Fast r-flip move evaluations via closed-form formulae for Boolean quadratic programming problems with generalized upper bound constraints

Anacleto, Eduardo A. J.; Meneses, Cláudio N.; Liang, Ricardo N.

doi:10.1016/j.cor.2021.105297

Cited by 4 publications

(2 citation statements)

References 28 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%

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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%

“…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%