The Pareto Tracer for General Inequality Constrained Multi-Objective Optimization Problems
Problems where several incommensurable objectives have to be optimized concurrently arise in many engineering and financial applications. Continuation methods for the treatment of such multi-objective optimization methods (MOPs) are very efficient if all objectives are continuous since in that case...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-12-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/25/4/80 |
| _version_ | 1827699649580892160 |
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| author | Fernanda Beltrán Oliver Cuate Oliver Schütze |
| author_facet | Fernanda Beltrán Oliver Cuate Oliver Schütze |
| author_sort | Fernanda Beltrán |
| collection | DOAJ |
| description | Problems where several incommensurable objectives have to be optimized concurrently arise in many engineering and financial applications. Continuation methods for the treatment of such multi-objective optimization methods (MOPs) are very efficient if all objectives are continuous since in that case one can expect that the solution set forms at least locally a manifold. Recently, the Pareto Tracer (PT) has been proposed, which is such a multi-objective continuation method. While the method works reliably for MOPs with box and equality constraints, no strategy has been proposed yet to adequately treat general inequalities, which we address in this work. We formulate the extension of the PT and present numerical results on some selected benchmark problems. The results indicate that the new method can indeed handle general MOPs, which greatly enhances its applicability. |
| first_indexed | 2024-03-10T13:54:38Z |
| format | Article |
| id | doaj.art-cf99f3cbcdc54d6ebd7d786f71d8cd4b |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-10T13:54:38Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-cf99f3cbcdc54d6ebd7d786f71d8cd4b2023-11-21T01:46:07ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472020-12-012548010.3390/mca25040080The Pareto Tracer for General Inequality Constrained Multi-Objective Optimization ProblemsFernanda Beltrán0Oliver Cuate1Oliver Schütze2Computer Science Department, Cinvestav-IPN, 07360 Mexico City, MexicoComputer Science Department, Cinvestav-IPN, 07360 Mexico City, MexicoComputer Science Department, Cinvestav-IPN, 07360 Mexico City, MexicoProblems where several incommensurable objectives have to be optimized concurrently arise in many engineering and financial applications. Continuation methods for the treatment of such multi-objective optimization methods (MOPs) are very efficient if all objectives are continuous since in that case one can expect that the solution set forms at least locally a manifold. Recently, the Pareto Tracer (PT) has been proposed, which is such a multi-objective continuation method. While the method works reliably for MOPs with box and equality constraints, no strategy has been proposed yet to adequately treat general inequalities, which we address in this work. We formulate the extension of the PT and present numerical results on some selected benchmark problems. The results indicate that the new method can indeed handle general MOPs, which greatly enhances its applicability.https://www.mdpi.com/2297-8747/25/4/80multi-objective optimizationPareto Tracercontinuationconstraint handling |
| spellingShingle | Fernanda Beltrán Oliver Cuate Oliver Schütze The Pareto Tracer for General Inequality Constrained Multi-Objective Optimization Problems Mathematical and Computational Applications multi-objective optimization Pareto Tracer continuation constraint handling |
| title | The Pareto Tracer for General Inequality Constrained Multi-Objective Optimization Problems |
| title_full | The Pareto Tracer for General Inequality Constrained Multi-Objective Optimization Problems |
| title_fullStr | The Pareto Tracer for General Inequality Constrained Multi-Objective Optimization Problems |
| title_full_unstemmed | The Pareto Tracer for General Inequality Constrained Multi-Objective Optimization Problems |
| title_short | The Pareto Tracer for General Inequality Constrained Multi-Objective Optimization Problems |
| title_sort | pareto tracer for general inequality constrained multi objective optimization problems |
| topic | multi-objective optimization Pareto Tracer continuation constraint handling |
| url | https://www.mdpi.com/2297-8747/25/4/80 |
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