A new exact method for linear bilevel problems with multiple objective functions at the lower level
•Exact method to optimize semivectorial bilevel linear problems.•The method explores efficient extreme solutions of a multiobjective linear problem.•New heuristic procedure for problems where the global optimum is difficult to reach.•The heuristic can lead to distinct final solutions using different...
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| Vydáno v: | European journal of operational research Ročník 303; číslo 1; s. 312 - 327 |
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| Jazyk: | angličtina |
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Elsevier B.V
16.11.2022
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| ISSN: | 0377-2217, 1872-6860 |
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| Abstract | •Exact method to optimize semivectorial bilevel linear problems.•The method explores efficient extreme solutions of a multiobjective linear problem.•New heuristic procedure for problems where the global optimum is difficult to reach.•The heuristic can lead to distinct final solutions using different starting points.•Implementation of an effective multiobjective simplex method.
In this paper we consider linear bilevel programming problems with multiple objective functions at the lower level. We propose a general-purpose exact method to compute the optimistic optimal solution, which is based on the search of efficient extreme solutions of an associated multiobjective linear problem with many objective functions. We also explore a heuristic procedure relying on the same principles. Although this procedure cannot ensure the global optimal solution but just a local optimum, it has shown to be quite effective in problems where the global optimum is difficult to obtain within a reasonable timeframe. A computational study is presented to evaluate the performance of the exact method and the heuristic procedure, comparing them with an exact and an approximate method proposed by other authors, using randomly generated instances. Our approach reveals interesting results in problems with few upper-level variables. |
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| AbstractList | •Exact method to optimize semivectorial bilevel linear problems.•The method explores efficient extreme solutions of a multiobjective linear problem.•New heuristic procedure for problems where the global optimum is difficult to reach.•The heuristic can lead to distinct final solutions using different starting points.•Implementation of an effective multiobjective simplex method.
In this paper we consider linear bilevel programming problems with multiple objective functions at the lower level. We propose a general-purpose exact method to compute the optimistic optimal solution, which is based on the search of efficient extreme solutions of an associated multiobjective linear problem with many objective functions. We also explore a heuristic procedure relying on the same principles. Although this procedure cannot ensure the global optimal solution but just a local optimum, it has shown to be quite effective in problems where the global optimum is difficult to obtain within a reasonable timeframe. A computational study is presented to evaluate the performance of the exact method and the heuristic procedure, comparing them with an exact and an approximate method proposed by other authors, using randomly generated instances. Our approach reveals interesting results in problems with few upper-level variables. |
| Author | Henggeler Antunes, Carlos Alves, Maria João |
