Abstract
The recently proposed Pareto Tracer method is an effective numerical continuation technique which allows performing movements along the set of KKT points of a given multi-objective optimization problem. The nature of this predictor-corrector method leads to constructing solutions along the Pareto set/front numerically; it applies to higher dimensions and can handle box and equality constraints. We argue that the right hybridization of multi-objective evolutionary algorithms together with specific continuation methods leads to fast and reliable algorithms. Moreover, due to the continuation technique, the resulting hybrid algorithm could have a certain advantage when handling, in particular, equality constraints. In this paper, we make the first effort to hybridize NSGA-II with the Pareto Tracer. To support our claims, we present some numerical results on continuously differentiable equality constrained bi-objective optimization test problems, to show that the resulting hybrid NSGAII/PT is highly competitive against some state-of-the-art algorithms for constrained optimization. Finally, we stress that the chosen approach could be applied to a more significant number of objectives with some adaptations of the algorithm, leading to a very promising research topic.
The authors acknowledge support for CONACyT project No. 285599 and IPN project SIP20181450.
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References
Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: multiobjective selection based on dominated hypervolume. Eur. J. Oper. Res. 181(3), 1653–1669 (2007)
Bosman, P.A.N., de Jong, E.D.: Exploiting gradient information in numerical multi-objective evolutionary optimization. In: Genetic and Evolutionary Computation Conference - GECCO 2005. ACM (2005)
Brown, M., Smith, R.E.: Directed multi-objective optimization. Int. J. Comput. Syst. Sig. 6(1), 3–17 (2005)
Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms. Wiley, New York (2001)
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)
Dilettoso, E., Rizzo, S.A., Salerno, N.: A weakly Pareto compliant quality indicator. Math. Comput. Appl. 22(1) (2017)
Dominguez-Isidro, S., Mezura-Montes, E.: The baldwin effect on a memetic differential evolution for constrained numerical optimization problems. In: Proceedings of the Genetic and Evolutionary Optimization Conference, pp. 1–8 (2017)
Fan, Z., et al.: An improved epsilon constraint handling method embedded in MOEA/D for constrained multi-objective optimization problems. In: 2016 IEEE Symposium Series on Computational Intelligence (SSCI), pp. 1–8 (2016)
Fliege, J., Drummond, L.M.G., Svaiter, B.F.: Newton’s method for multiobjective optimization. SIAM J. Optim. 20, 602–626 (2009)
Gerstl, K., Rudolph, G., Schütze, O., Trautmann, H.: Finding evenly spaced fronts for multiobjective control via averaging Hausdorff-measure. In: Proceedings of 8th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), pp. 1–6. IEEE Press (2011)
Hernández-Ocana, B., Mezura-Montes, E., del Pilar Pozos-Parra, M.: Evolutionary bacterial foraging algorithm to solve constrained numerical optimization problems. In: New Tendencies in Logic, Languages, Algorithms, and New Methods of Reasoning, pp. 29–42 (2016)
Hu, X., Huang, Z., Wang, Z.: Hybridization of the multi-objective evolutionary algorithms and the gradient-based algorithms. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 870–877 (2003)
Knowles, J., Corne, D.: Memetic algorithms for multiojective optimization: issues, methods and prospects. In: Hart, W.E., Smith, J.E., Krasnogor, N. (eds.) Recent Advances in Memetic Algorithms. STUDFUZZ, vol. 166, pp. 313–352. Springer, Heidelberg (2005). https://doi.org/10.1007/3-540-32363-5_14
Knowles, J.D., Corne, D.W.: M-PAES: a memetic algorithm for multiobjective optimization. In: Proceedings of the IEEE Congress on Evolutionary Computation, Piscataway, New Jersey, pp. 325–332 (2000)
Kukkonen, S., Lampinen, J.: GDE3: the third evolution step of generalized differential evolution. In: The 2005 IEEE Congress on Evolutionary Computation, vol. 1, pp. 443–450. IEEE (2005)
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)
Martín, A., Schütze, O.: Pareto tracer: a predictor-corrector method for multi-objective optimization problems. Eng. Optim. 50(3), 516–536 (2018)
Ong, Y.W., Keane, A.J.: Meta-Lamarckian learning in memetic algorithms. IEEE Trans. Evol. Comput. 8(2), 99–110 (2004)
Peitz, S., Dellnitz, M.: A survey of recent trends in multiobjective optimal control-surrogate models, feedback control and objective reduction. Math. Comput. Appl. 23(2) (2018)
Saha, A., Ray, T.: Equality constrained multi-objective optimization. In: 2012 IEEE Congress on Evolutionary Computation, CEC 2012, pp. 1–7, June 2012
Schütze, O., Coello Coello, C.A., Mostaghim, S., Talbi, E.-G., Dellnitz, M.: Hybridizing evolutionary strategies with continuation methods for solving multi-objective problems. Eng. Optim. 40(5), 383–402 (2008)
Schütze, O., Esquivel, X., Lara, A., Coello Coello, C.A.: Using the averaged Hausdorff distance as a performance measure in evolutionary multiobjective optimization. IEEE Trans. Evol. Comput. 16(4), 504–522 (2012)
Schütze, O., Alvarado, S., Segura, C., Landa, R.: Gradient subspace approximation: a direct search method for memetic computing. Soft Comput. 21(21), 6331–6350 (2017)
Takahama, T., Sakai, S.: Constrained optimization by the \(\epsilon \)-constrained differential evolution with gradient-based mutation and feasible elites (2006)
Takahama, T., Sakai, S., Iwane, N.: Solving nonlinear constrained optimization problems by the \(\varepsilon \) constrained differential evolution. In: IEEE 2006, vol. 3, pp. 2322–2327. IEEE (2006)
Trautmann, H., Wagner, T., Brockhoff, D.: R2-EMOA: focused multiobjective search using R2-indicator-based selection. In: Nicosia, G., Pardalos, P. (eds.) LION 2013. LNCS, vol. 7997, pp. 70–74. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-44973-4_8
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Cuate, O. et al. (2019). A New Hybrid Metaheuristic for Equality Constrained Bi-objective Optimization Problems. In: Deb, K., et al. Evolutionary Multi-Criterion Optimization. EMO 2019. Lecture Notes in Computer Science(), vol 11411. Springer, Cham. https://doi.org/10.1007/978-3-030-12598-1_5
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