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An orthogonal multi-relay network is investigated, where the transmissions are separated into two phases which are orthogonalized in time-frequency plane in order to satisfy practical constraints. In phase I, the source transmits to the relays and destination. In phase II, the relays transmit to the destination simultaneously. The capacity bounds on such orthogonal multi-relay networks are derived. We find that the optimal resource allocation problems for maximizing these capacity bounds are equivalent to the multi-objective optimization problems. We then propose a resource allocation scheme that converts such multi-objective optimization problems to the convex optimization problems. Simulation results show that our resource allocation has a significant impact on the performance.