| Author_xml | – sequence: 1 givenname: Maria João orcidid: 0000-0002-2268-0110 surname: Alves fullname: Alves, Maria João email: mjalves@fe.uc.pt organization: University of Coimbra, CeBER, Faculty of Economics, Portugal – sequence: 2 givenname: Carlos surname: Henggeler Antunes fullname: Henggeler Antunes, Carlos email: ch@deec.uc.pt organization: Department of Electrical and Computer Engineering, University of Coimbra, Portugal |
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| Cites_doi | 10.1023/A:1008215702611 10.1287/opre.28.3.785 10.1007/s12351-019-00534-9 10.1016/j.apm.2015.04.041 10.1016/0377-2217(90)90010-9 10.1109/TEVC.2017.2712906 10.1016/j.ejor.2008.06.026 10.1186/1029-242X-2014-164 10.1007/978-3-030-11482-4_10 10.1007/BF00933152 10.1016/j.cor.2017.12.014 10.1287/mnsc.30.8.1004 10.1007/BF01580111 10.1057/jors.1977.147 10.1007/s10107-016-1061-z 10.1016/j.ejor.2016.02.039 10.2298/FIL1408619Z 10.1016/j.ejor.2008.10.003 10.1016/j.omega.2010.02.002 10.1007/s10957-006-9150-4 10.1007/s12190-010-0430-7 |
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| Keywords | Multiobjective simplex method Linear bilevel optimization Multiple objective programming Semivectorial bilevel problem |
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| References | Bonnel, Morgan (bib0013) 2006; 131 Alves, Antunes, Carrasqueira (bib0002) 2015 Dempe (bib0016) 2002 Alves, Antunes, Costa (bib0003) 2019 Ankhili, Mansouri (bib0007) 2009; 197 Zionts, Wallenius (bib0031) 1980; 28 Antunes, Alves, Clímaco (bib0008) 2016 Ren, Wang (bib0024) 2016; 40 Evans, Steuer (bib0019) 1973; 5 Alves, Antunes, Costa (bib0004) 2021; 21 Löhne, Weißing (bib0022) 2017; 260 Schechter, Steuer (bib0026) 2005; 30 Zheng, Chen, Cao (bib0029) 2014; 28 Zheng, Wan (bib0030) 2011; 37 Bialas, Karwan (bib0011) 1984; 30 Bonnel (bib0012) 2006; 2 Benson (bib0010) 1998; 13 Fülöp (bib0020) 1993 Alves, Dempe, Júdice (bib0006) 2012; 61 Benson (bib0009) 1978; 26 Rudloff, Ulus, Vanderbei (bib0025) 2017; 163 Sinha, Malo, Deb (bib0027) 2018; 22 Alves, Antunes (bib0001) 2018; 92 Dempe, Mehlitz (bib0017) 2020; 69 Steuer (bib0028) 1986 Dauer, Liu (bib0015) 1990; 46 Lv, Wan (bib0023) 2014; 2014 Ehrgott (bib0018) 2005 Isermann (bib0021) 1977; 28 Alves, Costa (bib0005) 2009; 198 Calvete, Galé (bib0014) 2011; 39 Alves (10.1016/j.ejor.2022.02.047_bib0002) 2015 Ren (10.1016/j.ejor.2022.02.047_bib0024) 2016; 40 Dauer (10.1016/j.ejor.2022.02.047_bib0015) 1990; 46 Lv (10.1016/j.ejor.2022.02.047_bib0023) 2014; 2014 Bialas (10.1016/j.ejor.2022.02.047_bib0011) 1984; 30 Benson (10.1016/j.ejor.2022.02.047_bib0010) 1998; 13 Dempe (10.1016/j.ejor.2022.02.047_bib0017) 2020; 69 Sinha (10.1016/j.ejor.2022.02.047_bib0027) 2018; 22 Bonnel (10.1016/j.ejor.2022.02.047_bib0012) 2006; 2 Alves (10.1016/j.ejor.2022.02.047_bib0004) 2021; 21 Antunes (10.1016/j.ejor.2022.02.047_bib0008) 2016 Alves (10.1016/j.ejor.2022.02.047_bib0001) 2018; 92 Zheng (10.1016/j.ejor.2022.02.047_bib0029) 2014; 28 Calvete (10.1016/j.ejor.2022.02.047_bib0014) 2011; 39 Alves (10.1016/j.ejor.2022.02.047_bib0006) 2012; 61 Zheng (10.1016/j.ejor.2022.02.047_bib0030) 2011; 37 Zionts (10.1016/j.ejor.2022.02.047_bib0031) 1980; 28 Evans (10.1016/j.ejor.2022.02.047_bib0019) 1973; 5 Ankhili (10.1016/j.ejor.2022.02.047_bib0007) 2009; 197 Fülöp (10.1016/j.ejor.2022.02.047_bib0020) 1993 Isermann (10.1016/j.ejor.2022.02.047_bib0021) 1977; 28 Steuer (10.1016/j.ejor.2022.02.047_bib0028) 1986 Schechter (10.1016/j.ejor.2022.02.047_bib0026) 2005; 30 Dempe (10.1016/j.ejor.2022.02.047_bib0016) 2002 Rudloff (10.1016/j.ejor.2022.02.047_bib0025) 2017; 163 Ehrgott (10.1016/j.ejor.2022.02.047_bib0018) 2005 Benson (10.1016/j.ejor.2022.02.047_bib0009) 1978; 26 Bonnel (10.1016/j.ejor.2022.02.047_bib0013) 2006; 131 Löhne (10.1016/j.ejor.2022.02.047_bib0022) 2017; 260 Alves (10.1016/j.ejor.2022.02.047_bib0005) 2009; 198 Alves (10.1016/j.ejor.2022.02.047_bib0003) 2019 |
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