Nonlinear biobjective optimization: improvements to interval branch & bound algorithms

Interval based solvers are commonly used for solving single-objective nonlinear optimization problems. Their reliability and increasing performance make them useful when proofs of infeasibility and/or certification of solutions are a must. On the other hand, there exist only a few approaches dealing...

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Bibliographic Details
Published in:Journal of global optimization Vol. 75; no. 1; pp. 91 - 110
Main Authors: Araya, Ignacio, Campusano, Jose, Aliquintui, Damir
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2019
Springer
Springer Nature B.V
Subjects:
Algorithms
Computer Science
Mathematical optimization
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research/Decision Theory
Optimization
Real Functions
Solvers
Interval methods
Multiobjective optimization
Branch & bound
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:Interval based solvers are commonly used for solving single-objective nonlinear optimization problems. Their reliability and increasing performance make them useful when proofs of infeasibility and/or certification of solutions are a must. On the other hand, there exist only a few approaches dealing with nonlinear optimization problems, when they consider multiple objectives. In this paper, we propose a new interval branch & bound algorithm for solving nonlinear constrained biobjective optimization problems. Although the general strategy is based on other works, we propose some improvements related to the termination criteria, node selection, upperbounding and discarding boxes using the non-dominated set. Most of these techniques use and/or adapt components of IbexOpt, a state-of-the-art interval-based single-objective optimization algorithm. The code of our plugin can be found in our git repository ( https://github.com/INFPUCV/ibex-lib/tree/master/plugins/optim-mop ).
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-019-00768-z