Background

Meta-heuristics are high-level methods widely used in different fields of applications. To enhance their performance, they are often combined to concepts borrowed from machine learning and statistics in order to improve the quality of solutions and/or reduce the response time.

Aim

In this paper, we investigate the use of feature selection to speed-up the search process of Bee Swarm Optimisation (BSO) meta-heuristic in solving the MaxSAT problem.The general idea is to extract a subset of the most relevant features that describe an instance of a problem in order to reduce its size.

Proposed approach

We propose to translate a MaxSAT instance into a dataset following one of several representations proposed in this study, and then apply a FS technique to select the most relevant variables or clauses. Two data organizations are proposed depending on whether we want to remove variables or clauses. In addition, two data encodings can be used: binary encoding if we are only interested by the presence or not of a variable in a clause, and ternary encoding if we consider the information that it appears as a positive or negative literal. Moreover, we experiment two feature evaluation approaches: subset evaluation approach which returns the optimal subset, and individual evaluation which ranks the features and lets the user choose the number of features to remove. All possible combinations of data organization, data encoding and features evaluation approach lead to eight (08) variants of the hybrid algorithm, named FS-BSO.

Results

BSO and all the variants of FS-BSO have been applied to several instances of different benchmarks. The analysis of experimental results showed that in terms of solution quality, BSO gives the best results. However, FS-BSO algorithms achieve very good results and are statistically equivalent to BSO for some instances. In terms of execution time, all hybrid variants of FS-BSO are faster. In addition, results showed that removing clauses is slightly more advantageous in terms of solution quality whereas removing variables gives better execution times. Concerning data encoding, the results did not show any difference between the binary and ternary encodings.

Conclusion

In this paper, we investigated the possibility to speed-up BSO meta-heuristic in solving an instance of the MaxSAT problem by extracting a priori knowledge. Feature selection has been used as a preprocessing technique in order to reduce the instance size by selecting a subset of the most relevant vaiables/clauses. Results showed that there is a strong link between the reduction rate and solution quality, and that FS-BSO offers a better quality-time trade off.

中文翻译：

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基于特征选择的蜂群元启发式方法求解组合优化问题：MaxSAT案例研究

背景

元启发法是广泛应用于不同应用领域的高级方法。为了提高其性能，通常将它们与从机器学习和统计中借用的概念结合起来，以提高解决方案的质量和/或减少响应时间。

目标

在本文中，我们研究了使用特征选择来加快Bee Swarm优化（BSO）元启发式算法在解决MaxSAT问题中的搜索过程。总体思路是提取描述以下特征的最相关特征的子集实例以减小其大小。

拟议方法

我们建议按照本研究中提出的几种表示之一将MaxSAT实例转换为数据集，然后应用FS技术选择最相关的变量或子句。根据我们要删除变量还是从句，建议了两个数据组织。另外，可以使用两种数据编码：二进制编码（如果我们仅对子句中变量的存在或不感兴趣）和三元编码（如果我们认为该信息以正或负文字表示）。此外，我们实验了两种特征评估方法：子集评估方法，该方法返回最佳子集；以及个体评估，其对特征进行排名，并让用户选择要删除的特征数量。数据组织的所有可能组合，

结果

BSO和FS-BSO的所有变体已应用于不同基准的多个实例。对实验结果的分析表明，就溶液质量而言，BSO效果最佳。但是，FS-BSO算法取得了很好的结果，并且在某些情况下在统计上等效于BSO。在执行时间方面，FS-BSO的所有混合变体都更快。此外，结果表明，从子句的角度来看，从解决方案质量的角度来看，删除子句更具优势，而删除变量则可以缩短执行时间。关于数据编码，结果在二进制和三进制编码之间没有任何区别。

结论

在本文中，我们研究了通过提取先验知识来加速BSO元启发式算法解决MaxSAT问题实例的可能性。特征选择已被用作预处理技术，以通过选择最相关的物品/条款的子集来减小实例大小。结果表明，降低率和解决方案质量之间存在紧密的联系，并且FS-BSO提供了更好的质量与时间的权衡。