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Feature selection based bee swarm meta-heuristic approach for combinatorial optimisation problems: a case-study on MaxSAT

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Abstract

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.

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Notes

  1. Weka is an environment for knowledge analysis which provides a collection of machine learning algorithms for data mining tasks (http://www.cs.waikato.ac.nz/ml/weka/).

  2. all instances can be downloaded from http://www.cs.ubc.ca/~hoos/SATLIB/benchm.html.

  3. http://www.ibnbadis.cerist.dz/

  4. p-value is a probability which is compared to the threshold value \(\alpha \) to quantify the significance of the null hypothesis. If the p-value is less than or equal to \(\alpha \) then the null hypothesis is rejected, else it is accepted.

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Authors and Affiliations

  1. LMCS, Ecole nationale Supérieure d’Informatique, Oued Smar, Algiers, Algeria

    Souhila Sadeg & Karima Benatchba

  2. LCSI, Ecole nationale Supérieure d’Informatique, Oued Smar, Algiers, Algeria

    Leila Hamdad

  3. Ecole nationale Supérieure d’Informatique, Oued Smar, Algiers, Algeria

    Hadjer Chettab

  4. LORIA, Université de Lorraine, Metz, France

    Zineb Habbas

  5. School of Computer Science, University College Dublin, Dublin, Ireland

    M-Tahar Kechadi

Authors
  1. Souhila Sadeg
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  2. Leila Hamdad
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  3. Hadjer Chettab
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  4. Karima Benatchba
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  5. Zineb Habbas
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  6. M-Tahar Kechadi
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Correspondence to Souhila Sadeg.

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Sadeg, S., Hamdad, L., Chettab, H. et al. Feature selection based bee swarm meta-heuristic approach for combinatorial optimisation problems: a case-study on MaxSAT. Memetic Comp. 12, 283–298 (2020). https://doi.org/10.1007/s12293-020-00310-9

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