithms. In: International conference on evolutionary multi-criterion optimization, pp 406–421

  • Messac A, Mattson CA (2004) Normal constraint method with guarantee of even representation of complete Pareto frontier. AIAA J 42(10):2101–2111

    Google Scholar 

  • Messac A, Ismail-Yahaya A, Mattson CA (2003) The normalized normal constraint method for generating the Pareto frontier. Struct Multidiscip Optim 25(2):86–98

    Google Scholar 

  • Miettinen K (1999) Nonlinear multiobjective optimization. Springer, New York

    Google Scholar 

  • Mohammadi A, Omidvar MN, Li X (2013) A new performance metric for user-preference based multi-objective evolutionary algorithms. In: 2013 IEEE Congress on evolutionary computation (CEC), pp 2825–2832

  • Molina J, Santana LV, Hernández-Díaz AG, Coello Coello CA, Caballero R (2009) g-dominance: Reference point based dominance for multiobjective metaheuristics. Eur J Oper Res 197(2):685–692

    Google Scholar 

  • Moreno J, Ortega G, Filatovas E, Martínez JA, Garzón EM (2018) Improving the performance and energy of non-dominated sorting for evolutionary multiobjective optimization on GPU/CPU platforms. J Glob Optim 71(3):631–649

    Google Scholar 

  • Motta RS, Afonso SM, Lyra PR (2012) A modified NBI and NC method for the solution of N-multiobjective optimization problems. Struct Multidiscip Optim 46(2):239–259

    Google Scholar 

  • Ortega G, Filatovas E, Garzón E, Casado LG (2017) Non-dominated sorting procedure for Pareto dominance ranking on multicore CPU and/or GPU. J Glob Optim 69(3):607–627

    Google Scholar 

  • Petkus T, Filatovas E, Kurasova O (2009) Investigation of human factors while solving multiple criteria optimization problems in computer network. Technol Econ Dev Econ 15(3):464–479

    Google Scholar 

  • Purshouse RC, Deb K, Mansor MM, Mostaghim S, Wang R (2014) A review of hybrid evolutionary multiple criteria decision making methods. In: 2014 IEEE Congress on evolutionary computation, CEC’14), pp 1147–1154, IEEE

  • Redondo J, Fernández J, Álvarez J, Arrondo A, Ortigosa P (2015) Approximating the Pareto-front of a planar bi-objective competitive facility location and design problem. Comput Oper Res 62(1):337–349

    Google Scholar 

  • Roy PC, Islam MM, Deb K (2016) Best order sort: a new algorithm to non-dominated sorting for evolutionary multi-objective optimization. In: Proceedings of the 2016 on genetic and evolutionary computation conference companion, pp 1113–1120, ACM

  • Ruiz AB, Saborido R, Luque M (2015a) A preference-based evolutionary algorithm for multiobjective optimization: the weighting achievement scalarizing function genetic algorithm. J Glob Optim 62(1):101–129

  • Ruiz AB, Sindhya K, Miettinen K, Ruiz F, Luque M (2015b) E-NAUTILUS: a decision support system for complex multiobjective optimization problems based on the NAUTILUS method. Eur J Oper Res 246(1):218–231

  • Said LB, Bechikh S, Ghédira K (2010) The r-dominance: a new dominance relation for interactive evolutionary multicriteria decision making. IEEE Trans Evol Comput 14(5):801–818

    Google Scholar 

  • Santos J, Ferreira A, Flintsch G (2017) A multi-objective optimization-based pavement management decision-support system for enhancing pavement sustainability. J Clean Prod 164:1380–1393

    Google Scholar 

  • Shao L, Ehrgott M (2016) Discrete representation of non-dominated sets in multi-objective linear programming. Eur J Oper Res 255(3):687–698

    Google Scholar 

  • Siddiqui S, Azarm S, Gabriel SA (2012) On improving normal boundary intersection method for generation of Pareto frontier. Struct Multidiscip Optim 46(6):839–852

