Goal seeking Quadratic Unconstrained Binary Optimization
The Quadratic Unconstrained Binary Optimization (QUBO) modeling and solution framework is a requirement for quantum and digital annealers. However optimality for QUBO problems of any practical size is extremely difficult to achieve. In order to incorporate the problem-specific insights, a diverse se...
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| Vydáno v: | Results in control and optimization Ročník 7; s. 100125 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
01.06.2022
Elsevier |
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| ISSN: | 2666-7207, 2666-7207 |
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| Abstract | The Quadratic Unconstrained Binary Optimization (QUBO) modeling and solution framework is a requirement for quantum and digital annealers. However optimality for QUBO problems of any practical size is extremely difficult to achieve. In order to incorporate the problem-specific insights, a diverse set of solutions meeting an acceptable target metric or goal is the preference in high level decision making. In this paper, we present two alternatives for goal-seeking QUBO for minimizing the deviation from a given target as well as a range of values around a target. Experimental results illustrate the efficacy of the proposed approach over Constraint Programming for quickly finding a satisficing set of solutions. |
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| AbstractList | The Quadratic Unconstrained Binary Optimization (QUBO) modeling and solution framework is a requirement for quantum and digital annealers. However optimality for QUBO problems of any practical size is extremely difficult to achieve. In order to incorporate the problem-specific insights, a diverse set of solutions meeting an acceptable target metric or goal is the preference in high level decision making. In this paper, we present two alternatives for goal-seeking QUBO for minimizing the deviation from a given target as well as a range of values around a target. Experimental results illustrate the efficacy of the proposed approach over Constraint Programming for quickly finding a satisficing set of solutions. |
| ArticleNumber | 100125 |
| Author | Verma, Amit Lewis, Mark |
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| Cites_doi | 10.15388/Informatica.2006.138 10.1016/j.asoc.2019.105485 10.1016/0097-8485(90)80007-O 10.1007/BF00934527 10.1016/S0928-4869(97)00011-6 10.1007/s10472-011-9233-2 10.1007/s00291-003-0153-3 10.1016/j.knosys.2017.11.009 10.1016/j.neucom.2016.09.122 10.1007/s11590-019-01460-7 10.1007/s10732-011-9170-6 10.1007/s10288-009-0115-y 10.1057/jors.1990.166 10.1016/S0026-2714(96)00042-X 10.1016/j.ejor.2012.07.012 10.1007/s10878-014-9734-0 10.1016/j.asoc.2013.11.008 10.1007/s10288-019-00424-y 10.1023/B:ANOR.0000039522.58036.68 |
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| Keywords | Goal seeking What if Quadratic Unconstrained Binary Optimization Quantum computer Pseudo-Boolean optimization Goal programming |
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| References | Glover, Kochenberger, Du (b3) 2019; 17 Lovász, Pelikán, Vesztergombi (b19) 2006 Hannan (b15) 1980; 18 Beasley (b23) 1990; 41 Lewis, Verma, Eckdahl (b8) 2021 Palubeckis (b21) 2006; 17 Sherali, Soyster (b26) 1983; 39 Matheson (b5) 1990; 14 Zhou, Kong, Wu, Liu, Cai, Liu (b13) 2019; 81 Verma, Lewis (b14) 2020; 14 Stadler (b16) 2002 Marques-Silva, Argelich, Graça, Lynce (b9) 2011; 62 Zangari, Pozo, Santana, Mendiburu (b11) 2017; 246 Wang, Lü, Glover, Hao (b24) 2012; 223 Glover, Lü, Hao (b22) 2010; 8 Nethercote, Stuckey, Becket, Brand, Duck, Tack (b25) 2007 Zhou, Wang, Wu, Wu (b12) 2018; 141 Arsham (b7) 1997; 37 Verma, Lewis (b18) 2020 Taguchi, Cariapa (b4) 1993 Liefooghe, Verel, Hao (b10) 2014; 16 Kochenberger, Glover, Alidaee, Rego (b1) 