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New two-slope parameterized achievement scalarizing functions for nonlinear multiobjective optimization. (English) Zbl 1375.90277

Daras, Nicholas J. (ed.) et al., Operations research, engineering, and cyber security. Trends in applied mathematics and technology. Based on the presentations at the conference, Nea Peramos, Greece, May 2015. Cham: Springer (ISBN 978-3-319-51498-7/hbk; 978-3-319-51500-7/ebook). Springer Optimization and Its Applications 113, 403-422 (2017).
Summary: 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.
For the entire collection see [Zbl 1369.90003].

MSC:

90C29 Multi-objective and goal programming
65K05 Numerical mathematical programming methods
49M37 Numerical methods based on nonlinear programming
90C30 Nonlinear programming
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