    Google Scholar 

  • Siegmund F, Ng AH, Deb K (2012) Finding a preferred diverse set of Pareto-optimal solutions for a limited number of function calls. In: 2012 IEEE Congress on evolutionary computation, CEC’12, pp 1–8

  • Talbi EG (2009) Metaheuristics: from design to implementation, vol 74. Wiley, New York

    Google Scholar 

  • Tang S, Cai Z, Zheng J (2008) A fast method of constructing the non-dominated set: Arena’s principle. In: Fourth international conference on natural computation, ICNC’08, vol 1, pp 391–395, IEEE

  • Thiele L, Miettinen K, Korhonen PJ, Molina J (2009) A preference-based evolutionary algorithm for multi-objective optimization. Evol Comput 17(3):411–436

    Google Scholar 

  • Wickramasinghe UK, Carrese R, Li X (2010) Designing airfoils using a reference point based evolutionary many-objective particle swarm optimization algorithm. In: 2010 IEEE Congress on evolutionary computation, CEC’10, pp 1–8

  • Yuan X, Tian H, Yuan Y, Huang Y, Ikram RM (2015) An extended NSGA-III for solution multi-objective hydro-thermal-wind scheduling considering wind power cost. Energy Convers Manag 96:568–578

    Google Scholar 

  • Zapotecas Martínez S, Coello Coello CA (2010) a novel diversification strategy for multi-objective evolutionary algorithms. In: Proceedings of the 12th annual conference companion on genetic and evolutionary computation, GECCO’10, pp 2031–2034. ACM, New York, NY, USA

  • Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731

    Google Scholar 

  • Zhang X, Ye T, Cheng R, Jin Y (2012) An efficient approach to non-dominated sorting for evolutionary multi-objective optimization. IEEE Trans Evol Comput 19(2):201–213

    Google Scholar 

  • Zitzler E, Thiele L, Laumanns M, Fonseca CM, Da Fonseca VG (2003) Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans Evol Comput 7(2):117–132

    Google Scholar 

  • Zitzler E, Thiele L (1998) Multiobjective optimization using evolutionary algorithms—a comparative case study. In: Parallel problem solving from nature—PPSN V, Springer, pp 292–301

Download references

Acknowledgements

The research work of E. Filatovas was funded by a Grant (no. S-MIP-17-67) from the Research Council of Lithuania. The research work of J. L. Redondo and J. Fernández was funded by Grants from the Spanish Ministry of Economy and Competitiveness (MTM2015-70260-P, TIN2015-66680-C2-1-R, RTI2018-095993-B-100), Fundación Séneca (The Agency of Science and Technology of the Region of Murcia, 19241/PI/14 and 20817/PI/18), Junta de Andalucía (P12-TIC301, UAL18-TIC-A020-B), in part financed by the European Regional Development Fund (ERDF).

Author information

Authors and Affiliations

  1. Institute of Data Science and Digital Technologies, Vilnius University, Akademijos str. 4, 08663, Vilnius, Lithuania

    E. Filatovas & O. Kurasova

  2. Department of Informatics, Agrifood Campus of International Excellence (ceiA3), University of Almería, Ctra. Sacramento s/n. La Cañada de San Urbano, 04120, Almería, Spain

    J. L. Redondo

  3. Department of Statistics and Operations Research, University of Murcia, Campus de Espinardo, 30100, Espinardo, Murcia, Spain

    J. Fernández

Authors
  1. E. Filatovas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. Kurasova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. L. Redondo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. Fernández
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. Filatovas.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Filatovas, E., Kurasova, O., Redondo, J.L. et al. A reference point-based evolutionary algorithm for approximating regions of interest in multiobjective problems. TOP 28, 402–423 (2020). https://doi.org/10.1007/s11750-019-00535-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11750-019-00535-z

Keywords

Mathematics Subject Classification

Search

Navigation