Abstract
In Market Basket Analysis, the goal is to understand the human behavior in order to maximize sales. An evident behavior is to buy correlated items. As a consequence, the determination of a set of items with a large correlation with others is a valuable tool for Market Basket Analysis.
In this paper we address a combinatorial optimization problem that formalizes the previous application. Given a simple graph \(\mathcal {G}=(V,E)\) (where the nodes are items and links represent correlation), we want to find the clique \(\mathcal {C} \subseteq V\) such that the number of links shared between \(\mathcal {C}\) and \(V - \mathcal {C}\) is maximized. This problem is known in the literature as Max Cut-Clique (MCC).
The contributions of this paper are three-fold. First, the computational complexity of the MCC is established. Second, a full GRASP/VND methodology enriched with a Tabu Search is here developed, where the main ingredients are novel local searches and a Restricted Candidate List that trades greediness for randomization in a multi-start fashion. A Tabu Search is also included in order to avoid locally optimum solutions. Finally, a fair comparison with respect to recent heuristics reveals that our proposal is competitive with state-of-the-art solutions.
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Notes
- 1.
All the scripts are available at the following URL: https://www.fing.edu.uy/~lstabile/mcc-octave-source.zip.
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Acknowledgements
This work is partially supported by Project 395 CSIC I+D Sistemas Binarios Estocásticos Dinámicos. We would like to thank the reviewers for their insightful comments that simplified the readability of this paper.
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Bourel, M., Canale, E., Robledo, F., Romero, P., Stábile, L. (2019). A GRASP/VND Heuristic for the Max Cut-Clique Problem. In: Nicosia, G., Pardalos, P., Giuffrida, G., Umeton, R., Sciacca, V. (eds) Machine Learning, Optimization, and Data Science. LOD 2018. Lecture Notes in Computer Science(), vol 11331. Springer, Cham. https://doi.org/10.1007/978-3-030-13709-0_30
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