Multi-layered social networks consist of the fixed set of nodes linked by multiple connections. These connections may be derived from different types of user activities logged in the IT system. To calculate any structural measures for multi-layered networks this multitude of relations should be coped with in the parameterized way. Two separate algorithms for evaluation of shortest paths in the multi-layered social network are proposed in the paper. The first one is based on pre-processing - aggregation of multiple links into single multi-layered edges, whereas in the second approach, many edges are processed 'on the fly' in the middle of path discovery. Experimental studies carried out on the DBLP database converted into the multi-layered social network are presented as well.