### Two Tuned Multi-Objective Meta-Heuristic Algorithms for Solving a Fuzzy Multi-State Redundancy Allocation Problem Under Discount Strategies

Abstract

In this study, a bi-objective multi-state redundancy allocation problem of series-parallel systems consisting of some serial subsystems, each with non-repairable components in parallel, is investigated. Furthermore, due to uncertainty involved, both the performance rates and the availabilities of components are considered fuzzy. In addition, two strategies of all-unit and incremental-quantity discounts are used to purchase the components and that the fuzzy universal generating function (FUGF) is employed to evaluate the system availability. The aim is to find the optimal redundancy so as within limited budget and system weight the maximum system availability is obtained while the total cost is minimized. Since the bi-objective mathematical formulation of the problem is shown to be strongly NP-hard, a controlled elitism non-dominated ranked genetic algorithm (CE-NRGA) is developed to find the Pareto solutions of the problem at hand. Besides, since there is no-benchmark available in the literature, a non-dominated sorting genetic algorithm (NSGA-II) is utilized to validate the results obtained. To improve the performance of the adopted algorithms, a multi-objective version of the Taguchi method is used to tune the parameters of the algorithms. Finally, several numerical examples are generated to evaluate the efficiency of the algorithms for which a variety of multi-objective metrics is employed to compare the results.