Nonlinear biobjective optimization: improving the upper envelope using feasible line segments

Ignacio Araya (), Damir Aliquintui (), Franco Ardiles () and Braulio Lobo ()
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Ignacio Araya: Pontificia Universidad Católica de Valparaíso
Damir Aliquintui: Pontificia Universidad Católica de Valparaíso
Franco Ardiles: Pontificia Universidad Católica de Valparaíso
Braulio Lobo: Pontificia Universidad Católica de Valparaíso

Journal of Global Optimization, 2021, vol. 79, issue 2, No 12, 503-520

Abstract: Abstract In this work, we propose a segment-based representation for the upper bound of the non-dominated set in interval branch & bound solvers for biobjective non linear optimization. We ensure that every point over the upper line segments is dominated by at least one point in the feasible objective region. Segments are generated by linear envelopes of the image of feasible line segments. Finally, we show that the segment-based representation together with methods for generating upper line segments allows us to converge more quickly to the desired precision of the whole strategy. The code of our solver can be found in our git repository ( https://github.com/INFPUCV/ibex-lib/tree/master/plugins/optim-mop ).

Keywords: Interval methods; Branch & bound; Multiobjective optimization (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10898-021-00991-7

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