An interactive method for multiple-objective mathematical programming problems

W. S. Shin, Arunachalam Ravindran

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

An interactive method is developed for solving the general nonlinear multiple objective mathematical programming problems. The method asks the decision maker to provide partial information (local tradeoff ratios) about his utility (preference) function at each iteration. Using the information, the method generates an efficient solution and presents it to the decision maker. In so doing, the best compromise solution is sought in a finite number of iterations. This method differs from the existing feasible direction methods in that (i) it allows the decision maker to consider only efficient solutions throughout, (ii) the requirement of line search is optional, and (iii) it solves the problems with linear objective functions and linear utility function in one iteration. Using various problems selected from the literature, five line search variations of the method are tested and compared to one another. The nonexisting decision maker is simulated using three different recognition levels, and their impact on the method is also investigated.

Original languageEnglish (US)
Pages (from-to)539-561
Number of pages23
JournalJournal of Optimization Theory and Applications
Volume68
Issue number3
DOIs
StatePublished - Mar 1 1991

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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