One natural question when testing performance of global optimization algorithm is: how performances compare to a restart local search algorithm. One purpose of this paper is to provide results for such comparisons. To this end, the performances of a restart (advanced) local-search strategy, the CMA-ES with small initial step-size, are investigated on the 25 functions of the CEC 2005 real-parameter optimization test suit. The second aim is to clarify the theoretical background of the performance criterion proposed to quantitatively compare the search algorithms. The theoretical analysis allows us to generalize the criterion proposed and to define a new criterion that can be applied more appropriate in a different context.