Multi-objective optimization problems with fuzzy relation equation constraints

  • Authors:
  • Jiranut Loetamonphong;Shu-Cherng Fang;Robert E. Young

  • Affiliations:
  • Department of Industrial Engineering & Graduate Program in Operations Research, North Carolina State University, 2401 Stinson Drive, Campus Box 7906, Raleigh, NC;Department of Industrial Engineering & Graduate Program in Operations Research, North Carolina State University, 2401 Stinson Drive, Campus Box 7906, Raleigh, NC;Department of Industrial Engineering & Graduate Program in Operations Research, North Carolina State University, 2401 Stinson Drive, Campus Box 7906, Raleigh, NC

  • Venue:
  • Fuzzy Sets and Systems - Special issue: Optimization and decision support systems
  • Year:
  • 2002

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Abstract

This paper studies a new class of optimization problems which have multiple objective functions subject to a set of fuzzy relation equations. Since the feasible domain of such a problem is in general non-convex and the objective functions are not necessarily linear, traditional optimization methods may become ineffective and inefficient. Taking advantage of the special structure of the solution set, a reduction procedure is developed to simplify a given problem. Moreover, a genetic-based algorithm is proposed to find the "Pareto optimal solutions". The major components of the proposed algorithm together with some encouraging test results are reported.