Penalty and partitioning techniques to improve performance of QUBO solvers
Quadratic Unconstrained Binary Optimization (QUBO) modeling has become a unifying framework for solving a wide variety of both unconstrained as well as constrained optimization problems. More recently, QUBO (or equivalent −1/+1 Ising Spin) models are a requirement for quantum annealing computers. No...
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| Vydáno v: | Discrete optimization Ročník 44; s. 100594 |
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| Jazyk: | angličtina |
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Elsevier B.V
01.05.2022
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| ISSN: | 1572-5286, 1873-636X |
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| Abstract | Quadratic Unconstrained Binary Optimization (QUBO) modeling has become a unifying framework for solving a wide variety of both unconstrained as well as constrained optimization problems. More recently, QUBO (or equivalent −1/+1 Ising Spin) models are a requirement for quantum annealing computers. Noisy Intermediate-Scale Quantum (NISQ) computing refers to classical computing preparing or compiling problem instances for compatibility with quantum hardware architectures. The process of converting a constrained problem to a QUBO compatible quantum annealing problem is an important part of the quantum compiler architecture and specifically when converting constrained models to unconstrained the choice of penalty magnitude is not trivial because using a large penalty to enforce constraints can overwhelm the solution landscape, while having too small a penalty allows infeasible optimal solutions. In this paper we present NISQ approaches to bound the magnitude of the penalty scalar M and demonstrate efficacy on a benchmark set of problems having a single equality constraint and present a QUBO partitioning approach validated by experimentation. |
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| AbstractList | Quadratic Unconstrained Binary Optimization (QUBO) modeling has become a unifying framework for solving a wide variety of both unconstrained as well as constrained optimization problems. More recently, QUBO (or equivalent −1/+1 Ising Spin) models are a requirement for quantum annealing computers. Noisy Intermediate-Scale Quantum (NISQ) computing refers to classical computing preparing or compiling problem instances for compatibility with quantum hardware architectures. The process of converting a constrained problem to a QUBO compatible quantum annealing problem is an important part of the quantum compiler architecture and specifically when converting constrained models to unconstrained the choice of penalty magnitude is not trivial because using a large penalty to enforce constraints can overwhelm the solution landscape, while having too small a penalty allows infeasible optimal solutions. In this paper we present NISQ approaches to bound the magnitude of the penalty scalar M and demonstrate efficacy on a benchmark set of problems having a single equality constraint and present a QUBO partitioning approach validated by experimentation. |
| ArticleNumber | 100594 |
| Author | Verma, Amit Lewis, Mark |
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| Cites_doi | 10.1016/j.ejor.2012.07.012 10.1007/s10878-014-9734-0 10.1007/JHEP11(2019)128 10.1007/BF00202749 10.1057/jors.1990.166 10.22331/q-2018-08-06-79 10.1504/IJOR.2016.075647 10.3389/fict.2016.00014 10.3390/a12040077 10.1007/s10288-019-00424-y 10.1007/s10732-011-9170-6 10.1016/S0304-3975(97)00176-X 10.1080/01621459.1949.10483310 |
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| Keywords | Quadratic Unconstrained Binary Optimization Nonlinear optimization Pseudo-Boolean optimization Equality constraint Inequality constraint |
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| References | Vyskocil, Djidjev (b6) 2018 (b19) 2019 Kochenberger, Hao, Glover, Lewis, Lü, Wang, Wang (b1) 2014; 28 Metropolis, Ulam (b22) 1949; 44 Lovász, Pelikán, Vesztergombi (b14) 2006 Bian, Chudak, Israel, Lackey, Macready, Roy (b9) 2016; 3 Glover, Kochenberger, Du (b2) 2019; 17 Glover, Kochenberger, Alidaee, Amini (b11) 2002 Cormier, Di Sipio, Wittek (b5) 2019; 2019 Beasley (b16) 1990; 41 Vyskočil, Pakin, Djidjev (b8) 2019 Verma, Lewis (b10) 2019 Bontempi, Birattari (b15) 2005; 3 Angel, Zissimopoulos (b20) 1998; 191 Weinberger (b21) 1990; 63 Mooney, Tonetto, Hill, Hollenberg (b3) 2019 Vyskocil, Djidjev (b7) 2019; 12 Chicano, Alba (b13) 2013; 19 Wang, Lü, Glover, Hao (b18) 2012; 223 Preskill (b4) 2018; 2 Lewis, Kochenberger (b17) 2016; 26 Stadler (b12) 2002 Kochenberger (10.1016/j.disopt.2020.100594_b1) 2014; 28 (10.1016/j.disopt.2020.100594_b19) 2019 Vyskočil (10.1016/j.disopt.2020.100594_b8) 2019 Bontempi (10.1016/j.disopt.2020.100594_b15) 2005; 3 Cormier (10.1016/j.disopt.2020.100594_b5) 2019; 2019 Vyskocil (10.1016/j.disopt.2020.100594_b6) 2018 Glover (10.1016/j.disopt.2020.100594_b11) 2002 Wang (10.1016/j.disopt.2020.100594_b18) 2012; 223 Angel (10.1016/j.disopt.2020.100594_b20) 1998; 191 Preskill (10.1016/j.disopt.2020.100594_b4) 2018; 2 Metropolis (10.1016/j.disopt.2020.100594_b22) 1949; 44 Stadler (10.1016/j.disopt.2020.100594_b12) 2002 Lewis (10.1016/j.disopt.2020.100594_b17) 2016; 26 Verma (10.1016/j.disopt.2020.100594_b10) 2019 Lovász (10.1016/j.disopt.2020.100594_b14) 2006 Beasley (10.1016/j.disopt.2020.100594_b16) 1990; 41 Vyskocil (10.1016/j.disopt.2020.100594_b7) 2019; 12 Glover (10.1016/j.disopt.2020.100594_b2) 2019; 17 Bian (10.1016/j.disopt.2020.100594_b9) 2016; 3 Weinberger (10.1016/j.disopt.2020.100594_b21) 1990; 63 Mooney (10.1016/j.disopt.2020.100594_b3) 2019 Chicano (10.1016/j.disopt.2020.100594_b13) 2013; 19 |
| References_xml | – start-page: 183 year: 2002 end-page: 204 ident: b12 article-title: Fitness landscapes publication-title: Biological Evolution and Statistical Physics – year: 2006 ident: b14 article-title: Diskrete Mathematik – volume: 3 start-page: 14 year: 2016 ident: b9 article-title: Mapping constrained optimization problems to quantum annealing with application to fault diagnosis publication-title: Front. ICT – volume: 63 start-page: 325 year: 1990 end-page: 336 ident: b21 article-title: Correlated and uncorrelated fitness landscapes and how to tell the difference publication-title: Biol. Cybern. – start-page: 11 year: 2019 end-page: 22 ident: b8 article-title: Embedding inequality constraints for quantum annealing optimization publication-title: International Workshop on Quantum Technology and Optimization Problems – volume: 19 start-page: 711 year: 2013 end-page: 728 ident: b13 article-title: Elementary landscape decomposition of the 0-1 unconstrained quadratic optimization publication-title: J. Heuristics – volume: 223 start-page: 595 year: 2012 end-page: 604 ident: b18 article-title: Path relinking for unconstrained binary quadratic programming publication-title: European J. Oper. Res. – volume: 191 start-page: 229 year: 1998 end-page: 243 ident: b20 article-title: Autocorrelation coefficient for the graph bipartitioning problem publication-title: Theoret. Comput. Sci. – start-page: 111 year: 2002 end-page: 121 ident: b11 article-title: Solving quadratic knapsack problems by reformulation and tabu search: Single constraint case publication-title: Combinatorial and Global Optimization – year: 2019 ident: b19 article-title: Results – volume: 2 start-page: 79 year: 2018 ident: b4 article-title: Quantum computing in the nisq era and beyond publication-title: Quantum – volume: 12 start-page: 77 year: 2019 ident: b7 article-title: Embedding equality constraints of optimization problems into a quantum annealer publication-title: Algorithms – volume: 3 year: 2005 ident: b15 article-title: From linearization to lazy learning: a survey of divide-and-conquer techniques for nonlinear control publication-title: Int. J. Comput. Cogn. – volume: 44 start-page: 335 year: 1949 end-page: 341 ident: b22 article-title: The monte carlo method publication-title: J. Amer. Statist. Assoc. – volume: 2019 start-page: 128 year: 2019 ident: b5 article-title: Unfolding measurement distributions via quantum annealing publication-title: J. High Energy Phys. – start-page: 1 year: 2019 end-page: 13 ident: b10 article-title: Optimal quadratic reformulations of fourth degree pseudo-boolean functions publication-title: Optim. Lett. – volume: 41 start-page: 1069 year: 1990 end-page: 1072 ident: b16 article-title: Or-library: distributing test problems by electronic mail publication-title: J. Oper. Res. Soc. – volume: 26 start-page: 13 year: 2016 end-page: 33 ident: b17 article-title: Probabilistic multistart with path relinking for solving the unconstrained binary quadratic problem publication-title: Int. J. Oper. Res. – volume: 28 start-page: 58 year: 2014 end-page: 81 ident: b1 article-title: The unconstrained binary quadratic programming problem: a survey publication-title: J. Comb. Optim. – year: 2019 ident: b3 article-title: Mapping np-hard problems to restricted adiabatic quantum architectures – start-page: 1 year: 2018 end-page: 