Many companies developing real-time systems today have today no means for response time analysis, as their systems violate the assumptions of traditional analytical methods for response-time analysis and are too complex for exhaustive analysis using model checking. This paper presents a novel approach for best effort response time analysis targeting such systems, where probabilistic simulation is guided by a search algorithm of metaheuristic type, similar to genetic algorithms. The best effort approach means that the result is not guaranteed to be the worst-case response time, but also that the method scales to large industrial systems. The proposed method should be regarded as a form of testing, focusing on timing properties. An evaluation is presented which indicates that the proposed approach is significantly more efficient than traditional probabilistic simulation in finding extreme task response times. The paper also presents a method for finding good parameters for the search algorithm, in order to improve its efficiency.