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Last decade has noticed an enormous growth of Internet based information services and applications such as Email, Teleconferencing, Videophony or VoIP etc. All these applications have different QoS (Quality of Service) expectations (bandwidth, delay, jitter and reliability etc). The purpose and the benefits from these applications could be blemished if the underlying communication network does not fulfills the QoS requirements. However, different applications have different prioritized QoS requirements. Some applications put heavy demands of bandwidth, some require a more degree of reliability while some expect a negligible response time and so on. So there is always a need of routing strategy which is not only efficient and precise but guarantees the QoS measure as according to application's priorities also. Tackling the issue, this paper presents the use of priority based Evolutionary Multi-objective Optimization algorithms to find the optimal routes for the data flows of various QoS classes via optimizing multiple QoS parameters namely response time, bandwidth requirements and reliability according to their importance for the application under consideration.