Fuzzy Hybrid NSGA-II for Multi-Objective Reliability Decision-Making with Various Membership Functions

Abstract

Practically, reliability-based system design is modeled with flexibility and adaptability to the human decision-making process. Fuzzy set theory is a suitable technique for modeling and analyzing the system design in a better way. Generally, linear membership function is used to model the problem because of its simplicity. However, shapes of other membership functions such as quadratic, parabolic and hyperbolic can be considered for making empirical justification or assumption. Moreover, multi-objective optimization problems (MOOPs) are suggested to be solved using multi-objective evolutionary algorithms (MOEAs). The main reason for using MOEAs is to provide multiple trade-offs in one simulation run. However, it is not possible to generate the entire Pareto-optimal set in many complex applications. Keeping these views in mind, fuzzy hybrid non-dominated sorting genetic algorithm-II is proposed for multi-objective reliability-based system design problem with various membership functions. Non-dominated sorting genetic algorithm-II (NSGA-II) is one of the elitist MOEAs which has less computational complexity, elitist strategy, and parameter-less sharing approach. A fuzzy-based local search strategy is suggested to update the Pareto-optimal solutions from an NSGA-II simulation run and clustering technique gives a handful of solutions from a practical standpoint. The conflicting objectives such as maximization of system reliability and minimization of system cost are considered simultaneously in a numerical example of the over-speed protection system. A comparative analysis among these membership functions has been performed. Finally, the best compromise solution in each membership is obtained by the fuzzy ranking method.