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The store-carry-forward communication mode in delay tolerant networks closely depends on the opportunistic contacts between the nodes. In addition, there is a higher probability that a node can detect others if the beaconing rate is higher (although this consumes more energy). This study studies the optimal beaconing policy to obtain a trade-off between the performance and the energy consumption. In particular, the authors consider the case with multiple destinations. According to whether the destinations forward the message to others, they study the problem in non-replicative and replicative cases, respectively. First, a theoretical framework that can evaluate the trade-off under different beaconing policies is introduced for each case. Then, they formulate an optimisation problem based on these frameworks. Through Pontryagin's maximal principle, they obtain the optimal policies and prove that the optimal policies conform to the threshold form in both cases. The imulations show the accuracy of the theoretical frameworks. The numerical results show that they can obtain a better trade-off in the replicative case.