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If you've NEVER registered a DOI in your Lattes, check our tutorial!Multitask Wireless Sensor Networks (MWSNs) have gained attention for their ability to simultaneously monitor multiple applications, such as in smart cities. One of the main challenges in designing these networks is the efficient management of energy consumption, due to the limited battery life of the sensors. This paper proposes a new GRASP procedure aimed at optimizing energy usage in MWSNs. The algorithm's performance is compared with the best mathematical model from the literature on small- and medium-sized instances. For small instances, the proposed GRASP reached the optimal solution in 26 out of 30 cases. In medium-sized instances, it significantly outperformed the mathematical model, achieving better solutions in 10 out of 14 instances, whereas the model failed to find feasible solutions for all of them. Additionally, the neighborhood structure used in the local search led to an average improvement of 55\% over the initial solutions.
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