Containment of dynamic crimes such as kidnapping, bank robbery, hit-and-run, etc., is a challenging issue for law enforcement agencies as the criminal changes his location with time. This type of scenario is generally modelled as an escape interdiction game. We consider two types of players, namely multiple defenders and a single attacker. The defenders choose a sequence of junctions to protect, while the attacker chooses an escape path and the travel time on distinct edges along the path. Hence, both the defender strategy space and the continuous attacker strategy space suffer an exponential growth. This leads to major challenges in the computation of the optimal solution with respect to each player. We develop a double oracle Variable Neighborhood Search (VNS) based meta-heuristic algorithm for finding near-optimal defender and attacker strategies in a time efficient manner. We test the efficiency of this approach against an established exact algorithm named Escape Interdiction Game Solver (EIGS). We use EIGS to generate the benchmark results to check the performance of our heuristic. We also show that the performance of our approach is reasonably good under strict time limitations, as observed in practice.