A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III
In multi/many-objective evolutionary algorithms (MOEAs), to alleviate the degraded convergence pressure of Pareto dominance with the increase in the number of objectives, numerous modified dominance relationships were proposed. Recently, the strengthened dominance relation (SDR) has been proposed, w...
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2021-11-01
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| author | Saykat Dutta Sri Srinivasa Raju M Rammohan Mallipeddi Kedar Nath Das Dong-Gyu Lee |
| author_facet | Saykat Dutta Sri Srinivasa Raju M Rammohan Mallipeddi Kedar Nath Das Dong-Gyu Lee |
| author_sort | Saykat Dutta |
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| description | In multi/many-objective evolutionary algorithms (MOEAs), to alleviate the degraded convergence pressure of Pareto dominance with the increase in the number of objectives, numerous modified dominance relationships were proposed. Recently, the strengthened dominance relation (SDR) has been proposed, where the dominance area of a solution is determined by convergence degree and niche size (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>θ</mi><mo>¯</mo></mover></semantics></math></inline-formula>). Later, in controlled SDR (CSDR), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>θ</mi><mo>¯</mo></mover></semantics></math></inline-formula> and an additional parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> associated with the convergence degree are dynamically adjusted depending on the iteration count. Depending on the problem characteristics and the distribution of the current population, different situations require different values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>k</mi></semantics></math></inline-formula>, rendering the linear reduction of <i>k</i> based on the generation count ineffective. This is because a particular value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>k</mi></semantics></math></inline-formula> is expected to bias the dominance relationship towards a particular region on the Pareto front (PF). In addition, due to the same reason, using SDR or CSDR in the environmental selection cannot preserve the diversity of solutions required to cover the entire PF. Therefore, we propose an MOEA, referred to as NSGA-III*, where (1) a modified SDR (MSDR)-based mating selection with an adaptive ensemble of parameter <i>k</i> would prioritize parents from specific sections of the PF depending on <i>k</i>, and (2) the traditional weight vector and non-dominated sorting-based environmental selection of NSGA-III would protect the solutions corresponding to the entire PF. The performance of NSGA-III* is favourably compared with state-of-the-art MOEAs on DTLZ and WFG test suites with up to 10 objectives. |
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| spelling | doaj.art-b8050951ba5c4f06a3bf86b31cbf1c412023-11-23T00:13:51ZengMDPI AGMathematics2227-73902021-11-01922283710.3390/math9222837A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-IIISaykat Dutta0Sri Srinivasa Raju M1Rammohan Mallipeddi2Kedar Nath Das3Dong-Gyu Lee4Department of Mathematics, National Institute of Technology Silchar, Assam 788010, IndiaDepartment of Mathematics, National Institute of Technology Silchar, Assam 788010, IndiaDepartment of Artificial Intelligence, School of Electronics Engineering, Kyungpook National University, Daegu 41566, KoreaDepartment of Mathematics, National Institute of Technology Silchar, Assam 788010, IndiaDepartment of Artificial Intelligence, School of Electronics Engineering, Kyungpook National University, Daegu 41566, KoreaIn multi/many-objective evolutionary algorithms (MOEAs), to alleviate the degraded convergence pressure of Pareto dominance with the increase in the number of objectives, numerous modified dominance relationships were proposed. Recently, the strengthened dominance relation (SDR) has been proposed, where the dominance area of a solution is determined by convergence degree and niche size (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>θ</mi><mo>¯</mo></mover></semantics></math></inline-formula>). Later, in controlled SDR (CSDR), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>θ</mi><mo>¯</mo></mover></semantics></math></inline-formula> and an additional parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> associated with the convergence degree are dynamically adjusted depending on the iteration count. Depending on the problem characteristics and the distribution of the current population, different situations require different values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>k</mi></semantics></math></inline-formula>, rendering the linear reduction of <i>k</i> based on the generation count ineffective. This is because a particular value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>k</mi></semantics></math></inline-formula> is expected to bias the dominance relationship towards a particular region on the Pareto front (PF). In addition, due to the same reason, using SDR or CSDR in the environmental selection cannot preserve the diversity of solutions required to cover the entire PF. Therefore, we propose an MOEA, referred to as NSGA-III*, where (1) a modified SDR (MSDR)-based mating selection with an adaptive ensemble of parameter <i>k</i> would prioritize parents from specific sections of the PF depending on <i>k</i>, and (2) the traditional weight vector and non-dominated sorting-based environmental selection of NSGA-III would protect the solutions corresponding to the entire PF. The performance of NSGA-III* is favourably compared with state-of-the-art MOEAs on DTLZ and WFG test suites with up to 10 objectives.https://www.mdpi.com/2227-7390/9/22/2837convergencedecompositiondiversitydominanceensemble |
| spellingShingle | Saykat Dutta Sri Srinivasa Raju M Rammohan Mallipeddi Kedar Nath Das Dong-Gyu Lee A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III Mathematics convergence decomposition diversity dominance ensemble |
| title | A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III |
| title_full | A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III |
| title_fullStr | A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III |
| title_full_unstemmed | A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III |
| title_short | A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III |
| title_sort | mating selection based on modified strengthened dominance relation for nsga iii |
| topic | convergence decomposition diversity dominance ensemble |
| url | https://www.mdpi.com/2227-7390/9/22/2837 |
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