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Even self-deployment is one of the best strategies to deploy mobile sensors when the region of interest is unknown and manual deployment is infeasible. A widely used distributed algorithm, Lloyd`s method, can achieve even self-deployment. It however suffers from two critical issues when being used in mobile sensor networks. First, it does not consider limited sensor communication range. Second, it does not optimize sensor movement distances, and hence can lead to excessive energy consumption, a primary concern in sensor networks. This paper first formulates a locational optimization problem that achieves even deployment while it takes account of energy consumption due to sensor movement, and then proposes two iterative algorithms. The first algorithm, named Lloyd- α, reduces the movement step sizes in Lloyd`s method. It saves traveling distance while maintaining the convergence property. However …