This paper presents a real-coded memetic algorithm that combines a high diversity global exploration with an adaptive local search method to the most promising individuals that adjusts the local search probability and the local search depth. In our proposal we use the individual fitness to decide when local search will be applied (local search probability) and how many effort should be applied (the local search depth), focusing the local search effort on the most promising regions. We divide the individuals of the population into three different categories and we assign different values of the above local search parameters to the individual in function of the category to which that individual belongs. In this study, we analyze the performance of our proposal when tackling the test problems proposed for the Special Session of the IEEE Congress on Evolutionary Computation 2005