New Two-Slope Parameterized Achievement Scalarizing Functions for Nonlinear Multiobjective Optimization

  • Outi WilppuEmail author
  • Marko M. Mäkelä
  • Yury Nikulin
Part of the Springer Optimization and Its Applications book series (SOIA, volume 113)


Most of the methods for multiobjective optimization utilize some scalarization technique where several goals of the original multiobjective problem are converted into a single-objective problem. One common scalarization technique is to use the achievement scalarizing functions. In this paper, we introduce a new family of two-slope parameterized achievement scalarizing functions for multiobjective optimization. This family generalizes both parametrized ASF and two-slope ASF. With these two-slope parameterized ASF, we can guarantee (weak) Pareto optimality of the solutions produced, and every (weakly) Pareto optimal solution can be obtained. The 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 graphical illustrations of two-slope parameterized ASF and analyze sparsity of the solutions produced in convex and nonconvex testproblems.


Achievement scalarizing functions Multiobjective optimization Parameterization Pareto optimal solutions 

Mathematics Subject Classification

90C29 65K05 49M37 



The research has been financially supported by the Finnish Academy of Science and Letters (the Vilho, Yrjö and Kalle Väisälä Foundation), Emil Aaltonen Foundation and University of Turku Graduate School UTUGS Matti programme.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland

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