As Routing mechanism is a key to success of future communication networking, computing constrained shortest paths is fundamental to some important network functions such as QoS routing or traffic engineering. The problem is to find feasible paths satisfying QoS requirements and optimizing resource usage and degrading gracefully during periods of heavy load. This paper introduces a Quality of Service (QoS) routing protocol aimed to offload congested links while optimizing end-to-end delay. The proposed algorithm, called NOPAR "N-best Optimal Paths Ant Routing", extends the earlier N best Optimal path Q Routing Algorithm (NOQRA) by integrating the exploration and reinforcement function inspired by Ant Colony Optimization approaches. NOPAR uses a model combining both a stochastic planned pre-navigation for the exploration phase (forward ant) and a deterministic approach for the backward phase (backward ant). The introduced algorithm is compared with earlier version of NOQRA and the well-known routing algorithms such as SPF or OSPF. The performance analysis under simulation environment using OPNET demonstrates that NOPAR performs better than the classical approach especially over load high networks or link failures conditions.