Proportional symbol maps are an often used tool to aid cartographers and geo-science professionals to visualize data associated with events (e.g., earthquakes) or geo-positioned statistical data (e.g., population). At specific locations, symbols are placed and scaled so that their areas become proportional to the magnitudes of the events or data. Recent work approaches the problem of drawing these symbols algorithmically and defines metrics to be optimized to attain different kinds of drawings. We focus specifically on optimizing the visualization of physically realizable drawings of opaque disks by maximizing the sum of the visible borders of such disks. As this problem has been proven to be NP-hard, we provide an integer programming model for its solution along with decomposition techniques designed to decrease the size of input instances. We present computational experiments to assess the performance of our model as well as the effectiveness of our decomposition techniques.