Closed-form formulas for evaluating r-flip moves to the unconstrained binary quadratic programming problem

Anacleto, Eduardo A. J.; Meneses, Cláudio N.; Ravelo, Santiago Valdés

doi:10.1016/j.cor.2019.104774

Cited by 7 publications

(5 citation statements)

References 32 publications

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“…However, due to the complexity and practicality of QUBO, it is still necessary to provide results suitable for solving large-scale problems. In recent years, researchers have developed theoretical results to reduce the algorithmic implementation difficulty of QUBO, [11][12][13][14][15][16]. Our results in this paper also help to reduce the size and difficulty of the algorithmic implementation of these problems.…”

Section: Introductionmentioning

confidence: 78%

“…All algorithms found the best-known solution with a CPU time limit of 10 s. Thus, we only compared the results of large instances with high density and a size of 3000 to 8000 with the MST2 algorithm and the best algorithm among Algorithms 3-5. These benchmark instances with sizes of 3000 to 8000 have been reported by other researchers [5,12]. In addition, we generated some very-large-scale QUBO instances with a high density and size of 30,000 using the same parameters from the benchmark instances.…”

Section: Computational Resultsmentioning

confidence: 99%

“…This suggests the possibility of using alternative stopping criteria as a potential improvement in the future. Also, the application of an efficient strategy in evaluating flip moves has the potential to further improve the algorithm performance, as suggested by Anacleto et al [12].…”

Section: Computational Resultsmentioning

confidence: 99%

“…Alidaee and Kochenberger [11] introduced several theorems showing closed-form r-flip formulas for general pseudo-Boolean optimization. The authors in [12,13] recently provided closed-form formulas for evaluating r-flip rules in QUBO. In particular, Theorem 6 in [11] is specific to the f (x) = x T Qx problem.…”

Section: Previous Workmentioning

confidence: 99%

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An Efficient Closed-Form Formula for Evaluating r-Flip Moves in Quadratic Unconstrained Binary Optimization

Alidaee,

Wang,

Sua

2023

Algorithms

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Quadratic unconstrained binary optimization (QUBO) is a classic NP-hard problem with an enormous number of applications. Local search strategy (LSS) is one of the most fundamental algorithmic concepts and has been successfully applied to a wide range of hard combinatorial optimization problems. One LSS that has gained the attention of researchers is the r-flip (also known as r-Opt) strategy. Given a binary solution with n variables, the r-flip strategy “flips” r binary variables to obtain a new solution if the changes improve the objective function. The main purpose of this paper is to develop several results for the implementation of r-flip moves in QUBO, including a necessary and sufficient condition that when a 1-flip search reaches local optimality, the number of candidates for implementation of the r-flip moves can be reduced significantly. The results of the substantial computational experiments are reported to compare an r-flip strategy-embedded algorithm and a multiple start tabu search algorithm on a set of benchmark instances and three very-large-scale QUBO instances. The r-flip strategy implemented within the algorithm makes the algorithm very efficient, leading to very high-quality solutions within a short CPU time.

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Section: Introductionmentioning

confidence: 78%

Section: Computational Resultsmentioning

confidence: 99%

Section: Computational Resultsmentioning

confidence: 99%

Section: Previous Workmentioning

confidence: 99%

See 2 more Smart Citations

An Efficient Closed-Form Formula for Evaluating r-Flip Moves in Quadratic Unconstrained Binary Optimization

Alidaee,

Wang,

Sua

2023

Algorithms

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“…The authors in [8] present theoretical formulas based on partial derivatives for quickly determining effects of r-flips on the objective function. [9] proposed two formulas for quickly evaluating r-flip moves. However, the number of possible r-flip moves to evaluate grows exponentially and one-flip moves are the most commonly implemented approach.…”

Section: Introductionmentioning

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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A Multiobjective Memetic Algorithm for Multiobjective Unconstrained Binary Quadratic Programming Problem

Zhou

Kong

Yan

et al. 2021

Lecture Notes in Computer Science

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Closed-form formulas for evaluating r-flip moves to the unconstrained binary quadratic programming problem

Cited by 7 publications

References 32 publications

An Efficient Closed-Form Formula for Evaluating r-Flip Moves in Quadratic Unconstrained Binary Optimization

An Efficient Closed-Form Formula for Evaluating r-Flip Moves in Quadratic Unconstrained Binary Optimization

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

A Multiobjective Memetic Algorithm for Multiobjective Unconstrained Binary Quadratic Programming Problem

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