Optimizing survivability of multi-state systems with multi-level protection by multi-processor genetic algorithm

In this paper we consider vulnerable systems which can have different states corresponding to different combinations of available elements composing the system. Each state can be characterized by a performance rate, which is the quantitative measure of a systemʹs ability to perform its task. Both the impact of external factors (stress) and internal causes (failures) affect system survivability, which is determined as probability of meeting a given demand. In order to increase the survivability of the system, a multi-level protection is applied to its subsystems. This means that a subsystem and its inner level of protection are in their turn protected by the protection of an outer level. This double-protected subsystem has its outer protection and so forth. In such systems, the protected subsystems can be destroyed only if all of the levels of their protection are destroyed. Each level of protection can be destroyed only if all of the outer levels of protection are destroyed. We formulate the problem of finding the structure of series–parallel multi-state system (including choice of system elements, choice of structure of multi-level protection and choice of protection methods) in order to achieve a desired level of system survivability by the minimal cost. An algorithm based on the universal generating function method is used for determination of the system survivability. A multi-processor version of genetic algorithm is used as optimization tool in order to solve the structure optimization problem. An application example is presented to illustrate the procedure presented in this paper.