Redundancy optimization for multi-state system with fixed resource-requirements and unreliable sources

This paper considers a redundancy optimization problem for a multi-state system of: (1) elements that consume a fixed amount of resources to perform their task, and (2) a number of resource generating subsystems. The algorithm finds the optimal system-structure, subject to availability constraints, by choosing system elements from a list of available equipment. Each element is characterized by its productivity, availability, and cost. Elements of the main producing subsystem also have their specific resource consumption limitations. The objective is to minimize the sum of investment costs while satisfying demand, represented by a cumulative demand curve, with given probability. To solve the problem, a genetic algorithm is used for optimization. The procedure, based on the universal generating function, is used to evaluate the system-availability while assuming that the working elements of the main producing subsystem are chosen in such a way that the total system performance rate is maximal under given resource constraints. Examples demonstrate how to obtain the optimal structures of a simple 2-level system for various availability constraints