Multi-objective optimization with convex quadratic cost functions: A multi-parametric programming approach
•Formulation of the multi-objective optimization problem as a multi-parametric QCQP.•Derivation of suitable affine overestimators with a guaranteed bound of suboptimality.•Solution of the resulting mp-QP problem with state-of-the-art solvers, thus obtaining the Pareto front explicitly.•Numerical exa...
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| Vydáno v: | Computers & chemical engineering Ročník 85; s. 36 - 39 |
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02.02.2016
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| ISSN: | 0098-1354, 1873-4375 |
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| Abstract | •Formulation of the multi-objective optimization problem as a multi-parametric QCQP.•Derivation of suitable affine overestimators with a guaranteed bound of suboptimality.•Solution of the resulting mp-QP problem with state-of-the-art solvers, thus obtaining the Pareto front explicitly.•Numerical examples highlight the capabilities of this approach.
In this note we present an approximate algorithm for the explicit calculation of the Pareto front for multi-objective optimization problems featuring convex quadratic cost functions and linear constraints based on multi-parametric programming and employing a set of suitable overestimators with tunable suboptimality. A numerical example as well as a small computational study highlight the features of the novel algorithm. |
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| AbstractList | In this note we present an approximate algorithm for the explicit calculation of the Pareto front for multi-objective optimization problems featuring convex quadratic cost functions and linear constraints based on multi-parametric programming and employing a set of suitable overestimators with tunable suboptimality. A numerical example as well as a small computational study highlight the features of the novel algorithm. •Formulation of the multi-objective optimization problem as a multi-parametric QCQP.•Derivation of suitable affine overestimators with a guaranteed bound of suboptimality.•Solution of the resulting mp-QP problem with state-of-the-art solvers, thus obtaining the Pareto front explicitly.•Numerical examples highlight the capabilities of this approach. In this note we present an approximate algorithm for the explicit calculation of the Pareto front for multi-objective optimization problems featuring convex quadratic cost functions and linear constraints based on multi-parametric programming and employing a set of suitable overestimators with tunable suboptimality. A numerical example as well as a small computational study highlight the features of the novel algorithm. |
| Author | Pistikopoulos, Efstratios N. Oberdieck, Richard |
| Author_xml | – sequence: 1 givenname: Richard surname: Oberdieck fullname: Oberdieck, Richard organization: Department of Chemical Engineering, Centre for Process Systems Engineering, Imperial College London, London, United Kingdom – sequence: 2 givenname: Efstratios N. surname: Pistikopoulos fullname: Pistikopoulos, Efstratios N. email: stratos@tamu.edu organization: Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, TX, United States |
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| Cites_doi | 10.1016/j.compchemeng.2014.12.012 10.1002/nav.3800020106 10.1016/S0005-1098(01)00174-1 10.1080/10556780903239568 10.1007/s00158-003-0368-6 10.1007/BF01580665 10.1007/BF00539118 10.1021/ie970720n 10.1016/j.compchemeng.2014.04.003 10.1016/j.compchemeng.2015.07.013 10.1016/j.compchemeng.2015.01.013 10.1287/mnsc.23.2.159 10.1016/j.automatica.2011.06.019 10.1016/0377-2217(95)00040-2 |
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| SubjectTerms | Algorithms Approximation Chemical engineering Cost function Explicit Pareto front calculation Mathematical analysis Multi-objective optimization Multi-parametric programming Optimization Pareto optimality Programming |
| Title | Multi-objective optimization with convex quadratic cost functions: A multi-parametric programming approach |
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