Image segmentation is an indispensable part of computer vision applications, and image thresholding is a popular one due to its simplicity and robustness. Generalised Masi entropy (GME) is an image thresholding method that exploits the additive/non-extensive information using entropic measure (). shows the measure of degree of extensibility and non-extensibility available in an image. From the literature, all research considered it as a fixed coefficient, while finding a proper value for can enhance the efficacy of thresholding. This paper proposes a simple yet effective approach for adaptively finding a proper value for without any background knowledge regarding the distribution of histogram. To this end, a new representation is proposed so that it can be used with any type of population-based metaheuristic (PBMH) algorithms. For the optimisation process, we use differential evolution (DE), as a representative. In addition, to further improve efficacy, we improve DE algorithm based on one-step -means clustering, random-based sampling, Gaussian-based sampling, and opposition-based learning. Our extensive experiments compared to the most recent approaches on a set of benchmark images and in terms of several criteria clearly show that the proposed approach not only can find the proper value for automatically but also it can improve the efficacy of GME-based image thresholding methods.