How to evaluate multi label image retrieval model
First consider analyzing the results per class (with normal accuracy/F-score/whatever) - this way you can have a good idea of where the algorithm is doing well and where it may be improved.
Consider only the exact match. It's a "hit" if the algorithm got the exact labels that it should have. You can then use the hit count to calculate precision, recall and F-score.
Hamming Loss: this is a favorite of researchers in my experience, it represents the how many of the total labels were misclassified


The relevant Wikipedia article seems to agree with me and adds the Jaccard index to the mix.

The paper that presents the famous Classifier Chains method (READ J. et al, Classifier Chains for Multi-label Classification, 2009) uses four different evaluation methods: a accuracy variation that closely resembles Jaccard distance, a similarly changed F1-score, and a log-loss function. The fourth method they use to evaluate is the area under the Precision-Recall curve, but that's one I'd argue should not be used (see the work on Precision-Recall-Gain curves by Peter Flach).