The differential evolution (DE) is a well known population-based evolutionary algorithm that has shown capabilities for solving real-world problems such as resource allocation, multicast routing, and localization of target nodes. However, the accuracy of the DE, like other evolutionary algorithms, depends on the settings of its control parameters. The localization of target nodes is highly nonlinear and multi-modal, which may trap the DE in a local optimum. A local optimum may be avoided by a proper selection of the control parameters. One of the key control parameters is the population size (PS), which affects directly the localization accuracy and computational complexity. Finding an adequate PS throughout the evolution process is a challenging task. Even if an adequate PS is found it may not be the adequate PS anymore when the scenario of a problem changes. Although several approaches have been proposed for adapting the PS, they have not been evaluated when solving the localization problem. In this paper, a comprehensive comparison in terms of accuracy and computational demand is conducted among the state-of-the-art PS adaptation techniques when employed with the DE for solving the localization problem of target nodes in various scenarios. We also propose three new PS adaptation techniques, namely, exponential, parabolic, and logistic reduction. The results from extensive numerical simulations show that, after setting the initial PS properly, there is no technique that outperforms the others in practically all the scenario of the localization problem. Additionally, the DE with the proposed techniques provides competitive localization accuracy with considerably less computational complexity. Specifically, The proposed approaches reduce the computational demand by approximately 50 % over the standard DE in all the scenarios considered here.