The point-based robustness gap for uncertain multiobjective optimization
In robust single-objective optimization, the robustness gap is a measure of the distance between the robust optimal objective value and the optimal objective values of the scenarios. While robust multiobjective optimization is a growing field of study, no notion of a robustness gap has been proposed...
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| Veröffentlicht in: | Optimization Jg. 73; H. 6; S. 1897 - 1931 |
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| Abstract | In robust single-objective optimization, the robustness gap is a measure of the distance between the robust optimal objective value and the optimal objective values of the scenarios. While robust multiobjective optimization is a growing field of study, no notion of a robustness gap has been proposed. A concept of a point-based robustness gap for uncertain multiobjective optimization problems is introduced. The gap is defined as the minimal distance between the robust Pareto set and the Pareto sets of the scenarios. It is shown that the gap is zero whenever the uncertainty is constraint-wise and objective-wise, supplementing a major result about the single-objective robustness gap. Because the distance between Pareto sets is hard to compute, lower and upper bounds on the gap are constructed for convex problems. Specific results about the zero gap and the bounds are presented for linear problems. Numerical examples are included. |
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| AbstractList | In robust single-objective optimization, the robustness gap is a measure of the distance between the robust optimal objective value and the optimal objective values of the scenarios. While robust multiobjective optimization is a growing field of study, no notion of a robustness gap has been proposed. A concept of a point-based robustness gap for uncertain multiobjective optimization problems is introduced. The gap is defined as the minimal distance between the robust Pareto set and the Pareto sets of the scenarios. It is shown that the gap is zero whenever the uncertainty is constraint-wise and objective-wise, supplementing a major result about the single-objective robustness gap. Because the distance between Pareto sets is hard to compute, lower and upper bounds on the gap are constructed for convex problems. Specific results about the zero gap and the bounds are presented for linear problems. Numerical examples are included. |
| Author | Krüger, Corinna Schöbel, Anita Fritzen, Lena Wiecek, Margaret M. |
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| Cites_doi | 10.1006/jmaa.1999.6541 10.1002/mcda.1653 10.1137/130939596 10.1016/j.ejor.2007.03.048 10.1016/j.ejor.2013.02.037 10.1287/educ.2016.0153 10.1287/moor.23.4.769 10.1016/0022-247X(68)90201-1 10.1007/s00291-015-0418-7 10.1016/j.ejor.2020.09.045 10.1007/s101070100286 10.1007/978-1-4757-2827-9 10.1007/978-3-642-02886-1 10.1023/A:1021765131316 10.1016/j.ejor.2014.10.027 10.1186/1687-1812-2014-83 10.1007/BF00936168 10.1016/j.na.2016.01.002 10.1080/03052150008941314 10.1287/opre.33.5.1074 10.1016/S0167-6377(99)00016-4 10.1137/0134018 10.1063/1.2715540 10.1515/9781400831050 10.1016/j.ejor.2017.02.014 10.1007/978-3-642-50280-4 10.1016/j.ejor.2018.08.020 10.1007/s10107-018-1235-y 10.1007/s10479-017-2751-5 10.1007/s10898-017-0518-9 10.1016/j.ejor.2013.10.028 10.1137/08073682X 10.1016/j.ejor.2016.01.015 10.1007/978-1-4615-2025-2_4 10.1016/j.ejor.2021.03.068 10.1016/j.ejor.2014.03.013 10.1016/j.ejor.2018.07.035 |
