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Recent studies have shown that the use of mobile sinks and Network Coding (NC) and determining the Sink Optimal Route (SOR) in wireless sensor networks (WSNs) reduces the energy consumption. The purpose of this paper is to determine the multicast SOR to move mobile sinks at specific deadline using NC and modeling and problem formulating based on a Mixed Integer Linear Programming (MILP) in WSNs. In this paper, we first show that finding the SOR is NP-hard, and then for determining the SOR, several convex optimization models are presented using Support Vector Regression (SVR). Solving these models in a polynomial time is not possible due to various parameters and limited resources of WSNs. To solve this problem in polynomial time, a Tabu Search algorithm is proposed to reduce runtime and energy consumption. Simulation results show that optimization models and proposed Tabu Search algorithm significantly reduce energy consumption and required time for computing than non-NC methods.

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