Deriving Compact QUBO Models via Multilevel Constraint Transformation
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917630138384384 |
|---|---|
| author | Pichugina, Oksana Tan, Yingcong Beck, Christopher |
| author_facet | Pichugina, Oksana Tan, Yingcong Beck, Christopher |
| contents | With the advances in customized hardware for quantum annealing and digital/CMOS Annealing, Quadratic Unconstrained Binary Optimization (QUBO) models have received growing attention in the optimization literature. Motivated by an existing general-purpose approach that derives QUBO models from binary linear programs (BLP), we propose a novel Multilevel Constraint Transformation Scheme (MLCTS) that derives QUBO models with fewer ancillary binary variables. We formulate sufficient conditions for the existence of a compact QUBO formulation (i.e., in the original BLP decision space) in terms of constraint levelness and demonstrate the flexibility and applicability of MLCTS on synthetic examples and several well-known combinatorial optimization problems, i.e., the Maximum 2-Satisfiability Problem, the Linear Ordering Problem, the Community Detection Problem, and the Maximum Independence Set Problem. For a proof-of-concept, we compare the performance of two QUBO models for the latter problem on both a general-purpose software-based solver and a hardware-based QUBO solver. The MLCTS-derived models demonstrate significantly better performance for both solvers, in particular, solving up to seven times more instances with the hardware-based approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03610 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deriving Compact QUBO Models via Multilevel Constraint Transformation Pichugina, Oksana Tan, Yingcong Beck, Christopher Quantum Physics Optimization and Control With the advances in customized hardware for quantum annealing and digital/CMOS Annealing, Quadratic Unconstrained Binary Optimization (QUBO) models have received growing attention in the optimization literature. Motivated by an existing general-purpose approach that derives QUBO models from binary linear programs (BLP), we propose a novel Multilevel Constraint Transformation Scheme (MLCTS) that derives QUBO models with fewer ancillary binary variables. We formulate sufficient conditions for the existence of a compact QUBO formulation (i.e., in the original BLP decision space) in terms of constraint levelness and demonstrate the flexibility and applicability of MLCTS on synthetic examples and several well-known combinatorial optimization problems, i.e., the Maximum 2-Satisfiability Problem, the Linear Ordering Problem, the Community Detection Problem, and the Maximum Independence Set Problem. For a proof-of-concept, we compare the performance of two QUBO models for the latter problem on both a general-purpose software-based solver and a hardware-based QUBO solver. The MLCTS-derived models demonstrate significantly better performance for both solvers, in particular, solving up to seven times more instances with the hardware-based approach. |
| title | Deriving Compact QUBO Models via Multilevel Constraint Transformation |
| topic | Quantum Physics Optimization and Control |
| url | https://arxiv.org/abs/2404.03610 |