Abstract
Extensive efforts so far have been devoted to the design of effective surrogate models aiming at reducing the computational cost for solving expensive black-box continuous optimization problems. There are, however, relatively few investigations on the development of methodologies for combinatorial domains. In this work, we rely on the mathematical foundations of discrete Walsh functions in order to derive a surrogate model for pseudo-boolean optimization functions. Specifically, we model such functions by means of Walsh expansion. By conducting a comprehensive set of experiments on \(nk\)-landscapes, we provide empirical evidence on the accuracy of the proposed model. In particular, we show that a Walsh-based surrogate model can outperform the recently-proposed discrete model based on Kriging.
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Notes
- 1.
Indeed, the matrix \((\varphi _k(x_j))_{jk}\) of dimension \(2^n \times 2^n\) is a Hadamard matrix.
- 2.
Packages CEGO and LARS on CRAN: https://cran.r-project.org.
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Acknowledgments
This research was partially conducted in the scope of the MOD\(\bar{\text {O}}\) International Associated Laboratory, and was partially supported by the French National Research Agency (BigMO project, ANR-16-CE23-0013-01).
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Verel, S., Derbel, B., Liefooghe, A., Aguirre, H., Tanaka, K. (2018). A Surrogate Model Based on Walsh Decomposition for Pseudo-Boolean Functions. In: Auger, A., Fonseca, C., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds) Parallel Problem Solving from Nature – PPSN XV. PPSN 2018. Lecture Notes in Computer Science(), vol 11102. Springer, Cham. https://doi.org/10.1007/978-3-319-99259-4_15
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