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| References | e_1_3_2_27_1 Berge C. (e_1_3_2_30_1) 1963 e_1_3_2_28_1 e_1_3_2_29_1 e_1_3_2_42_1 e_1_3_2_20_1 e_1_3_2_41_1 e_1_3_2_21_1 e_1_3_2_22_1 e_1_3_2_23_1 e_1_3_2_24_1 e_1_3_2_25_1 e_1_3_2_26_1 Kim NTB (e_1_3_2_36_1) 2000; 25 e_1_3_2_40_1 e_1_3_2_39_1 e_1_3_2_9_1 e_1_3_2_17_1 e_1_3_2_38_1 e_1_3_2_8_1 Ehrgott M. (e_1_3_2_16_1) 2005 e_1_3_2_18_1 e_1_3_2_7_1 e_1_3_2_19_1 Kuroiwa D (e_1_3_2_10_1) 2012; 40 e_1_3_2_2_1 e_1_3_2_31_1 e_1_3_2_33_1 e_1_3_2_11_1 e_1_3_2_32_1 e_1_3_2_6_1 e_1_3_2_12_1 e_1_3_2_35_1 e_1_3_2_5_1 e_1_3_2_13_1 e_1_3_2_34_1 e_1_3_2_4_1 e_1_3_2_14_1 e_1_3_2_37_1 e_1_3_2_3_1 e_1_3_2_15_1 |
| References_xml | – ident: e_1_3_2_26_1 doi: 10.1006/jmaa.1999.6541 – volume: 25 start-page: 101 issue: 1 year: 2000 ident: e_1_3_2_36_1 article-title: Normal cones to a polyhedral convex set and generating efficient faces in linear multiobjective programming publication-title: Acta Math Vietnam – ident: e_1_3_2_17_1 doi: 10.1002/mcda.1653 – volume-title: Topological spaces: including a treatment of multi-valued functions, vector spaces and convexity year: 1963 ident: e_1_3_2_30_1 – ident: e_1_3_2_8_1 doi: 10.1137/130939596 – ident: e_1_3_2_35_1 doi: 10.1016/j.ejor.2007.03.048 – ident: e_1_3_2_20_1 doi: 10.1016/j.ejor.2013.02.037 – ident: e_1_3_2_4_1 doi: 10.1287/educ.2016.0153 – volume: 40 start-page: 305 issue: 2 year: 2012 ident: e_1_3_2_10_1 article-title: On robust multiobjective optimization publication-title: Vietnam J Math – ident: e_1_3_2_14_1 doi: 10.1287/moor.23.4.769 – ident: e_1_3_2_27_1 doi: 10.1016/0022-247X(68)90201-1 – ident: e_1_3_2_3_1 doi: 10.1007/s00291-015-0418-7 – ident: e_1_3_2_11_1 doi: 10.1016/j.ejor.2020.09.045 – volume-title: Multicriteria optimization year: 2005 ident: e_1_3_2_16_1 – ident: e_1_3_2_31_1 doi: 10.1007/s101070100286 – ident: e_1_3_2_24_1 doi: 10.1007/978-1-4757-2827-9 – ident: e_1_3_2_28_1 doi: 10.1007/978-3-642-02886-1 – ident: e_1_3_2_39_1 doi: 10.1023/A:1021765131316 – ident: e_1_3_2_19_1 doi: 10.1016/j.ejor.2014.10.027 – ident: e_1_3_2_42_1 doi: 10.1186/1687-1812-2014-83 – ident: e_1_3_2_23_1 doi: 10.1007/BF00936168 – ident: e_1_3_2_6_1 doi: 10.1016/j.na.2016.01.002 – ident: e_1_3_2_33_1 doi: 10.1080/03052150008941314 – ident: e_1_3_2_37_1 doi: 10.1287/opre.33.5.1074 – ident: e_1_3_2_15_1 doi: 10.1016/S0167-6377(99)00016-4 – ident: e_1_3_2_25_1 doi: 10.1137/0134018 – ident: e_1_3_2_32_1 doi: 10.1063/1.2715540 – ident: e_1_3_2_2_1 doi: 10.1515/9781400831050 – ident: e_1_3_2_38_1 doi: 10.1016/j.ejor.2017.02.014 – ident: e_1_3_2_29_1 doi: 10.1007/978-3-642-50280-4 – ident: e_1_3_2_5_1 doi: 10.1016/j.ejor.2018.08.020 – ident: e_1_3_2_41_1 doi: 10.1007/s10107-018-1235-y – ident: e_1_3_2_22_1 doi: 10.1007/s10479-017-2751-5 – ident: e_1_3_2_13_1 doi: 10.1007/s10898-017-0518-9 – ident: e_1_3_2_7_1 doi: 10.1016/j.ejor.2013.10.028 – ident: e_1_3_2_34_1 doi: 10.1137/08073682X – ident: e_1_3_2_21_1 doi: 10.1016/j.ejor.2016.01.015 – ident: e_1_3_2_40_1 doi: 10.1007/978-1-4615-2025-2_4 – ident: e_1_3_2_9_1 doi: 10.1016/j.ejor.2021.03.068 – ident: e_1_3_2_12_1 doi: 10.1016/j.ejor.2014.03.013 – ident: e_1_3_2_18_1 doi: 10.1016/j.ejor.2018.07.035 |
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| SubjectTerms | efficient solution minmax optimization Multi-criteria programming Multiple objective analysis Pareto optimization pareto outcome robust optimization Robustness Upper bounds |
| Title | The point-based robustness gap for uncertain multiobjective optimization |
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