On the Behaviour of the (1+1)-ES for a Simple Constrained Problem
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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
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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