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Mobile ad-hoc network (MANET) is a collection of wireless mobile computers forming a temporary network without any fixed infrastructure or wired backbone. Topological changes in MANET frequently render routing paths unusable. A suitable technique for addressing this problem is to enhance the diversity of paths between the source and destination. However, multipath routing is a challenging task. In particular, the correlation between the failures of the paths in a path set should be as small as possible. Shared nodes and links between the paths are usual failure points. Disjointed path sets require the multiple paths to be link-disjoint or node-disjoint. However, selecting an optimal path set is an NP-complete problem. Artificial neural networks have been proposed as computational tools to solve constrained optimisation problems. The use of Hopfield neural network as a path set selection algorithm is explored. Since this algorithm produces a set of backup paths with much higher reliability, it is beneficial for MANETs. We use link expiration time (LET) between two nodes to estimate link reliability. In this approach, node-disjoint and link-disjoint path sets can be found simultaneously with route discovery algorithm. So, if someone wants to find both node-disjoint and link-disjoint path sets, there is no need to submit extra control messages, as overhead, to the MANET. Simulation results show that the proposed protocol can find path sets with higher reliability in comparison to the other recent proposed algorithms.