In data mining and machine learning, the definition of the distance between two data points substantially affects clustering and classification tasks. We propose a distance metric learning (DML) method for multi-label clustering, that uses evolutionary multi-objective optimization and a cluster validity measure with a neighbor relation that simultaneously evaluates inter- and intra-clusters. The proposed method produces clustering results considering multiple class labels and allows the induction of knowledge regarding relations between class labels in multi-label clustering or between objective functions and elements in transform matrix. Experimental results have shown that the proposed DML method produces better transform matrices than single-objective optimization and is helpful in finding the attributes that affect the trade-off relationship among objective functions.