NSGA-II Based Analysis of Fuzzy Multi-objective Reliability-Redundancy Allocation Problem Using Various Membership Functions

摘要

In the broadest sense, reliability is a measure of performance of the system under the stated conditions. The reliability-redundancy allocation problem gives a highly reliable system in the presence of optimal redundant components. This design is the most preferred by the design engineer. During the designing phase of the system, all the design data involved in the system are not very precise. Various types of uncertainties such as expert's information character, qualitative statements, vagueness, incompleteness, unclear system boundaries, inability to evaluate the relative importance of the objectives, etc., are typical for many practical problems. Fuzzy set theory is an efficient technique to tackle such types of uncertainties in the system design problem. In this paper, the goals of the fuzzy multi-objective reliability-redundancy allocation problem are specified by various membership functions such as linear, quadratic, parabolic, and hyperbolic. An efficient multi-objective evolutionary algorithm, namely, NSGA-II is employed to solve it. The Pareto-optimal fronts for the various membership functions are shown in both the membership and objective spaces. Fuzzy ranking method then finds the best compromise solution for each membership function. Finally, the performance of membership functions is ranked by the data envelopment analysis by taking cost criteria (cost, weight, and volume) as inputs and benefit criteria (reliability and maximum satisfaction level) as outputs of the system. The effectiveness of the proposed approach is illustrated by a numerical example of the over-speed protection system for a gas turbine. A comparative analysis of the proposed approach is given with the existing approach.