Abstract
This paper studies the behaviour of the (1 + 1)-ES when applied to a linear problem with a single linear constraint. It goes beyond previous work by considering constraint planes that do not contain the gradient direction. The behaviour of the distance of the search point from the constraint plane forms a Markov chain. The limit distribution of that chain is approximated using an exponential model, and progress rates and success probabilities are derived. Consequences for the working of step length adaptation mechanisms based on success probabilities are discussed.
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References
Arnold, D.V.: On the use of evolution strategies for optimising certain positive definite quadratic forms. In: Proceedings of the 2007 Genetic and Evolutionary Computation Conference — GECCO 2007, pp. 634–641. ACM Press, New York (2007)
Arnold, D.V., MacLeod, A.: Step length adaptation on ridge functions. Evolutionary Computation 16(2), 151–184 (2008)
Bäck, T., Fogel, D.B., Michalewicz, Z.: Handbook of Evolutionary Computation. Oxford University Press, Oxford (1997)
Beyer, H.-G.: Ein Evolutionsverfahren zur mathematischen Modellierung stationärer Zustände in dynamischen Systemen. PhD thesis, Hochschule für Architektur und Bauwesen, Weimar (1989)
Beyer, H.-G.: The Theory of Evolution Strategies. Springer, Heidelberg (2001)
Coello Coello, C.A.: Constraint-handling techniques used with evolutionary algorithms. In: Proceedings of the 2007 Genetic and Evolutionary Computation Conference — GECCO 2007, pp. 3057–3077. ACM Press, New York (2007)
Kramer, O., Schwefel, H.-P.: On three new approaches to handle constraints within evolution strategies. Natural Computing 5(4), 363–385 (2006)
Liang, J.J., Runarsson, T.P., Mezura-Montes, E., Clerc, M., Suganthan, P.N., Coello Coello, C.A., Deb, K.: Problem definitions and evaluation criteria for the CEC 2006 Special Session on Constrained Real-Parameter Optimization. Technical report, Nanyang Technological University, Singapore (2006)
Meyer-Nieberg, S., Beyer, H.-G.: Why noise be good: Additive noise on the sharp ridge. In: Proceedings of the 2008 Genetic and Evolutionary Computation Conference — GECCO 2008, may, ACM Press, New York (to appear, 2008)
Montes, E.M., Coello Coello, C.A.: A simple multi-membered evolution strategy to solve constrained optimization problems. IEEE Transactions on Evolutionary Computation 9(1), 1–17 (2005)
Oyman, A.I., Deb, K., Beyer, H.-G.: An alternative constraint handling method for evolution strategies. In: Proc. of the 1999 IEEE Congress on Evolutionary Computation, pp. 612–619. IEEE Computer Society Press, Los Alamitos (1999)
Rechenberg, I.: Evolutionsstrategie — Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Friedrich Frommann Verlag (1973)
Rechenberg, I.: Evolutionsstrategie ‘94. Friedrich Frommann Verlag (1994)
Runarsson, T.P., Yao, X.: Stochastic ranking for constrained evolutionary optimization. IEEE Transactions on Evolutionary Computation 4(3), 274–283 (2000)
Schwefel, H.-P.: Numerical Optimization of Computer Models. Wiley, Chichester (1981)
Schwefel, H.-P.: Evolution and Optimum Seeking. Wiley, Chichester (1995)
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Arnold, D.V., Brauer, D. (2008). On the Behaviour of the (1+1)-ES for a Simple Constrained Problem. 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_1
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DOI: https://doi.org/10.1007/978-3-540-87700-4_1
Publisher Name: Springer, Berlin, Heidelberg
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