2004; 26 Arsham (b6) 1998; 6 Kochenberger, Hao, Glover, Lewis, Lü, Wang (b2) 2014; 28 Chicano, Alba (b17) 2013; 19 Palubeckis (b20) 2004; 131 Kochenberger (10.1016/j.rico.2022.100125_b2) 2014; 28 Hannan (10.1016/j.rico.2022.100125_b15) 1980; 18 Liefooghe (10.1016/j.rico.2022.100125_b10) 2014; 16 Chicano (10.1016/j.rico.2022.100125_b17) 2013; 19 Wang (10.1016/j.rico.2022.100125_b24) 2012; 223 Beasley (10.1016/j.rico.2022.100125_b23) 1990; 41 Verma (10.1016/j.rico.2022.100125_b18) 2020 Arsham (10.1016/j.rico.2022.100125_b6) 1998; 6 Glover (10.1016/j.rico.2022.100125_b22) 2010; 8 Taguchi (10.1016/j.rico.2022.100125_b4) 1993 Kochenberger (10.1016/j.rico.2022.100125_b1) 2004; 26 Zhou (10.1016/j.rico.2022.100125_b13) 2019; 81 Arsham (10.1016/j.rico.2022.100125_b7) 1997; 37 Nethercote (10.1016/j.rico.2022.100125_b25) 2007 Verma (10.1016/j.rico.2022.100125_b14) 2020; 14 Stadler (10.1016/j.rico.2022.100125_b16) 2002 Glover (10.1016/j.rico.2022.100125_b3) 2019; 17 Marques-Silva (10.1016/j.rico.2022.100125_b9) 2011; 62 Lovász (10.1016/j.rico.2022.100125_b19) 2006 Zhou (10.1016/j.rico.2022.100125_b12) 2018; 141 Sherali (10.1016/j.rico.2022.100125_b26) 1983; 39 Matheson (10.1016/j.rico.2022.100125_b5) 1990; 14 Palubeckis (10.1016/j.rico.2022.100125_b20) 2004; 131 Lewis (10.1016/j.rico.2022.100125_b8) 2021 Zangari (10.1016/j.rico.2022.100125_b11) 2017; 246 Palubeckis (10.1016/j.rico.2022.100125_b21) 2006; 17 |
| References_xml | – start-page: 183 year: 2002 end-page: 204 ident: b16 article-title: Fitness landscapes publication-title: Biological evolution and statistical physics – volume: 246 start-page: 58 year: 2017 end-page: 68 ident: b11 article-title: A decomposition-based binary ACO algorithm for the multiobjective UBQP publication-title: Neurocomputing – volume: 17 start-page: 279 year: 2006 end-page: 296 ident: b21 article-title: Iterated tabu search for the unconstrained binary quadratic optimization problem publication-title: Informatica – volume: 37 start-page: 391 year: 1997 end-page: 395 ident: b7 article-title: Goal-seeking problem in discrete event systems simulation publication-title: Microelectron Reliab – volume: 16 start-page: 10 year: 2014 end-page: 19 ident: b10 article-title: A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming publication-title: Appl Soft Comput – year: 1993 ident: b4 article-title: Taguchi on robust technology development – volume: 14 start-page: 49 year: 1990 end-page: 57 ident: b5 article-title: A critical comparison of least absolute deviation fitting (robust) and least squares fitting: The importance of error distributions publication-title: Comput Chem – volume: 141 start-page: 18 year: 2018 end-page: 30 ident: b12 article-title: A multi-objective tabu search algorithm based on decomposition for multi-objective unconstrained binary quadratic programming problem publication-title: Knowl-Based Syst – volume: 28 start-page: 58 year: 2014 end-page: 81 ident: b2 article-title: The unconstrained binary quadratic programming problem: a survey publication-title: J Comb Optim – volume: 131 start-page: 259 year: 2004 end-page: 282 ident: b20 article-title: Multistart tabu search strategies for the unconstrained binary quadratic optimization problem publication-title: Ann Oper Res – start-page: 1 year: 2021 end-page: 23 ident: b8 article-title: Qfold: a new modeling paradigm for the RNA folding problem publication-title: J Heuristics – volume: 62 start-page: 317 year: 2011 end-page: 343 ident: b9 article-title: Boolean lexicographic optimization: algorithms & applications publication-title: Ann Math Artif Intell – volume: 18 start-page: 300 year: 1980 end-page: 309 ident: b15 article-title: Nondominance in goal programming publication-title: INFOR: Inf Syst Oper Res – volume: 223 start-page: 595 year: 2012 end-page: 604 ident: b24 article-title: Path relinking for unconstrained binary quadratic programming publication-title: European J Oper Res – volume: 14 start-page: 1557 year: 2020 end-page: 1569 ident: b14 article-title: Optimal quadratic reformulations of fourth degree pseudo-boolean functions publication-title: Optim Lett – volume: 19 start-page: 711 year: 2013 end-page: 728 ident: b17 article-title: Elementary landscape decomposition of the 0-1 unconstrained quadratic optimization publication-title: J Heuristics – year: 2020 ident: b18 article-title: Penalty and partitioning techniques to improve performance of qubo solvers publication-title: Discrete Optim – volume: 41 start-page: 1069 year: 1990 end-page: 1072 ident: b23 article-title: OR-library: distributing test problems by electronic mail publication-title: J Oper Res Soc – volume: 39 start-page: 173 year: 1983 end-page: 186 ident: b26 article-title: Preemptive and nonpreemptive multi-objective programming: Relationship and counterexamples publication-title: J Optim Theory Appl – year: 2006 ident: b19 article-title: Diskrete mathematik – volume: 26 start-page: 237 year: 2004 end-page: 250 ident: b1 article-title: A unified modeling and solution framework for combinatorial optimization problems publication-title: OR Spectrum – volume: 81 year: 2019 ident: b13 article-title: Ensemble of multi-objective metaheuristic algorithms for multi-objective unconstrained binary quadratic programming problem publication-title: Appl Soft Comput – volume: 8 start-page: 239 year: 2010 end-page: 253 ident: b22 article-title: Diversification-driven tabu search for unconstrained binary quadratic problems publication-title: 4OR – start-page: 529 year: 2007 end-page: 543 ident: b25 article-title: MiniZinc: Towards a standard CP modelling language publication-title: International conference on principles and practice of constraint programming – volume: 6 start-page: 1 year: 1998 end-page: 22 ident: b6 article-title: Algorithms for sensitivity information in discrete-event systems simulation publication-title: Simul Pract Theory – volume: 17 start-page: 335 year: 2019 end-page: 371 ident: b3 article-title: Quantum bridge analytics I: a tutorial on formulating and using QUBO models publication-title: 4OR – volume: 18 start-page: 300 issue: 4 year: 1980 ident: 10.1016/j.rico.2022.100125_b15 article-title: Nondominance in goal programming publication-title: INFOR: Inf Syst Oper Res – volume: 17 start-page: 279 issue: 2 year: 2006 ident: 10.1016/j.rico.2022.100125_b21 article-title: Iterated tabu search for the unconstrained binary quadratic optimization problem publication-title: Informatica doi: 10.15388/Informatica.2006.138 – volume: 81 year: 2019 ident: 10.1016/j.rico.2022.100125_b13 article-title: Ensemble of multi-objective metaheuristic algorithms for multi-objective unconstrained binary quadratic programming problem publication-title: Appl Soft Comput doi: 10.1016/j.asoc.2019.105485 – volume: 14 start-page: 49 issue: 1 year: 1990 ident: 10.1016/j.rico.2022.100125_b5 article-title: A critical comparison of least absolute deviation fitting (robust) and least squares fitting: The importance of error distributions publication-title: Comput Chem doi: 10.1016/0097-8485(90)80007-O – volume: 39 start-page: 173 issue: 2 year: 1983 ident: 10.1016/j.rico.2022.100125_b26 article-title: Preemptive and nonpreemptive multi-objective programming: Relationship and counterexamples publication-title: J Optim Theory Appl doi: 10.1007/BF00934527 – volume: 6 start-page: 1 issue: 1 year: 1998 ident: 10.1016/j.rico.2022.100125_b6 article-title: Algorithms for sensitivity information in discrete-event systems simulation publication-title: Simul Pract Theory doi: 10.1016/S0928-4869(97)00011-6 – volume: 62 start-page: 317 issue: 3 year: 2011 ident: 10.1016/j.rico.2022.100125_b9 article-title: Boolean lexicographic optimization: algorithms & applications