This paper suggests a hybrid NSGA-II based decision-making method in a fuzzy multi-objective reliability optimization problem. Multi-objective evolutionary algorithms (MOEAs) are popular techniques to be solved various kinds of multiobjective optimization problems efficiently. NSGA-II is one of the elitist MOEAs, which is largely used in engineering design problems. The reliability-based system design problem comprises various kinds of uncertainties such as expert's information character, qualitative statements, vagueness, incompleteness, unclear system boundaries, etc. Fuzzy optimization techniques can be useful during the initial stage of the conceptual design of a system. In many complex problems, it is not possible to produce the entire Pareto-optimal set in one simulation run. Apart from this, getting a well diverse solution set is another important phenomenon in this field. The proposed approach finds the optimal system design by resolving these issues in a fuzzy multi-objective reliability optimization problem. A numerical example of the overspeed protection system consisting of three mutually conflicting objectives such as system reliability, system cost, and system weight is considered with several design constraints to illustrate the method. Finally, the results obtained by the proposed approach are discussed with the existing approach.
Practically, reliability-based system designs are modeled in various kinds of uncertainty such as expert's information character, qualitative statements, vagueness, etc. Fuzzy set theory is suitable for tackling such types of uncertainty effectively. In most of the practical situations, where reliability enhancement is an essential requirement, decision-making is a complicated task due to the presence of several mutually conflicting objectives such as system's cost, weight, and volume. To solve such problems, multiobjective evolutionary algorithms (MOEAs) are efficient techniques for finding multiple Pareto-optimal solutions in a single simulation run. This paper applies an elitist MOEA, namely, NSGA-II to fuzzy multi-objective reliability optimization problem consisting of conflicting objectives such as system reliability and its cost. Linguistic hedges (or modifiers) are used to modify the Pareto-optimal solution set obtained by NSGA-II in terms of the membership grades of the objective values. The max-min composition of the membership grades gives the maximum satisfaction level to each possible combination of the linguistic hedges. After that, fuzzy rule-based system (FRBS) is proposed for evaluating the system efficiency to each case which is used in the decision-making of reliability. A numerical example is given to illustrate the method. Finally, the proposed approach is comparatively studied with the existing approach.
In Bulk Power System Reliability Evaluation (BPSRE), realistic operating condition constraints are important issues. The limits based on stability and voltage considerations should be adhered to at all times to prevent blackouts, as voltage collapse problems account for uncertainties in power system operation, which is due to uncontrollable progressive decline in voltage.The aspects of uncertainties about future load growth, fuel cost, environmental regulations, etc., are di cult to specify properly within a long-term forecasting probabilistic model. On the other hand, the simple LP models are inadequate in satisfying realistic system objectives and constraints. Dynamical feature of load modeling may be critical in the computation of voltage collapserelated bulk power system reliability indices. Also, the control problem has attracted greater interest as the desire to transport power over longer distances has increased.In this work, while formulating mathematical formulation by considering the voltage collapse phenomena in the existing framework of BPSRE, the reactive power control variables are optimized by using Fuzzy linear programming. The uncertainties in system probabilistic parameters, like Forced Outage Rates, which aOE ects largely the nal indices, are also de ned using the concept of Fuzzy Number and Linguistic variables. The new indices are found to re ect the integration of probabilistic models and fuzzy concepts. The proposed method has been tested on AEP-14 bus test system, and the results are compared with conventional ones and presented to demonstrate the eOE ect of uncertainties in the system probabilistic parameters.
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