FUZZY MULTI-OBJECTIVE RELIABILITY ANALYSIS USING NSGA-II

Abstract

Reliability is one of the crucial design parameters that affect the system design problems significantly. In many practical situations, where reliability enhancement is involved, the decision-making is complicated due to the presence of several mutually conflicting objectives such as cost, weight, volume, etc. The presence of mutually conflicting objectives in a problem gives rise to a set of optimal solutions, largely known as Pareto-optimal solutions, instead of a single solution. While moving from one Pareto point to another, a certain amount of sacrifice always occurs in one objective to achieve a certain amount of gain in the other. Since the final solution of the decision-maker is always a trade-off between the design parameters, it is preferred to study the entire Pareto-optimal solution set. However, the preference-based approach (Priori) can be at best unless and until a reliable and accurate preference vector is available, otherwise, such methods are highly subjective and not straight-forward to the particular users. Moreover, in the decision-making of reliability, various kinds of uncertainty, i.e., expert’s information character, qualitative statements, vagueness, etc., are involved. Keeping these views in mind, the multi-objective reliability optimization problem is formulated in a fuzzy environment using the membership function. This formulation does not require any kind of aggregate operators and an efficient MOEA (Posteriori), namely, NSGA-II is employed to maximize all the membership functions of the objectives simultaneously. The Pareto-optimal solutions are found in the domain of fuzzy objectives i.e., in terms of the membership grades. These membership grades give multiple trade-offs optimal solutions in the objective space. However, one feasible solution is ultimately required as per the demand of the system design. In order to achieve it, various methodologies such as fuzzy decision-making, fuzzy coordination, fuzzy rule-based system, analyzing various membership functions, and fuzzy-based hybrid NSGA-II have been proposed. The proposed methodologies could be highly effective in getting the best “trade-off” or “compromise solution” in a fuzzy environment. Theoretical analysis of the methodology is presented step by step in each chapter. The results obtained in the thesis are based on evaluations of the numerical experiments performed in the reliability-based system design problems. Apart from this, the preference-based approach, heuristics and other MOEAs (like SPEA2, PESA-II, MOPSO) have been comparatively studied. This thesis is categorized into eight chapters. The first chapter gives an introduction, the basic concept of multi-objective optimization, classical methods, description of MOEAs, and multi-objective reliability models. The second chapter describes the basics of the NSGA-II and its ii application to fuzzy multi-objective reliability problems. The efficacy of the NSGA-II is shown over the preference-based approach to multi-objective reliability optimization. The third chapter presents the decision-making such as TOPSIS and Shannon’s entropy to find the best trade-off from the NSGA-II simulation run. It is based on the Euclidean distances from the ideal and anti-ideal points in the solution space measured by the membership grades. The fourth chapter solves a fuzzy coordination-based multi-objective reliability problem using NSGA-II. Hypervolume metric shows that the coordination-based simulation outperforms in the search space. On the basis of this assumption, a decision support system (DSS) is created to choose the best optimal design. The fifth chapter is another decision-making approach which is based on a fuzzy rule-based system (FRBS). It is mentioned that FRBS is another point to make a decision in the form of system efficiency. The sixth chapter investigates the optimal solution based on various membership functions such as linear, quadratic, parabolic, and hyperbolic. It is conjectured that empirical justification is required in the decision-making. The seventh chapter searches the optimal design of the reliability system using fuzzy-based hybrid NSGA-II. Three mutually conflicting objectives such as maximization of reliability of the system, minimization of the system cost and minimization of the system weight are considered. Finally, the eighth chapter concludes the overall work and gives its future perspectives in this direction.