11 ident: b6 article-title: Simple constraint embedding for quantum annealers publication-title: 2018 IEEE International Conference on Rebooting Computing – volume: 17 start-page: 335 year: 2019 end-page: 371 ident: b2 article-title: Quantum bridge analytics i: a tutorial on formulating and using qubo models publication-title: 4OR – start-page: 111 year: 2002 ident: 10.1016/j.disopt.2020.100594_b11 article-title: Solving quadratic knapsack problems by reformulation and tabu search: Single constraint case – start-page: 11 year: 2019 ident: 10.1016/j.disopt.2020.100594_b8 article-title: Embedding inequality constraints for quantum annealing optimization – volume: 223 start-page: 595 issue: 3 year: 2012 ident: 10.1016/j.disopt.2020.100594_b18 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.disopt.2020.100594_b1 article-title: The unconstrained binary quadratic programming problem: a survey publication-title: J. Comb. Optim. doi: 10.1007/s10878-014-9734-0 – volume: 2019 start-page: 128 issue: 11 year: 2019 ident: 10.1016/j.disopt.2020.100594_b5 article-title: Unfolding measurement distributions via quantum annealing publication-title: J. High Energy Phys. doi: 10.1007/JHEP11(2019)128 – year: 2019 ident: 10.1016/j.disopt.2020.100594_b19 – volume: 63 start-page: 325 issue: 5 year: 1990 ident: 10.1016/j.disopt.2020.100594_b21 article-title: Correlated and uncorrelated fitness landscapes and how to tell the difference publication-title: Biol. Cybern. doi: 10.1007/BF00202749 – volume: 41 start-page: 1069 issue: 11 year: 1990 ident: 10.1016/j.disopt.2020.100594_b16 article-title: Or-library: distributing test problems by electronic mail publication-title: J. Oper. Res. Soc. doi: 10.1057/jors.1990.166 – volume: 2 start-page: 79 year: 2018 ident: 10.1016/j.disopt.2020.100594_b4 article-title: Quantum computing in the nisq era and beyond publication-title: Quantum doi: 10.22331/q-2018-08-06-79 – volume: 26 start-page: 13 issue: 1 year: 2016 ident: 10.1016/j.disopt.2020.100594_b17 article-title: Probabilistic multistart with path relinking for solving the unconstrained binary quadratic problem publication-title: Int. J. Oper. Res. doi: 10.1504/IJOR.2016.075647 – year: 2019 ident: 10.1016/j.disopt.2020.100594_b3 – volume: 3 start-page: 14 year: 2016 ident: 10.1016/j.disopt.2020.100594_b9 article-title: Mapping constrained optimization problems to quantum annealing with application to fault diagnosis publication-title: Front. ICT doi: 10.3389/fict.2016.00014 – start-page: 1 year: 2019 ident: 10.1016/j.disopt.2020.100594_b10 article-title: Optimal quadratic reformulations of fourth degree pseudo-boolean functions publication-title: Optim. Lett. – year: 2006 ident: 10.1016/j.disopt.2020.100594_b14 – volume: 12 start-page: 77 issue: 4 year: 2019 ident: 10.1016/j.disopt.2020.100594_b7 article-title: Embedding equality constraints of optimization problems into a quantum annealer publication-title: Algorithms doi: 10.3390/a12040077 – volume: 3 issue: 1 year: 2005 ident: 10.1016/j.disopt.2020.100594_b15 article-title: From linearization to lazy learning: a survey of divide-and-conquer techniques for nonlinear control publication-title: Int. J. Comput. Cogn. – start-page: 1 year: 2018 ident: 10.1016/j.disopt.2020.100594_b6 article-title: Simple constraint embedding for quantum annealers – volume: 17 start-page: 335 issue: 4 year: 2019 ident: 10.1016/j.disopt.2020.100594_b2 article-title: Quantum bridge analytics i: a tutorial on formulating and using qubo models publication-title: 4OR doi: 10.1007/s10288-019-00424-y – start-page: 183 year: 2002 ident: 10.1016/j.disopt.2020.100594_b12 article-title: Fitness landscapes – volume: 19 start-page: 711 issue: 4 year: 2013 ident: 10.1016/j.disopt.2020.100594_b13 article-title: Elementary landscape decomposition of the 0-1 unconstrained quadratic optimization publication-title: J. Heuristics doi: 10.1007/s10732-011-9170-6 – volume: 191 start-page: 229 issue: 1–2 year: 1998 ident: 10.1016/j.disopt.2020.100594_b20 article-title: Autocorrelation coefficient for the graph bipartitioning problem publication-title: Theoret. Comput. Sci. doi: 10.1016/S0304-3975(97)00176-X – volume: 44 start-page: 335 issue: 247 year: 1949 ident: 10.1016/j.disopt.2020.100594_b22 article-title: The monte carlo method publication-title: J. Amer. Statist. Assoc. doi: 10.1080/01621459.1949.10483310 |
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| Title | Penalty and partitioning techniques to improve performance of QUBO solvers |
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