publication-title: Ann Math Artif Intell doi: 10.1007/s10472-011-9233-2 – start-page: 183 year: 2002 ident: 10.1016/j.rico.2022.100125_b16 article-title: Fitness landscapes – year: 2020 ident: 10.1016/j.rico.2022.100125_b18 article-title: Penalty and partitioning techniques to improve performance of qubo solvers publication-title: Discrete Optim – volume: 26 start-page: 237 issue: 2 year: 2004 ident: 10.1016/j.rico.2022.100125_b1 article-title: A unified modeling and solution framework for combinatorial optimization problems publication-title: OR Spectrum doi: 10.1007/s00291-003-0153-3 – volume: 141 start-page: 18 year: 2018 ident: 10.1016/j.rico.2022.100125_b12 article-title: A multi-objective tabu search algorithm based on decomposition for multi-objective unconstrained binary quadratic programming problem publication-title: Knowl-Based Syst doi: 10.1016/j.knosys.2017.11.009 – year: 1993 ident: 10.1016/j.rico.2022.100125_b4 – start-page: 529 year: 2007 ident: 10.1016/j.rico.2022.100125_b25 article-title: MiniZinc: Towards a standard CP modelling language – volume: 246 start-page: 58 year: 2017 ident: 10.1016/j.rico.2022.100125_b11 article-title: A decomposition-based binary ACO algorithm for the multiobjective UBQP publication-title: Neurocomputing doi: 10.1016/j.neucom.2016.09.122 – year: 2006 ident: 10.1016/j.rico.2022.100125_b19 – volume: 14 start-page: 1557 issue: 6 year: 2020 ident: 10.1016/j.rico.2022.100125_b14 article-title: Optimal quadratic reformulations of fourth degree pseudo-boolean functions publication-title: Optim Lett doi: 10.1007/s11590-019-01460-7 – volume: 19 start-page: 711 issue: 4 year: 2013 ident: 10.1016/j.rico.2022.100125_b17 article-title: Elementary landscape decomposition of the 0-1 unconstrained quadratic optimization publication-title: J Heuristics doi: 10.1007/s10732-011-9170-6 – volume: 8 start-page: 239 issue: 3 year: 2010 ident: 10.1016/j.rico.2022.100125_b22 article-title: Diversification-driven tabu search for unconstrained binary quadratic problems publication-title: 4OR doi: 10.1007/s10288-009-0115-y – volume: 41 start-page: 1069 issue: 11 year: 1990 ident: 10.1016/j.rico.2022.100125_b23 article-title: OR-library: distributing test problems by electronic mail publication-title: J Oper Res Soc doi: 10.1057/jors.1990.166 – volume: 37 start-page: 391 issue: 3 year: 1997 ident: 10.1016/j.rico.2022.100125_b7 article-title: Goal-seeking problem in discrete event systems simulation publication-title: Microelectron Reliab doi: 10.1016/S0026-2714(96)00042-X – volume: 223 start-page: 595 issue: 3 year: 2012 ident: 10.1016/j.rico.2022.100125_b24 article-title: Path relinking for unconstrained binary quadratic programming publication-title: European J Oper Res doi: 10.1016/j.ejor.2012.07.012 – volume: 28 start-page: 58 issue: 1 year: 2014 ident: 10.1016/j.rico.2022.100125_b2 article-title: The unconstrained binary quadratic programming problem: a survey publication-title: J Comb Optim doi: 10.1007/s10878-014-9734-0 – start-page: 1 year: 2021 ident: 10.1016/j.rico.2022.100125_b8 article-title: Qfold: a new modeling paradigm for the RNA folding problem publication-title: J Heuristics – volume: 16 start-page: 10 year: 2014 ident: 10.1016/j.rico.2022.100125_b10 article-title: A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming publication-title: Appl Soft Comput doi: 10.1016/j.asoc.2013.11.008 – volume: 17 start-page: 335 issue: 4 year: 2019 ident: 10.1016/j.rico.2022.100125_b3 article-title: Quantum bridge analytics I: a tutorial on formulating and using QUBO models 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| SubjectTerms | Goal programming Goal seeking Pseudo-Boolean optimization Quadratic Unconstrained Binary Optimization Quantum computer What if |
| Title | Goal seeking Quadratic Unconstrained Binary Optimization |
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