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Two-Slope Parameterized Achievement Scalarizing Functions for Multiobjective Optimization

Outi Wilppu, Marko M. Mäkelä, Yury Nikulin, Two-Slope Parameterized Achievement Scalarizing Functions for Multiobjective Optimization. TUCS Technical Reports 1114, TUCS, 2014.

Abstract:

Most of the methods for multiobjective optimization utilize some scalarization technique where several goals of the original multiobjective problem are converted to one single-objective problem. One common scalarization technique is a use of achievement scalarizing functions. In this paper, we introduce a new family of two-slope parameterized achievement scalarizing functions for multiobjective optimization. With these two-slope parameterized ASFs we can guarantee the (weak) Pareto optimality of the solutions produced and every (weakly) Pareto optimal solution can be obtained. Parameterization of this kind gives a systematic way to produce different solutions from the same preference information. With two weighting vectors depending on the achievability of the reference point there is no need for any assumptions about the reference point. In addition to theory, we give the graphical illustrations of two-slope parameterized ASFs and analyze the quality of the solutions produced in convex and nonconvex testproblems.

Files:

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BibTeX entry:

@TECHREPORT{tWiMxNi14a,
  title = {Two-Slope Parameterized Achievement Scalarizing Functions for Multiobjective Optimization},
  author = {Wilppu, Outi and Mäkelä, Marko M. and Nikulin, Yury},
  number = {1114},
  series = {TUCS Technical Reports},
  publisher = {TUCS},
  year = {2014},
}

Belongs to TUCS Research Unit(s): Turku Optimization Group (TOpGroup)

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