A weighted K-means clustering approach to solve the redundancy allocation problem of systems having components with different failures

Abstract

A nonlinear integer programming model is developed in this article to solve redundancy allocation problems with multiple components having different failure rates in the series–parallel configuration using an active strategy. The main objective of this research is to select the number and the type of each component in subsystems so as the reliability of the system under certain constraints is maximized. To this aim, a weighted K-means clustering method is proposed, in which the analytical network process is employed to assign weights to the components of each cluster. As the proposed model belongs to the class of nondeterministic polynomial-time hardness problems, precise solution methods cannot solve it in large scale. Therefore, an invasive weed optimization algorithm, due to its proven high efficiency, is utilized to solve the problem. As there is no benchmark available in the literature, a harmony search algorithm and a genetic algorithm are employed as well to validate the results obtained. In order to find better solutions, response surface methodology is used to tune the parameters of the solution algorithms. Some numerical illustrations are solved in the end to not only show the application of the proposed methodology but also to validate the solution obtained and to compare the performance of the three solution algorithms. Experimental results are generally in favor of the invasive weed optimization.