Minmax defense strategy for complex multi-state systems

This paper presents a general optimization methodology that merges game theory and multi-state system survivability theory. The defender has multiple alternatives of defense strategy that presumes separation and protection of system elements. The attacker also has multiple alternatives of its attack strategy based on a combination of different possible attack actions against different groups of system elements. The defender minimizes, and the attacker maximizes, the expected damage caused by the attack (taking into account the unreliability of system elements and the multi-state nature of complex series–parallel systems). The problem is defined as a two-period minmax non-cooperative game between the defender who moves first and the attacker who moves second. An exhaustive minmax optimization algorithm is presented based on a double-loop genetic algorithm for determining the solution. A universal generating function technique is applied for evaluating the losses caused by system performance reduction. Illustrative examples with solutions are presented.