Reliability optimization of multi-state weighted k-out-of-n systems by fuzzy mathematical programming and genetic algorithm

This paper proposes two fuzzy mathematical models for reliability optimization of multi-state weighted k-out- of-n systems. In this approach, we consider fuzzy constraint for reliability that enables us to apply different weights for the fuzzy constraint and the objective function with their importance factors. Universal generation function (UGF) technique is employed for computing the system reliability based on the fuzzy mathematical model. And then, genetic algorithm (GA) is used as the efficient optimization tool to facilitate the approach in finding optimum solutions for reliability-cost objective function at combinatorial and NP-hard applications. Finally, a numerical example is illustrated for demonstrating the flexibility and effectiveness of the approach.