Discovering gene co-regulatory relationships is one of most important research in DNA microarray data analysis. The problem of gene specific co-regulation discovery is to, for a particular gene of interest (called target gene), identify the condition subsets where strong gene co-regulations of the target gene are observed and its co-regulated genes in these condition subsets. The co-regulations are local in the sense that they occur in some subsets of full experimental conditions. The study on this problem can contribute to better understanding and characterizing the target gene during the biological activity involved. In this paper, we propose an innovative method for finding gene specific co-regulations using genetic algorithm (GA). A sliding window is used to delimit the allowed length of conditions in which gene co-regulations occur and an ad hoc GA, called the progressive GA, is performed in each window position to find those condition subsets having high fitness. It is called progressive because the initial population for the GA in a window position inherits the top-ranked individuals obtained in its preceding window position, enabling the GA to achieve a better accuracy than the non-progressive algorithm. kNN Lookup Table is utilized to substantially speed up fitness evaluation in the GA. Experimental results with a real-life gene expression data demonstrate the efficiency and effectiveness of our technique in discovering gene specific co-regulations.