Abstract
The optimum of numerical problems quite often lies on the constraint boundary or even in a vertex of the feasible search space. In such cases the evolutionary algorithm (EA) frequently suffers from premature convergence because of a low success probability near the constraint boundaries. We analyze premature fitness stagnation and the success rates experimentally for an EA using self-adaptive step size control. For a (1+1)-EA with a Rechenberg-like step control mechanism we prove premature step size reduction at the constraint boundary. The proof is based on a success rate analysis considering a simplified mutation distribution model. From the success rates and the possible state transitions, the expected step size change can be derived at each step. We validate the theoretical model with an experimental analysis.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Beyer, H.-G., Schwefel, H.-P.: Evolution strategies - A Comprehensive Introduction. Natural Computing 1, 3–52 (2002)
Hansen, N.: An Analysis of Mutative Sigma Self-Adaptation on Linear Fitness Functions. Evolutionary Computation 14(3), 255–275 (2006)
Joines, J., Houck, C.: On the Use of Non-Stationary Penalty Functions to Solve Nonlinear Constrained Optimization Problems with GAs. In: Fogel, D.B. (ed.) Proceedings of the Conference on Evolutionary Computation, pp. 579–584. IEEE Press, Orlando (1994)
Kramer, O., Schwefel, H.-P.: On Three New Approaches to Handle Constraints Within Evolution Strategies. Natural Computing 5(4), 363–385 (2006)
Kramer, O., Ting, C.-K., Büning, H.K.: A New Mutation Operator for Evolution Strategies for Constrained Problems. In: Proceedings of the Congress on Evolutionary Computation - CEC 2005, pp. 2600–2606 (2005)
Liang, K.-H., Yao, X., Liu, Y., Newton, C.S., Hoffman, D.: An Experimental Investigation of Self-Adaptation in Evolutionary Programming. In: Porto, V.W., Waagen, D. (eds.) EP 1998. LNCS, vol. 1447, pp. 291–300. Springer, Heidelberg (1998)
Meyer-Nieberg, S., Beyer, H.-G.: Self-Adaptation in Evolutionary Algorithms. In: Lobo, F.G., Lima, C.F., Michalewicz, Z. (eds.) Parameter Setting in Evolutionary Algorithms. Springer, Berlin (2007)
Rudolph, G.: Self-Adaptive Mutations Lead to Premature Convergence. IEEE Transactions on Evolutionary Computation 5(4), 410–414 (2001)
Schwefel, H.-P.: Evolution and Optimum Seeking. In: Sixth-Generation Computer Technology. Wiley Interscience, New York (1995)
Stone, C., Smith, J.: Strategy Parameter Variety in Self-Adaptation of Mutation Rates. In: Proceedings of the Genetic and Evolutionary Computation Conference - GECCO 2002, pp. 586–593. Morgan Kaufmann Publishers, San Francisco (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kramer, O. (2008). Premature Convergence in Constrained Continuous Search Spaces. In: Rudolph, G., Jansen, T., Beume, N., Lucas, S., Poloni, C. (eds) Parallel Problem Solving from Nature – PPSN X. PPSN 2008. Lecture Notes in Computer Science, vol 5199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87700-4_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-87700-4_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87699-1
Online ISBN: 978-3-540-87700-4
eBook Packages: Computer ScienceComputer Science (R0)