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Multi-Protocol Label Switching for Traffic Engineering (MPLS-TE) technology is an intelligent and advanced tool for handling traffic through the core networks and implementing new services based on virtual transport. Since MPLS-TE combines channel and network layer mechanisms, network administrators can optimally integrate and allocate the traffic loads while maintaining the speed of technologies such as Asynchronous Transfer Mode (ATM) technology. In this paper, the problem of the developed algorithm of multi-path routing which allows us to determine the optimum number of independent shortest paths is theoretically solved. In details, the article proposes a way for finding the set of shortest paths using Dijkstra's algorithm, and then determination of the maximum flow for each of the shortest paths based on the mathematical concepts and finally, introducing the solution of the multi-criteria optimization problem for a set of shortest paths. According to our approach, optimizing the use of resources in the core networks is possible with using the MPLS-TE technology.