Abstract
Instance space analysis extends the algorithm selection framework by enabling the visualisation of problem instances via dimensionality reduction (DR). The lower dimensional projection can also be used as input to predict algorithm performance, or to perform algorithm selection. In this paper we consider two supervised DR methods - partial least squares (PLS) and linear discriminant analysis (LDA) - both as visualisation tools and for the purpose of constructing classification models for algorithm selection. Multinomial logistic regression models are used for the classification problem. We compare PLS and LDA to DR methods previously used in this context on three combinatorial optimisation problems, and show that these methods are as competitive.
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References
Rice, J.R.: The algorithm selection problem. In: Rubinoff, M., Yovits, M.C. (eds.) Advances in Computers, vol. 15, pp. 65–118. Elsevier, Amsderdam (1976)
Smith-Miles, K., Muñoz, M.A.: Instance space analysis for algorithm testing: methodology and software tools. ACM Comput. Surv. 55, 1–31 (2022)
Alipour, H., Muñoz, M.A., Smith-Miles, K.: Enhanced instance space analysis for the maximum flow problem. Eur. J. Oper. Res. 304(2), 411–428 (2023)
Smith-Miles, K., Baatar, D., Wreford, B., Lewis, R.: Towards objective measures of algorithm performance across instance space. Comput. Oper. Res. 45, 12–24 (2014)
Smith-Miles, K., Christiansen, J., Muñoz, M.A.: Revisiting where are the hard knapsack problems? Via instance space analysis. Comput. Oper. Res. 128, 105184 (2021)
Muñoz, M.A., Villanova, L., Baatar, D., Smith-Miles, K.: Instance spaces for machine learning classification. Mach. Learn. 107(1), 109–147 (2017). https://doi.org/10.1007/s10994-017-5629-5
Abdi, H.: Partial least squares regression and projection on latent structure regression (PLS regression). WIREs Comput. Stat. 2(1), 97–106 (2010)
Barker, M., Rayens, W.: Partial least squares for discrimination. J. Chemom. 17(3), 166–173 (2003)
Pihera, J., Musliu, N.: Application of machine learning to algorithm selection for TSP. In: 2014 IEEE 26th International Conference on Tools with Artificial Intelligence, pp. 47–54 (2014)
Vidal, T.: Hybrid genetic search for the CVRP: open-source implementation and SWAP* neighborhood. Comput. Oper. Res. 140, 105643 (2022)
Rasku, J., Kärkkäinen, T., Musliu, N.: Feature extractors for describing vehicle routing problem instances. In: OpenAccess Series in Informatics, vol. 50, pp. 7.1–7.13 (2016)
Smith-Miles, K., Muñoz, M., Neelofar: Melbourne algorithm test instance library with data analytics (MATILDA) (2020). https://matilda.unimelb.edu.au/
Espadoto, M., Martins, R.M., Kerren, A., Hirata, N.S.T., Telea, A.C.: Toward a quantitative survey of dimension reduction techniques. IEEE Trans. Vis. Comput. Graph. 27(3), 2153–2173 (2021)
Acknowledgements
This paper is based on work completed while Danielle Notice was part of the EPSRC funded STOR-i Centre for Doctoral Training (EP/S022252/1). This work was also funded in part by Tesco Stores Limited.
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Notice, D., Pavlidis, N.G., Kheiri, A. (2024). Supervised Dimensionality Reduction for the Algorithm Selection Problem. In: Zheng, H., Glass, D., Mulvenna, M., Liu, J., Wang, H. (eds) Advances in Computational Intelligence Systems. UKCI 2024. Advances in Intelligent Systems and Computing, vol 1462. Springer, Cham. https://doi.org/10.1007/978-3-031-78857-4_7
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