We propose a Visual Decision-Guided Tool that integrates optimization programming into geo-data visualization to determine the best path for rescue and recovery missions. First, we will develop the Top-k Objected-oriented Smoothest Paths model which captures the object dynamics of geospatial temporal network in a terrain over a time horizon. These objects include stationary entities, mobile objects, and route segments. Second, we will extend the Smoothest Path Algorithm (SPA) to be a dynamic learning algorithm, i.e., the Time-varying Smoothest Path Algorithm, which integrates the object dynamics to learn the top-k smoothest routes at each instance of time. The main advantage offered by the SPA extension is its lower logarithmic time complexity, i.e., O(NlogN), where N is the number of nodes in a terrain. Finally, we will develop a new design of visual displays that enable military operators to analyze other crucial factors, such as vehicle types, weather severity, and soldiers' specialty levels, which are required to be interpreted by human perception, cognition, and knowledge to select the best path among the top-k smoothest routes at each instance of time for rescue and recovery missions.