Optimising a nonlinear utility function in multi-objective integer programming

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Ozlen M., AZİZOĞLU M., Burton B. A.

JOURNAL OF GLOBAL OPTIMIZATION, vol.56, no.1, pp.93-102, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 56 Issue: 1
  • Publication Date: 2013
  • Doi Number: 10.1007/s10898-012-9921-4
  • Journal Name: JOURNAL OF GLOBAL OPTIMIZATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.93-102
  • Middle East Technical University Affiliated: Yes

Abstract

In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop a general optimisation algorithm for use with k objectives, and we illustrate our approach using a tri-objective integer programming problem.