Practical solutions for multi-objective optimization: An application to system reliability design problems

Heidi A. Taboada, Fatema Baheranwala, David W. Coit, Naruemon Wattanapongsakorn

Research output: Contribution to journalArticlepeer-review

108 Scopus citations


For multiple-objective optimization problems, a common solution methodology is to determine a Pareto optimal set. Unfortunately, these sets are often large and can become difficult to comprehend and consider. Two methods are presented as practical approaches to reduce the size of the Pareto optimal set for 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 objective function priorities. In the second approach, we used data mining clustering techniques to group the data by using the k-means algorithm to find clusters of similar solutions. This provides the decision maker with just k general solutions to choose from. With 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. These are solutions where a small improvement in one objective would lead to a large deterioration in at least one other objective. To demonstrate 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.

Original languageEnglish (US)
Pages (from-to)314-322
Number of pages9
JournalReliability Engineering and System Safety
Issue number3
StatePublished - Mar 2007

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Industrial and Manufacturing Engineering


  • Clustering analysis
  • Multi-objective optimization
  • Pareto optimal set
  • System reliability


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