Data Clustering of Solutions for Multiple Objective System Reliability Optimization Problems

This paper proposes a practical methodology for the solution of multi-objective system reliability optimization problems. The new method is based on the sequential combination of multi-objective evolutionary algorithms and data clustering on the prospective solutions to yield a smaller, more manageable sets of prospective solutions. Existing methods for multiple objective problems involve either the consolidation of all objectives into a single objective, or the determination of a Pareto-optimal set. In this paper, a new approach, involving post-Pareto clustering is proposed, offering a compromise between the two traditional approaches. In many real-life multi-objective optimization problems, the Pareto-optimal set can be extremely large or even contain an infinite number of solutions. Broad and detailed knowledge of the system is required during the decision making process in discriminating among the solutions contained in the Pareto-optimal set to eliminate the less satisfactory trade-offs and to select the most promising solution(s) for system implementation. The well-known reliability optimization problem, the redundancy allocation problem (RAP), was formulated as a multi-objective problem with the system reliability to be maximized, and cost and weight of the system to be minimized. A multiple stage process was performed to identify promising solutions. The Pareto-optimal set was initially obtained using the fast elitist nondominated sorting genetic algorithm (NSGA-II). The decision-making stage was then performed with the aid of data clustering techniques to prune the size of the Pareto-optimal set and obtain a smaller 2 representation of the multi-objective design space; thereby making it easier for the decision-maker to find satisfactory and meaningful trade-offs, and to select a preferred final design solution.