Abstract
This paper presents a convergence rate comparison of five different derivative-free numerical optimization techniques across a set of 50 benchmark objective functions. Results suggest that Adaptive Memory Programming for constrained Global Optimization, and a variant of Simulated Annealing are two of the fastest-converging numerical optimization techniques in this set. Lastly, there is a mechanism for expanding the set of optimization algorithms provided.
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Notes
- 1.
The computation of \(n(\{i \in T_\alpha \text{ s.t. } v \le i\})\) in the upper product sum can be done in \(log(n(T_\alpha ))\) if each \(T_\alpha \) is sorted. \(n_{avg}\) represents the average number of trials for all \(\alpha \in A\).
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Acknowledgments
This research project was funded by the Roanoke College Mathematics Computer Science and Physics Department. The python code for AMPGO and the benchmarking library were a result of the freely available work done by Andrea Gavana at [9].
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Lux, T. (2016). Convergence Rate Evaluation of Derivative-Free Optimization Techniques. In: Pardalos, P., Conca, P., Giuffrida, G., Nicosia, G. (eds) Machine Learning, Optimization, and Big Data. MOD 2016. Lecture Notes in Computer Science(), vol 10122. Springer, Cham. https://doi.org/10.1007/978-3-319-51469-7_21
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