Quality of service (QoS) routing is one of the critical challenges in wireless sensor networks (WSNs), especially for surveillance systems. Multihop data transmission of WSNs, due to the high packet loss and energy-efficiency, requires reliable links for end-to-end data delivery. Current multipath routing works can provision QoS requirements like end-to-end reliability and delay, but suffer from a significant energy cost. To improve the efficiency of the network with multiconstraints QoS parameters, in this paper we model the problem as a multiconstrained optimal path problem and propose a distributed learning automaton (DLA) based algorithm to preserve it. The proposed approach leverages the advantage of DLA to find the smallest number of nodes to preserve the desired QoS requirements. It takes several QoS routing constraints like end-to-end reliability and delay into account in path selection. We simulate the proposed algorithm, and the obtained results verify the effectiveness of our solution. The results demonstrate that our algorithm has a better performance than current state-of-the-art competitive algorithms in terms of end-to-end delay and energy-efficiency.