Abstract:

How well an optimization algorithm satisfies short-term and long-term goals, can be verified using appropriate test functions, respective convergence measures, theoretical analysis, and simulations. This paper analyses the convergence behavior of the evolution strategy (ES) at the parabolic ridge function using the standard  -ES. Some further results are given for the case of more general ridge functions. The results obtained are counter-intuitive and different from if not contrary to those obtained from the sphere model theory. Furthermore, using static analysis, we show that the progress rate and the quality gain possess entirely different characteristics.

Keywords. ridge functions, Evolution Strategy, elitist ES, progress rate, quality gain, convergence behavior.

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