Abstract
In the last decade, there has been a growing interest in multi-objective evolutionary algorithms that use performance indicators to guide the search. A simple and effective one is the \(\mathcal {S}\)-Metric Selection Evolutionary Multi-Objective Algorithm (SMS-EMOA), which is based on the hypervolume indicator. Even though the maximization of the hypervolume is equivalent to achieving Pareto optimality, its computational cost increases exponentially with the number of objectives, which severely limits its applicability to many-objective optimization problems. In this paper, we present a parallel version of SMS-EMOA, where the execution time is reduced through an asynchronous island model with micro-populations, and diversity is preserved by external archives that are pruned to a fixed size employing a recently created technique based on the Parallel-Coordinates graph. The proposed approach, called \(\mathcal {S}\)-PAMICRO (PArallel MICRo Optimizer based on the \(\mathcal {S}\) metric), is compared to the original SMS-EMOA and another state-of-the-art algorithm (HypE) on the WFG test problems using up to 10 objectives. Our experimental results show that \(\mathcal {S}\)-PAMICRO is a promising alternative that can solve many-objective optimization problems at an affordable computational cost.
C.A. Coello Coello—Author gratefully acknowledges support from CONACyT project no. 221551.
E. Alba—Author is partially funded by the Spanish MINECO and FEDER project TIN2014-57341-R (http://moveon.lcc.uma.es).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
A solution \(\varvec{x} \in \mathcal {S}\) dominates a solution \(\varvec{y} \in \mathcal {S}\) (\(\varvec{x} \prec \varvec{y}\)) if and only if \(\forall i \in \left\{ 1,\ldots ,m\right\} \), \(f_{i}(\varvec{x}) \le f_{i}(\varvec{y})\) and \(\exists j \in \left\{ 1,\ldots ,m\right\} \), \(f_{j}(\varvec{x}) < f_{j}(\varvec{y})\).
- 2.
A density estimator models the distribution of a population, by measuring the similarity degree among individuals.
- 3.
Two solutions \(\varvec{x}, \varvec{y} \in \mathcal {S}\) are incomparable if neither \(\varvec{x} \prec \varvec{y}\) nor \(\varvec{y} \prec \varvec{x}\) holds.
- 4.
Diversity refers to achieving a uniform distribution of solutions covering all regions of the objective function space.
- 5.
. - 6.
A performance indicator, defined as
, measures the quality of an approximation set (the final population of a MOEA). - 7.
This is known as migration.
- 8.
Available at http://computacion.cs.cinvestav.mx/~rhernandez.
- 9.
.
, measures the quality of an approximation set (the final population of a MOEA).References
Adra, S.F., Fleming, P.J.: Diversity management in evolutionary many-objective optimization. IEEE Trans. Evol. Comput. 15(2), 183–195 (2011)
Bader, J., Zitzler, E.: HypE: an algorithm for fast hypervolume-based many-objective optimization. Evol. Comput. 19(1), 45–76 (2011)
Bringmann, K., Friedrich, T.: Don’t be greedy when calculating hypervolume contributions. In: FOGA 2009: Proceedings of the Tenth ACM SIGEVO Workshop on Foundations of Genetic Algorithms, Orlando, Florida, USA, pp. 103–112. ACM, January 2009
Coello Coello, C.A., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-objective Problems, 2nd edn. Springer, New York (2007). ISBN 978-0-387-33254-3
Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Syst. 9, 115–148 (1995)
Emmerich, M.T.M., Beume, N., Naujoks, B.: An EMO algorithm using the hypervolume measure as selection criterion. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 62–76. Springer, Heidelberg (2005)
Fleischer, M.: The measure of Pareto optima applications to multi-objective metaheuristics. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 519–533. Springer, Heidelberg (2003)
Hernández Gómez, R., Coello Coello, C.A.: A multi-objective evolutionary algorithm based on parallel coordinates. In: Proceedings of the 2016 Genetic and Evolutionary Computation Conference (GECCO 2016), New York, NY, USA. ACM Press (2016, in press)
Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Evolutionary many-objective optimization: a short review. In: IEEE Congress on Evolutionary Computation, CEC 2008 (IEEE World Congress on Computational Intelligence), pp. 2419–2426, June 2008
Klinkenberg, J.-W., Emmerich, M.T.M., Deutz, A.H., Shir, O.M., Bäck, T.: A reduced-cost SMS-EMOA using Kriging, self-adaptation, and parallelization. In: Ehrgott, M., Naujoks, B., Stewart, T.J., Wallenius, J. (eds.) Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems, vol. 634, pp. 301–311. Springer, Heidelberg (2010)
Li, B., Li, J., Tang, K., Yao, X.: Many-objective evolutionary algorithms: a survey. ACM Comput. Surv. 48(1), 13:1–13:35 (2015)
Lopez, E.M., Antonio, L.M., Coello Coello, C.A.: A GPU-based algorithm for a faster hypervolume contribution computation. In: Gaspar-Cunha, A., Henggeler Antunes, C., Coello Coello, C.A. (eds.) EMO 2015. LNCS, vol. 9019, pp. 80–94. Springer, Heidelberg (2015)
Lücken, C., Barán, B., Brizuela, C.: A survey on multi-objective evolutionary algorithms for many-objective problems. Comput. Optim. Appl. 58(3), 707–756 (2014)
Luna, F., Alba, E.: Parallel multiobjective evolutionary algorithms. In: Kacprzyk, J., Pedrycz, W. (eds.) Springer Handbook of Computational Intelligence, pp. 1017–1031. Springer, Heidelberg (2015)
Van Veldhuizen, D.A., Zydallis, J.B., Lamont, G.B.: Considerations in engineering parallel multiobjective evolutionary algorithms. IEEE Trans. Evol. Comput. 7(2), 144–173 (2003)
Wagner, T., Beume, N., Naujoks, B.: Pareto-, aggregation-, and indicator-based methods in many-objective optimization. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 742–756. Springer, Heidelberg (2007)
While, L., Bradstreet, L., Barone, L.: A fast way of calculating exact hypervolumes. IEEE Trans. Evol. Comput. 16(1), 86–95 (2012)
Zhou, A., Bo-Yang, Q., Li, H., Zhao, S.-Z., Suganthan, P., Zhang, Q.: Multiobjective evolutionary algorithms: a survey of the state of the art. Swarm Evol. Comput. 1(1), 32–49 (2011)
Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Hernández Gómez, R., Coello Coello, C.A., Alba, E. (2016). A Parallel Version of SMS-EMOA for Many-Objective Optimization Problems. In: Handl, J., Hart, E., Lewis, P., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds) Parallel Problem Solving from Nature – PPSN XIV. PPSN 2016. Lecture Notes in Computer Science(), vol 9921. Springer, Cham. https://doi.org/10.1007/978-3-319-45823-6_53
Download citation
DOI: https://doi.org/10.1007/978-3-319-45823-6_53
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-45822-9
Online ISBN: 978-3-319-45823-6
eBook Packages: Computer ScienceComputer Science (R0)