Logical and inequality implications for reducing the size and difficulty of quadratic unconstrained binary optimization problems

Glover, Fred; Lewis, Mark; Kochenberger, Gary A.

doi:10.1016/j.ejor.2017.08.025

Cited by 26 publications

(18 citation statements)

References 17 publications

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“…The mean and standard deviation were computed over five runs. Before solving the QUBO problems, we applied preprocessing techniques, reducing their size and difficulty [11]. This proved effective and eliminated a great many variables.…”

Section: Results For the Quantum Version Of Bidvitmentioning

confidence: 99%

“…Solutions to (P5) can be approximated using heuristics such as simulated annealing [32], path relinking [25], tabu search [25], and parallel tempering [38]. Before solving (P5), it is advisable to reduce its size and difficulty by making use of logical implications among the coefficients [11]. This involves fixing every variable that corresponds to a node that has no neighbours to one, as it necessarily is included in an ε-dense subset.…”

Section: Chunk Coarseningmentioning

confidence: 99%

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A Quantum Annealing-Based Approach to Extreme Clustering

Jaschek

Bucyk

Oberoi

2020

Advances in Intelligent Systems and Computing

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Clustering, or grouping, dataset elements based on similarity can be used not only to classify a dataset into a few categories, but also to approximate it by a relatively large number of representative elements. In the latter scenario, referred to as extreme clustering, datasets are enormous and the number of representative clusters is large. We have devised a distributed method that can efficiently solve extreme clustering problems using quantum annealing. We prove that this method yields optimal clustering assignments under a separability assumption, and show that the generated clustering assignments are of comparable quality to those of assignments generated by common clustering algorithms, yet can be obtained a full order of magnitude faster.

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Section: Results For the Quantum Version Of Bidvitmentioning

confidence: 99%

Section: Chunk Coarseningmentioning

confidence: 99%

A Quantum Annealing-Based Approach to Extreme Clustering

Jaschek

Bucyk

Oberoi

2020

Advances in Intelligent Systems and Computing

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“…implemented the methods from Glover et al (18) for this article. However, we do not provide details, but rather concentrate on MaxCut reduction techniques in the following.…”

Section: Post-processingmentioning

confidence: 99%

Faster exact solution of sparse MaxCut and QUBO problems

Rehfeldt¹,

Koch²,

Shinano³

2022

Preprint

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The maximum-cut problem is one of the fundamental problems in combinatorial optimization. With the advent of quantum computers, both the maximum-cut and the equivalent quadratic unconstrained binary optimization problem have experienced much interest in recent years.This article aims to advance the state of the art in the exact solution of both problems-by using mathematical programming techniques on digital computers. The main focus lies on sparse problem instances, although also dense ones can be solved. We enhance several algorithmic components such as reduction techniques and cutting-plane separation algorithms, and combine them in an exact branch-and-cut solver. Furthermore, we provide a parallel implementation. The new solver is shown to significantly outperform existing state-of-the-art software for sparse MaxCut and QUBO instances. Furthermore, we improve the best known bounds for several instances from the 7th DIMACS Challenge and the QPLIB, and solve some of them (for the first time) to optimality.

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“…For testing we use the QUBO instances presented in [20] and [21]. The algorithms were implemented in Python 3.6.…”

Section: Computational Experimentsmentioning

confidence: 99%

“…The experiments were performed on a 3.40 GHz Intel Core i7 processor with 16 GB RAM running 64 bit Windows 7 OS. The datasets described in [20] have 1000 nodes while the ORLIB instances [21] have 1000 and 2500 nodes. Our experiments utilize a path relinking and tabu search based QUBO solver.…”

Section: Computational Experimentsmentioning

confidence: 99%

Constraint Programming to Discover One-Flip Local Optima of Quadratic Unconstrained Binary Optimization Problems

Verma¹,

Lewis²

2021

Preprint

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The broad applicability of Quadratic Unconstrained Binary Optimization (QUBO) constitutes a general-purpose modeling framework for combinatorial optimization problems and are a required format for gate array and quantum annealing computers. QUBO annealers as well as other solution approaches benefit from starting with a diverse set of solutions with local optimality an additional benefit. This paper presents a new method for generating a set of one-flip local optima leveraging constraint programming. Further, as demonstrated in experimental testing, analysis of the solution set allows the generation of soft constraints to help guide the optimization process.

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Logical and inequality implications for reducing the size and difficulty of quadratic unconstrained binary optimization problems

Cited by 26 publications

References 17 publications

A Quantum Annealing-Based Approach to Extreme Clustering

A Quantum Annealing-Based Approach to Extreme Clustering

Faster exact solution of sparse MaxCut and QUBO problems

Constraint Programming to Discover One-Flip Local Optima of Quadratic Unconstrained Binary Optimization Problems

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