Genetic algorithm for solving bi-objective redundancy allocation problem with k-out-of-n subsystems

Reliability optimization problem is an important type of optimization problems that has many practical applications in the real-world systems such as manufacturing systems, telecommunication systems, transformation systems and electrical systems. This research focuses on redundancy allocation problem (RAP) that is a special type of reliability optimization problems. A bi-objective RAP, which is related to a system of s independent k-out-of-n subsystems in series, is considered in this study. Maximization of the system reliability and minimization of the system cost are the objectives of the problem, and the system is constrained by a predefined weight. The components of a subsystem are supposed to be non identical. To deal with this problem, we propose some multi-objective meta-heuristic algorithms based on the elitist non-dominated sorting genetic algorithm (NSGA-II). New modified methods of diversity preservation and constraint handling are introduced in this study. According to these methods and some existing methods, we propose four multi-objective genetic algorithms for solving the considered problem. A numerical example, a statistical method and three performance metrics are utilized for analyzing and comparing the performance of these four genetic algorithms. The comparison represents the positive effect of modified methods of diversity preservation and constraint handling on the performance of the algorithms.