Data Clustering of Solutions for Multiple Objective System Reliability Optimization Problems

Abstract

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. A 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 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.

Key Words:

• Data mining
• multiple objective genetic algorithms (MOGA)
• system reliability optimization

Additional information

Notes on contributors

Heidi A. Taboada

Heidi A. Taboada PhD Candidate in the Department of Industrial & Systems Engineering at Rutgers University, Piscataway, NJ. She has an MS in Industrial & Systems Engineering from Rutgers University (2005), an MS in Industrial Engineering (Minor in Quality) from Instituto Tecnológico de Celaya (2002), and a BS in Biochemical Engineering from Instituto Tecnológico de Zacatepec (2000). Her research interests lie in the areas of applied operations research, multiple objective optimization, biologically inspired methods and algorithms, including evolutionary computation, reliability modeling and optimization, and data mining.

David W. Coit

David W. Coit Associate Professor in the Department of Industrial & Systems Engineering at Rutgers University. He received a BS degree in Mechanical Engineering from Cornell University, an MBA from Rensselaer Polytechnic Institute, and MS & PhD in Industrial Engineering from the University of Pittsburgh. In 1999, he was awarded a CAREER grant from NSF to study reliability optimization. He also has over ten years of experience working for IIT Research Institute (IITRI), Rome, NY (IITRI is now called Alion Science & Technology), where he was a reliability analyst, project manager, and an engineering group manager. His current research involves reliability prediction & optimization, risk analysis, and multi-criteria optimization considering uncertainty. He is a member of IIE and INFORMS.