In this paper, we present NSGA-II-SVM (Non-dominated Sorting Genetic Algorithm with Support Vector Machine Guidance), a novel learnable evolutionary and search-based testing algorithm that leverages Support Vector Machine (SVM) classification models to direct the search towards failure-revealing test inputs. Supported by genetic search, NSGA-II-SVM creates iteratively SVM-based models of the test input space, learning which regions in the search space are promising to be explored. A subsequent sampling and repetition of evolutionary search iterations allow to refine and make the model more accurate in the prediction. Our preliminary evaluation of NSGA-II-SVM by testing an Automated Valet Parking system shows that NSGA-II-SVM is more effective in identifying more critical test cases than a state of the art learnable evolutionary testing technique as well as naive random search.