Improved Heatmap Visualization of Pareto-Optimal Set in Multi-Objective Optimization of Defensive Strategy

It is an important task in network security management to use defensive strategy to mitigate security risk. We obtain the Pareto-optimal set of defensive strategy using multi-objective optimization algorithm (MOO) based on attack tree. However, decision maker (DM) may find it problematic to select an appropriate defensive strategy from the Pareto-optimal set, and visualization of the Pareto-optimal set is an effective method. In well-known spectral seriation of heatmap, there exist problem of mapping identical objective values of the Pareto-optimal set to different colors. And there still exist problem of weak flexibility and interactivity while the original spectral seriation of heatmap doesn't provide interface for DM. We improve the clarity by mapping identical objective values to the same color through assigning identical ranked values for identical objective values, and increase interactivity by allowing DM reorder objects and solutions or set interested solutions. Finally, the most suitable defensive strategy will be obtained from the improved heatmap easily. Application and advantages of the proposed approach are illustrated through a case study.