Abstract
Many practical optimization problems are constrained black boxes. Covariance Matrix Adaptation Evolution Strategies (CMA-ES) belong to the most successful black box optimization methods. Up to now no sophisticated constraint handling method for Covariance Matrix Adaptation optimizers has been proposed. In our novel approach we learn a meta-model of the constraint function and use this surrogate model to adapt the covariance matrix during the search at the vicinity of the constraint boundary. The meta-model can be used for various purposes, i.e. rotation of the mutation ellipsoid, checking the feasibility of candidate solutions or repairing infeasible mutations by projecting them onto the constraint surrogate function. Experimental results show the potentials of the proposed approach.
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References
Coello Coello, C.A.: Theoretical and numerical constraint handling techniques used with evolutionary algorithms: A survey of the state of the art. Computer Methods in Applied Mechanics and Engineering 191(11-12), 1245–1287 (2002)
Hansen, N.: The CMA evolution strategy: A tutorial. Technical report, TU Berlin, ETH Zürich (2005)
Jimenez, F., Verdegay, J.L.: Evolutionary techniques for constrained optimization problems. In: Zimmermann, H.-J. (ed.) 7th European Congress on Intelligent Techniques and Soft Computing (EUFIT 1999). Verlag Mainz, Aachen (1999)
Kramer, O.: Self-Adaptive Heuristics for Evolutionary Computation. Springer, Berlin (2008)
Kuri-Morales, A., Quezada, C.V.: A universal eclectic genetic algorithm for constrained optimization. In: Proceedings 6th European Congress on Intelligent Techniques and Soft Computing (EUFIT 1998), September 1998, pp. 518–522. Verlag Mainz, Aachen (1998)
Marsaglia, G.: Choosing a point from the surface of a sphere. The Annals of Mathematical Statistics 43, 645–646 (1972)
Michalewicz, Z., Fogel, D.B.: How to Solve It: Modern Heuristics. Springer, Berlin (2000)
Ostermeier, A., Gawelczyk, A., Hansen, N.: A derandomized approach to self adaptation of evolution strategies. Evolutionary Computation 2(4), 369–380 (1994)
Schwefel, H.-P.: Evolution and Optimum Seeking. Sixth-Generation Computer Technology. Wiley Interscience, New York (1995)
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Kramer, O., Barthelmes, A., Rudolph, G. (2009). Surrogate Constraint Functions for CMA Evolution Strategies. In: Mertsching, B., Hund, M., Aziz, Z. (eds) KI 2009: Advances in Artificial Intelligence. KI 2009. Lecture Notes in Computer Science(), vol 5803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04617-9_22
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DOI: https://doi.org/10.1007/978-3-642-04617-9_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04616-2
Online ISBN: 978-3-642-04617-9
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