The paper presents a heuristic backward path tracing algorithm in combination with optimization EASI model for effective estimation of time delay remaining after detection TTR. The heuristic backward search algorithm is implemented based on a graph-based model representation of a hypothetical facility for visual path tracing and planning. A comparative analysis between the implementation of non-heuristic and heuristic search for the most vulnerable adversary paths identification in terms of the shortest distance (d), probability of detection (PD), and probability of interruption (PI) on different intrusion detection fields is carried out and in detail discussed. The comparison results show that the global optimal solutions can be obtained using the heuristic backward path tracing algorithm with high search efficiency and accuracy. The knotty problem encountered in unknown path generation under uncertainties for calculating TTR and PI is effectively solved for admissible and consistent heuristic function design.