— Memetic algorithms (MAs) combine the global exploration abilities of evolutionary algorithms with a local search to further improve the solutions. While a neighborhood can be easily defined for discrete individual representations, local search within real-valued domains requires an appropriate choice of the local search method. If the subject of optimization shows discontinuous behavior, a standard hill-climbing routine cannot be successfully applied. Thus, in this paper we present a general approach that defines a quasi-discrete neighborhood for real-valued variables by applying problem-specific selfimposed constraints. Thereby, knowledge about properties of good solutions can be easily integrated into the search process and discontinuous parts can be found. Satisfying results can be obtained faster while all important issues in the design of MAs are preserved.