Alidaee, B.; Wang, H.; Sua, L.S. An Efficient Closed-Form Formula for Evaluating r-Flip Moves in Quadratic Unconstrained Binary Optimization. Algorithms2023, 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.
Alidaee, B.; Wang, H.; Sua, L.S. An Efficient Closed-Form Formula for Evaluating r-Flip Moves in Quadratic Unconstrained Binary Optimization. Algorithms2023, 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.
