在二次无约束二元优化中评估 r 翻转移动的高效闭式公式

IF 1.8 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Algorithms Pub Date : 2023-12-05 DOI:10.3390/a16120557
B. Alidaee, Haibo Wang, L. Sua
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引用次数: 0

摘要

二次型无约束二元优化(QUBO)是一个典型的NP-hard问题,具有大量的应用。局部搜索策略(LSS)是最基本的算法概念之一,已成功地应用于各种复杂的组合优化问题。一种获得研究人员关注的LSS是r-flip(也称为r-Opt)策略。给定一个有n个变量的二元解,r-flip策略“翻转”r个二元变量以获得一个新的解,如果这些变化改善了目标函数。本文的主要目的是开发几个在QUBO中实现r-flip移动的结果,包括当1-flip搜索达到局部最优时,实现r-flip移动的候选数可以显着减少的充分必要条件。在一组基准实例和三个非常大规模的QUBO实例上进行了大量的计算实验,比较了嵌入r-flip策略的算法和多开始禁忌搜索算法。算法中实现的r-flip策略使得算法非常高效,在较短的CPU时间内产生非常高质量的解决方案。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An Efficient Closed-Form Formula for Evaluating r-Flip Moves in Quadratic Unconstrained Binary Optimization
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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来源期刊
Algorithms
Algorithms Mathematics-Numerical Analysis
CiteScore
4.10
自引率
4.30%
发文量
394
审稿时长
11 weeks
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