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International Conference on Parallel Problem Solving from Nature

PPSN 2018: Parallel Problem Solving from Nature – PPSN XV pp 335–346Cite as

Towards a More General Many-objective Evolutionary Optimizer

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11101))

Abstract

Recently, it has been shown that the current Many-Objective Evolutionary Algorithms (MaOEAs) are overspecialized in solving certain benchmark problems. This overspecialization is due to a high correlation between the Pareto fronts of the test problems with the convex weight vectors commonly used by MaOEAs. The main consequence of such overspecialization is the inability of these MaOEAs to solve the minus versions of well-known benchmarks (e.g., the DTLZ\(^{-1}\) test suite). In furtherance of avoiding this issue, we propose a novel steady-state MaOEA that does not require weight vectors and uses a density estimator based on the IGD\(^+\) indicator. Moreover, a fast method to calculate the IGD\(^+\) contributions is integrated in order to reduce the computational cost of the proposed approach, which is called IGD\(^+\)-MaOEA. Our proposed approach is compared with NSGA-III, MOEA/D, IGD\(^+\)-EMOA (the previous ones employ convex weight vectors) and SMS-EMOA on the test suites DTLZ and DTLZ\(^{-1}\), using the hypervolume indicator. Our experimental results show that IGD\(^+\)-MaOEA is a more general optimizer than MaOEAs that need a set of convex weight vectors and it is competitive and less computational expensive than SMS-EMOA.

The first author acknowledges support from CONACyT and CINVESTAV-IPN to pursue graduate studies in Computer Science. The second author gratefully acknowledges support from CONACyT project no. 221551.

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Notes

  1. 1.

    Given two solutions \({\varvec{u}}, {\varvec{v}} \in \mathbb {R}^m\), \({\varvec{u}}\) dominates \({\varvec{v}}\) (denoted as \({\varvec{u}} \prec {\varvec{v}}\)), if and only if \(u_i \le v_i\) for all \(i=1, \dots , m\) and there exists at least an index \(j \in \{1, \dots , m\}\) such that \(u_i < v_i\). In case \(u_i \le v_i\) for all \(i=1, \dots , m\), \({\varvec{u}}\) is said to weakly dominate \({\varvec{v}}\) (denoted as \({\varvec{u}} \preceq {\varvec{v}}\)).

  2. 2.

    A unary performance indicator I is a function that assigns a real value to a set of m-dimensional vectors.

  3. 3.

    Let A and B be two non-empty sets of m-dimensional vectors and let I be a unary indicator. I is weakly Pareto-compliant if and only if A weakly dominates B implies \(I(A) \le I(B)\) (assuming minimization of I).

  4. 4.

    Simulated binary crossover (SBX) and polynomial-based mutation operators are employed [8].

  5. 5.

    The source code of IGD\(^+\)-MaOEA is available at http://computacion.cs.cinvestav.mx/~jfalcon/IGD+-MOEA.html.

  6. 6.

    We used the implementation available at: http://web.ntnu.edu.tw/~tcchiang/publications/nsga3cpp/nsga3cpp.htm.

  7. 7.

    We used the implementation available at: http://dces.essex.ac.uk/staff/zhang/webofmoead.htm.

  8. 8.

    The source code was provided by its author, Edgar Manoatl Lopez.

  9. 9.

    We employed the implementation available at jMetal 4.5.

References

  1. Coello, C.A.C., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-objective Problems, 2nd edn. Springer, New York (2007). https://doi.org/10.1007/978-0-387-36797-2. ISBN 978-0-387-33254-3

    Book  MATH  Google Scholar 

  2. Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Evolutionary many-objective optimization: a short review. In: 2008 Congress on Evolutionary Computation (CEC 2008), Hong Kong, pp. 2424–2431. IEEE Service Center, June 2008

    Google Scholar 

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

    Article  Google Scholar 

  4. 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. Evol. Comput. 18(4), 577–601 (2014)

    Article  Google Scholar 

  5. Lopez, E.M., Coello, C.A.C.: IGD\(^+\)-EMOA: a multi-objective evolutionary algorithm based on IGD\(^{+}\). In: 2016 IEEE Congress on Evolutionary Computation (CEC 2016), Vancouver, Canada, 24–29 July 2016, pp. 999–1006. IEEE Press (2016). ISBN 978-1-5090-0623-9

    Google Scholar 

  6. Gómez, R.H., Coello, C.A.C.: Improved metaheuristic based on the \(R2\) indicator for many-objective optimization. In: 2015 Genetic and Evolutionary Computation Conference (GECCO 2015), Madrid, Spain, July 11–15 2015, pp. 679–686. ACM Press (2015). ISBN 978-1-4503-3472-3

    Google Scholar 

  7. Ishibuchi, H., Setoguchi, Y., Masuda, H., Nojima, Y.: Performance of decomposition-based many-objective algorithms strongly depends on pareto front shapes. IEEE Trans. Evol. Comput. 21(2), 169–190 (2017)

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: multiobjective selection based on dominated hypervolume. Eur. J. Oper. Res. 181(3), 1653–1669 (2007)

    Article  Google Scholar 

  10. Fleischer, M.: The measure of pareto optima applications to multi-objective metaheuristics. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Thiele, L., Deb, K. (eds.) EMO 2003. LNCS, vol. 2632, pp. 519–533. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36970-8_37

    Chapter  Google Scholar 

  11. Ishibuchi, H., Masuda, H., Tanigaki, Y., Nojima, Y.: Modified distance calculation in generational distance and inverted generational distance. In: Gaspar-Cunha, A., Henggeler Antunes, C., Coello, C.C. (eds.) EMO 2015. LNCS, vol. 9019, pp. 110–125. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-15892-1_8

    Chapter  Google Scholar 

  12. Falcón-Cardona, J.G., Coello, C.A.C.: Multi-objective evolutionary hyper-heuristic based on multiple indicator-based density estimators. In: 2018 Genetic and Evolutionary Computation Conference (GECCO 2018), Kyoto, Japan, 15–19 July 2018. ACM Press (To be published)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Science Department, CINVESTAV-IPN, Av. IPN No. 2508, Col. San Pedro Zacatenco, 07300, México D.F., Mexico

    Jesús Guillermo Falcón-Cardona & Carlos A. Coello Coello

Authors
  1. Jesús Guillermo Falcón-Cardona
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  2. Carlos A. Coello Coello
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Correspondence to Jesús Guillermo Falcón-Cardona .

Editor information

Editors and Affiliations

  1. Inria Saclay, Palaiseau, France

    Anne Auger

  2. University of Coimbra, Coimbra, Portugal

    Carlos M. Fonseca

  3. University of Coimbra, Coimbra, Portugal

    Nuno Lourenço

  4. University of Coimbra, Coimbra, Portugal

    Penousal Machado

  5. University of Coimbra, Coimbra, Portugal

    Luís Paquete

  6. Colorado State University, Fort Collins, Colorado, USA

    Darrell Whitley

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Falcón-Cardona, J.G., Coello Coello, C.A. (2018). Towards a More General Many-objective Evolutionary Optimizer. In: Auger, A., Fonseca, C., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds) Parallel Problem Solving from Nature – PPSN XV. PPSN 2018. Lecture Notes in Computer Science(), vol 11101. Springer, Cham. https://doi.org/10.1007/978-3-319-99253-2_27

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  • DOI: https://doi.org/10.1007/978-3-319-99253-2_27

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