The ability to compare two or more images, or finding duplicate images in a large collection, is a very tricky matter, for this reason All scientific research in this field are aimed at studying how to describe and achieve what is best for quantifying the difference between two images because it's often needed in automated visual inspection. In this paper, we propose an improved algorithm for 2D image comparing based on Hausdorff Distance which is used to measure the degree of similarity or dissimilarity between two objects to make matching more efficiently. In this case we used Genetic Algorithm wish is a powerful and attractive procedure for function optimization, but the solution generated by this technique do not guarantee to be the global optimal. A follow-up optimization scheme such as the line search method is applied, which is capable of finding the minimum value of a unimodal function over a finite search interval. The experimental results show that the proposed method is capable of matching 2D shape with higher speed and precision.