Markov Chain Analysis of Evolution Strategies on a Linear Constraint   Optimization Problem
  This paper analyses a $(1,\lambda)$-Evolution Strategy, a randomised comparison-based adaptive search algorithm, on a simple constraint optimisation problem. The algorithm uses resampling to handle the constraint and optimizes a linear function with a linear constraint. Two cases are investigated: first the case where the step-size is constant, and second the case where the step-size is adapted using path length control. We exhibit for each case a Markov chain whose stability analysis would allow us to deduce the divergence of the algorithm depending on its internal parameters. We show divergence at a constant rate when the step-size is constant. We sketch that with step-size adaptation geometric divergence takes place. Our results complement previous studies where stability was assumed. 
Alexandre Chotard (INRIA Saclay - Ile de France, LRI), Anne Auger   (INRIA Saclay - Ile de France), Nikolaus Hansen (INRIA S...
cs.NE math.OC