Magnetic Resonance Imaging (MRI) is a non-invasive imaging modality that is a cornerstone of diagnostic radiology. Clinical MRI scans capture a single image to highlight a single tissue property. The intensity difference between different regions of this image shows disease states that a radiologist can interpret. Magnetic Resonance Fingerprinting (MRF) is a recently proposed novel MRI technique. MRF allows the capture of multiple MR images in a single scan. This enables clinicians to analyze multiple tissue properties, potentially increasing the sensitivity of diagnosis and also allowing for the diagnosis of novel diseases. However, it is more challenging to analyze MRF images, because MRF produces much larger and noisier data than MRI. In this paper, we show how AI techniques can help solve this problem. Using a hybrid search strategy combining simulated annealing with pattern search, we show it is possible to tractably reconstruct multiple tissue properties from a single MRF image. This is a key step towards the deployment of MRF for radiological diagnosis.