Optimal patrol strategies against attacker's persistent attack with multiple resources

In recent years, terrorist organizations' activates are various (e.g., igniting a bomb, shooting). Thus, it is difficult to predict the target which will be attacked and how to implement attacks by attackers. Although security agencies may have some knowledge of adversaries, potential targets can't be covered by sufficient security resources all the time due to limited security resources. There are generally two forms of attacks. One is instantaneous attack such as igniting a bomb. The other is persistent attack like shooting and knife attack. Most studies assumed that the site of the deploying resources is completely protected, but ignored the attacker's attack ability will exceed defender's defense ability in the case of persistent attacks. An example of the typical persistent attack is a terrorist attack happening in Kunming, China on March 1, 2014, which caused large losses. In this paper, we first explore the attacker's persistent attack with multiple resources like Kunming attack and make four contributions: 1) A new Stackelberg game model to formulate the problem for attacker's persistent attack with multiple resources; 2) A novel algorithm to compute the optimal mixed patrol strategy for the defender; 3) A modified double-oracle algorithm to further scale up the algorithm; and 4) Extensive experiments to show solution quality and scalability of proposed algorithms.