Genetic Algorithm Based Reliability Optimization in Interval Environment

The objective of this chapter is to develop and solve the reliability optimization problems of series-parallel, parallel-series and complicated system considering the reliability of each component as interval valued number. For optimization of system reliability and system cost separately under resource constraints, the corresponding problems have been formulated as constrained integer/mixed integer programming problems with interval objectives with the help of interval arithmetic and interval order relations. Then the problems have been converted into unconstrained optimization problems by two different penalty function techniques. To solve these problems, two different real coded genetic algorithms (GAs) for interval valued fitness function with tournament selection, whole arithmetical crossover and non-uniform mutation for floating point variables, uniform crossover and uniform mutation for integer variables and elitism with size one have been developed. To illustrate the models, some numerical examples have been solved and the results have been compared. As a special case, taking lower and upper bounds of the interval valued reliabilities of component as same the corresponding problems have been solved and the results have been compared with the results available in the existing literature. Finally, to study the stability of the proposed GAs with respect to the different GA parameters (like, population size, crossover and mutation rates), sensitivity analyses have been shown graphically.