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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| Published in: | Discrete optimization Vol. 44; p. 100594 |
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| Language: | English |
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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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