Quantitative comparison of approximate solution sets for Bi-criteria optimization problems

W. Matthew Carlyle, John Fowler, Esma Gel, Bosun Kim

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


We present the Integrated Preference Functional (IPF) for comparing the quality of proposed sets of near-pareto-optimal solutions to bi-criteria optimization problems. Evaluating the quality of such solution sets is one of the key issues in developing and comparing heuristics for multiple objective combinatorial optimization problems. The IPF is a set functional that, given a weight density function provided by a decision maker and a discrete set of solutions for a particular problem, assigns a numerical value to that solution set. This value can be used to compare the quality of different sets of solutions, and therefore provides a robust, quantitative approach for comparing different heuristic, a posteriori solution procedures for difficult multiple objective optimization problems. We provide specific examples of decision maker preference functions and illustrate the calculation of the resulting IPF for specific solution sets and a simple family of combined objectives.

Original languageEnglish (US)
Pages (from-to)63-82
Number of pages20
JournalDecision Sciences
Issue number1
StatePublished - Dec 1 2003


  • Evaluating the Quality of Approximate Solution Sets
  • Multiple Criteria Decision Making
  • Multiple Objective Metaheuristics

ASJC Scopus subject areas

  • Business, Management and Accounting(all)
  • Strategy and Management
  • Information Systems and Management
  • Management of Technology and Innovation


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