Abstract
The development cycle of high-performance optimization algorithms requires the algorithm designer to make several design decisions. These decisions range from implementation details to the setting of parameter values for testing intermediate designs. Proper parameter setting can be crucial for the effective assessment of algorithmic components because a bad parameter setting can make a good algorithmic component perform poorly. This situation may lead the designer to discard promising components that just happened to be tested with bad parameter settings. Automatic parameter tuning techniques are being used by practitioners to obtain peak performance from already designed algorithms. However, automatic parameter tuning also plays a crucial role during the development cycle of optimization algorithms. In this paper, we present a case study of a tuning-in-the-loop approach for redesigning a particle swarm-based optimization algorithm for tackling large-scale continuous optimization problems. Rather than just presenting the final algorithm, we describe the whole redesign process. Finally, we study the scalability behavior of the final algorithm in the context of this special issue.
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Notes
The terms “large-scale” and “high-dimensional” are used interchangeably in this paper.
In this paper, we focus on the minimization case.
For conciseness, we present here only the most relevant results. The complete set of results can be found in this paper’s companion website (http://iridia.ulb.ac.be/supp/IridiaSupp2010-011).
We remind the reader that the complete set of results can be found in http://iridia.ulb.ac.be/supp/IridiaSupp2010-011.
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Acknowledgments
The work described in this paper was supported by the META-X project, an Action de Recherche Concertée funded by the Scientific Research Directorate of the French Community of Belgium. Thomas Stützle acknowledges support from the F.R.S-FNRS of the French Community of Belgium of which he is a Research Associate. The authors thank Manuel López-Ibáñez for adapting the code of iterated F-race to deal with the tuning task studied in this paper.
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Appendix
Appendix
1.1 Benchmark functions
A set of 19 scalable benchmark functions was used in this paper. Their mathematical definition is shown in Table 14. These functions were proposed by Herrera et al. (2010). The source code that implements them was also provided by them (available from Lozano and Herrera 2010).
For functions F 1–F 11 (and some of the hybrid functions, F 12–F 19), candidate solutions, x, are transformed as z = x − o before evaluation. This transformation shifts the optimal solution from the origin of the coordinate system to o, with o ∈ [X min, X max]n. For function F 3, the transformation is z = x − o + 1. Hybrid functions combine two basic functions. The combination procedure is shown in (Herrera et al. 2010). The parameter m ns is used to control the number of components that are taken from a nonseparable function (functions F 3, F 5, F 9, and F 10). The higher m ns , the larger the number of components evaluated that come from a nonseparable function.
1.2 Ranges and setting of free and fixed algorithm parameters
During tuning, the number of free parameters and their corresponding range or domain has to be given to iterated F-race. The list of free parameters and their corresponding range or domain as used with iterated F-race is given in Table 15. A description of their meaning and effect is given in the main text.
Other parameter settings for IPSOLS, for both tuned and nontuned versions, remained fixed. A list of them with their settings is shown in Table 16.
1.3 Iterated F-race parameter setting
Iterated F-race (Balaprakash et al. 2007; Birattari et al. 2010) has a number of parameters that need to be set before it can be used. The parameters setting used in our work is shown in Table 17.
In iterated F-race, the number of iterations L is equal to 2 + round(log2(d)), where d is the number of parameters to tune. In iterated F-race, each iteration has a different maximum number of evaluations. This number, denoted by B l , is equal to (B − B used)/(L − l + 1), where l is the iteration counter, B is the overall maximum number of evaluations, and B used is the number of evaluations used until iteration l − 1. The number of candidate configurations tested during iteration l is equal to ⌊B l /μ l ⌋. For more information on the parameters of iterated F-race and their effect, please see (Balaprakash et al. 2007; Birattari et al. 2010).
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Montes de Oca, M.A., Aydın, D. & Stützle, T. An incremental particle swarm for large-scale continuous optimization problems: an example of tuning-in-the-loop (re)design of optimization algorithms. Soft Comput 15, 2233–2255 (2011). https://doi.org/10.1007/s00500-010-0649-0
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DOI: https://doi.org/10.1007/s00500-010-0649-0