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This paper introduces a novel multicopy routing protocol, called Self-Adaptive Utility-based Routing Protocol (SAURP), for Delay Tolerant Networks (DTNs) that are possibly composed of a vast number of devices in miniature such as smart phones of heterogeneous capacities in terms of energy resources and buffer spaces. SAURP is characterized by the ability of identifying potential opportunities for forwarding messages to their destinations via a novel utility function-based mechanism, in which a suite of environment parameters, such as wireless channel condition, nodal buffer occupancy, and encounter statistics, are jointly considered. Thus, SAURP can reroute messages around nodes experiencing high-buffer occupancy, wireless interference, and/or congestion, while taking a considerably small number of transmissions. The developed utility function in SAURP is proved to be able to achieve optimal performance, which is further analyzed via a stochastic modeling approach. Extensive simulations are conducted to verify the developed analytical model and compare the proposed SAURP with a number of recently reported encounter-based routing approaches in terms of delivery ratio, delivery delay, and the number of transmissions required for each message delivery. The simulation results show that SAURP outperforms all the counterpart multicopy encounter-based routing protocols considered in the study.