Article
Version 1
Preserved in Portico This version is not peer-reviewed
An Efficient Closed-form Formula for Evaluating r-flip Moves in Quadratic Unconstrained Binary Optimization
Version 1
: Received: 15 November 2023 / Approved: 16 November 2023 / Online: 17 November 2023 (08:10:27 CET)
A peer-reviewed article of this Preprint also exists.
Alidaee, B.; Wang, H.; Sua, L.S. An Efficient Closed-Form Formula for Evaluating r-Flip Moves in Quadratic Unconstrained Binary Optimization. Algorithms 2023, 16, 557. Alidaee, B.; Wang, H.; Sua, L.S. An Efficient Closed-Form Formula for Evaluating r-Flip Moves in Quadratic Unconstrained Binary Optimization. Algorithms 2023, 16, 557.
Abstract
The 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 that 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 get a new solution if the changes improve the objective function. The main purpose of this paper is to develop several results for 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, very high-quality solutions within a short CPU time.
Keywords
Combinatorial optimization; Quadratic unconstrained binary optimization; Local optimality; r-flip local optimality
Subject
Business, Economics and Management, Business and Management
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment