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Mobile ad-hoc network (MANET) is a dynamic collection of mobile computers without the need for any existing infrastructure. Nodes in a MANET act as hosts and routers. Designing of robust routing algorithms for MANETs is a challenging task. Disjoint multipath routing protocols address this problem and increase the reliability, security and lifetime of network. However, selecting an optimal multipath is an NP-complete problem. In this paper, Hopfield neural network (HNN) which its parameters are optimized by particle swarm optimization (PSO) algorithm is proposed as multipath routing algorithm. Link expiration time (LET) between each two nodes is used as the link reliability estimation metric. This approach can find either node-disjoint or link-disjoint paths in singlephase route discovery. Simulation results confirm that PSO-HNN routing algorithm has better performance as compared to backup path set selection algorithm (BPSA) in terms of the path set reliability and number of paths in the set.