Multilevel optimal Threshold selection is important and comprehensively used in the area of image processing. Mostly, entropic information-based Threshold selection techniques are used. These methods make use of the entropy of the distribution of the grey levels of an image. However, entropy Functions largely depend on spatial distribution of the image. This makes the methods inefficient when the distribution of the grey information of an image is not uniform. To solve this problem, a novel non-entropic method for multilevel optimal Threshold selection is proposed. In this contribution, simple numbers (pixel counts), explicitly free from the spatial distribution, are used. A novel non-entropic objective Function is proposed. It is used for multilevel Threshold selection by maximizing the partition score using the adaptive equilibrium method. A new theoretical derivation for the fitness Function is highlighted. The key to the achievement is the exploitation of the score among classes, reinforcing an improvised Threshold selection process. Standard test images are considered for the experiment. The performances are compared with state-of-the-art entropic value-based methods used for multilevel Threshold assortment and are found better. It is revealed that the results obtained using the suggested technique are encouraging both qualitatively and quantitatively. The newly proposed method would be very useful for solving different real-world engineering optimization problems.