Abstract
When multi-objective genetic algorithms are applied to real-world problems for deriving Pareto-optimal solutions, the high calculation cost becomes a problem. One solution to this problem is to use a small population size. However, this often results in loss of diversity of the solutions, and therefore solutions with sufficient precision cannot be derived. To overcome this difficulty, the solutions should be replaced when they have converged on a certain point. To perform this replacement, inverse analysis is required to derive the design variables from objects as the solutions are located in the objective space. For this purpose, an Artificial Neural Network (ANN) is applied. Using ANN, the solutions concentrating on certain points are replaced and the diversity of the solutions is maintained. In this paper, a new mechanism using ANN to maintain the diversity of the solutions is proposed. The proposed mechanism was introduced into NSGA-II and applied to test functions. In some functions, the proposed mechanism was useful compared to the conventional method. In other numerical experiments, the results of the proposed algorithm with large populations are discussed and the effectiveness of the proposed mechanism is also described.
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References
Julio l.: hierarchical variable selection in polynomial regression models. http://www.jstor.org/view/00031305/di020596/02p0164o/0
Bishop, C.: Neural networks for pattern recognition. Oxford University Press, Oxford (1997)
Chiba, K., Obayashi, S.: High-fidelity multidisciplinary design op- timization of aerostructural wing shape for regional jet. In: 23rd Applied Aerody- namics Conference (2005)
Deb, K., Meyarivan, T.: Constrained test problems for multi-objective evolu- tionary optimization. In: KanGAL report 200005, Indian Institute of Technology, Kanpur, India (2000)
Gaspar-Cunha, A., Vieira, A.: A hybrid multi-objective evolution- ary algorithm using an inverse neural network (2004)
Henseler, J.: Back propagation. In: Braspenning, P.J., Weijters, A.J.M.M.T., Thuijsman, F. (eds.) Artificial Neural Networks. LNCS, vol. 931, pp. 37–66. Springer, Heidelberg (1995)
Deb, A.P.K., Agrawal, S., Meyarivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: Nsga-ii. In: KanGAL report 200001, Indian Institute of Technology, Kanpur, India (2000)
Tan, K.C., Lee, T.H., Khor, E.F.: Increamenting multi-objective evolutionary al- gorithms: Performance studies and comparisons. In: First International Conference on Evolutionary Multi-Criterion Optimization, pp. 111–125 (2001)
Knowles, J.D., Corne, D.W.: Approximating the nondominated front using the pareto archived evolution strategy, volume 8, pp. 149 – 172 (2000)
Bull, L.: On modelbased evolutionary computation (1999)
Hayman, S.: The mcculloch-pitts model. IEEE Int. Conf. Neural. Netw. Proc. 6, 4438–4439 (1999)
Sacks, J., et al.: Statistical Science 4, 409–435 (1989)
Griffin, I., Adra, S.F., Hamody, A.I., Fleming, P.J.: A hybrid multi-objective evolutionary algorithm using an inverse neural network for air- craft control system designa. In: 2005 IEEE Congress on Evolutionary Computation (CEC’2005), vol. 1, pp. 1–8. IEEE, Los Alamitos (2005)
Shaffer, J.D.: Multiple objective optimization with vector evaluated genetic algo-rithms, pp. 93–100 (1985)
Sirai, H.N.T., Arakawa, M.: Application of rbf network in approximate optimization in satisfcing method. In: Design and Systems, vol.14, pp. 85–86 (2004)
Kamiura, J., Watanabe, S., Hiroyasu, H., Hiroyasu, T., Miki, M.: Multi-objective op- timization of diesel engine emissions and fuel economy using genetic algorithms and phenomenological model. In: SAE 2002 Powertrain and Fluid Systems Conference (2002)
Todoroki, A.: Response surface method, http://orida.mes.titech.ac.jp/responsesurface.pdf
Fujita, K., Kounoe, Y.: Third-order polynominal response surface with opti- mal selection of interaction terms for global approximation. In: Design and Systems, volume 15, pp. 31 – 34
Zitzler, E., Laumanns, M., Thiele, L.: Spea2: Improving the performance of the strength pareto evolutionary algorithm. In: Technical Report 103, Computer Engineering and Communication Networks Lab (TIK), Swiss Federal Institute of Technology (ETH) Zurich (2001)
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Kobayashi, K., Hiroyasu, T., Miki, M. (2007). Mechanism of Multi-Objective Genetic Algorithm for Maintaining the Solution Diversity Using Neural Network. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds) Evolutionary Multi-Criterion Optimization. EMO 2007. Lecture Notes in Computer Science, vol 4403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70928-2_19
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DOI: https://doi.org/10.1007/978-3-540-70928-2_19
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