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This paper addresses the challenge of moving objects in a mobile wireless sensor network, considering the deployment of a limited number of mobile wireless sensor nodes within a predetermined area to provide coverage for moving objects traveling on a predetermined trajectory. Because of the insufficient number and limited sensing range of mobile wireless sensors, the entire object’s trajectory cannot be covered by all deployed sensors. To address this problem and provide complete coverage, sensors must move from one point of the trajectory to another. The frequent movement quickly depletes the sensors’ batteries. Therefore, solving the moving object coverage problem requires an optimized movement repertoire where (1) the total moving distance is minimized and (2) the remaining energy is also as balanced as possible for mobile sensing. Herein, we used a genetic algorithm (GA) and a discrete particle swarm optimization algorithm (DPSO) to manage the complexity of the problem, compute feasible and quasi-optimal trajectories for mobile sensors, and determine the demand for movement among nodes. Simulations revealed that the GA produced trajectories significantly superior to those produced by the DPSO in terms of total traveled distance and balance of residual energy.