双随机矩阵模型在二次分配问题中的应用。

IF 4.6 2区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Valentino Santucci, Josu Ceberio
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引用次数: 0

摘要

几十年来,排列问题一直受到组合优化界的关注,因为它们带来了挑战。虽然它们的解决方案自然地编码为排列,但在每个问题中,用于优化它们的信息可能会有很大的不同。本文以二次分配问题(QAP)为例,提出在分布估计算法框架下使用双随机矩阵(DSMs)。为此,我们设计了有效的学习和采样方案,使概率模型能够有效地迭代更新。在常用的QAP基准上进行的实验证明,无论是在有效性还是计算效率方面,双随机矩阵都优于其他四种排列模型。此外,对QAP和线性排序问题(LOP)的结构进行的额外分析表明,dsm很适合处理分配问题,但它们也具有处理排序问题(如LOP)的有趣功能。文章最后描述了dsm在其他优化范例(如遗传算法或基于模型的梯度搜索)中的潜在用途。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the use of the Doubly Stochastic Matrix models for the Quadratic Assignment Problem.

Permutation problems have captured the attention of the combinatorial optimization community for decades due to the challenge they pose. Although their solutions are naturally encoded as permutations, in each problem, the information to be used to optimize them can vary substantially. In this article, we consider the Quadratic Assignment Problem (QAP) as a case study, and propose using Doubly Stochastic Matrices (DSMs) under the framework of Estimation of Distribution Algorithms. To that end, we design efficient learning and sampling schemes that enable an effective iterative update of the probability model. Conducted experiments on commonly adopted benchmarks for the QAP prove doubly stochastic matrices to be preferred to other four models for permutations, both in terms of effectiveness and computational efficiency. Moreover, additional analyses performed on the structure of the QAP and the Linear Ordering Problem (LOP) show that DSMs are good to deal with assignment problems, but they have interesting capabilities to deal also with ordering problems such as the LOP. The article concludes with a description of the potential uses of DSMs for other optimization paradigms, such as genetic algorithms or model-based gradient search.

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来源期刊
Evolutionary Computation
Evolutionary Computation 工程技术-计算机:理论方法
CiteScore
6.40
自引率
1.50%
发文量
20
审稿时长
3 months
期刊介绍: Evolutionary Computation is a leading journal in its field. It provides an international forum for facilitating and enhancing the exchange of information among researchers involved in both the theoretical and practical aspects of computational systems drawing their inspiration from nature, with particular emphasis on evolutionary models of computation such as genetic algorithms, evolutionary strategies, classifier systems, evolutionary programming, and genetic programming. It welcomes articles from related fields such as swarm intelligence (e.g. Ant Colony Optimization and Particle Swarm Optimization), and other nature-inspired computation paradigms (e.g. Artificial Immune Systems). As well as publishing articles describing theoretical and/or experimental work, the journal also welcomes application-focused papers describing breakthrough results in an application domain or methodological papers where the specificities of the real-world problem led to significant algorithmic improvements that could possibly be generalized to other areas.
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