Practical Solutions of Multi-objective System Reliability Design Problems Using Genetic Algorithms

Two methods are presented as practical approaches to reduce the size of the Pareto optimal set of multiple-objective system reliability design problems. The first method is a pseudo-ranking scheme that helps the decision-maker select solutions that reflect his/her preferences. In the second approach we used clustering techniques used in data mining, to group the data by using the k-means algorithm to find clusters of similar solutions, which allows the decision-maker to have just k solutions to choose from without using any objective function preference information. Under this second method, from the clustered Pareto optimal set, we attempted to find solutions which are likely to be more relevant to the decision-maker, which are solutions where a small improvement in one objective would lead to a large deterioration in at least one other objective. To show how these methods work, the well-known Redundancy Allocation Problem was solved as a multiple objective problem by using the NSGA genetic algorithm to initially find the Pareto optimal solutions, and then, the two proposed methods are applied to prune the Pareto set.