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Sensors in most wireless sensor networks (WSNs) work with batteries as their energy source, it is usually infeasible to recharge or replace batteries when they discharge. Thus, solving the efficient-energy coverage (EEC) problem is an important issue for a WSN. Therefore, it is necessary to schedule the activities of the devices in a WSN to save the network's limited energy and prolong its lifetime. In this paper, we propose an ant-colony-based acheduling algorithm (ACB-SA) to solve the EEC problem. Our algorithm is a simplified version of the conventional ant colony optimization algorithm, optimized for solving the EEC problem. We also use the probability sensor detection model and apply our proposed algorithm to a heterogeneous sensor set, which represents a more realistic approach to solving the EEC problem. Simulation results are performed to verify the effectiveness of the ACB-SA for solving the EEC problem in comparison with other algorithms.