Benchmarking Parameter-Free AMaLGaM on Functions With and Without Noise

Abstract

We describe a parameter-free estimation-of-distribution algorithm (EDA) called the adapted maximum-likelihood Gaussian model iterated density-estimation evolutionary algorithm (AMaLGaM-ID[Formula: see text]A, or AMaLGaM for short) for numerical optimization. AMaLGaM is benchmarked within the 2009 black box optimization benchmarking (BBOB) framework and compared to a variant with incremental model building (iAMaLGaM). We study the implications of factorizing the covariance matrix in the Gaussian distribution, to use only a few or no covariances. Further, AMaLGaM and iAMaLGaM are also evaluated on the noisy BBOB problems and we assess how well multiple evaluations per solution can average out noise. Experimental evidence suggests that parameter-free AMaLGaM can solve a wide range of problems efficiently with perceived polynomial scalability, including multimodal problems, obtaining the best or near-best results among all algorithms tested in 2009 on functions such as the step-ellipsoid and Katsuuras, but failing to locate the optimum within the time limit on skew Rastrigin-Bueche separable and Lunacek bi-Rastrigin in higher dimensions. AMaLGaM is found to be more robust to noise than iAMaLGaM due to the larger required population size. Using few or no covariances hinders the EDA from dealing with rotations of the search space. Finally, the use of noise averaging is found to be less efficient than the direct application of the EDA unless the noise is uniformly distributed. AMaLGaM was among the best performing algorithms submitted to the BBOB workshop in 2009.

Smart grid initialization reduces the computational complexity of multi-objective image registration based on a dual-dynamic transformation model to account for large anatomical differences

“…The length of the long run is based on the time that is expected to be required to obtain high-quality results. Specifically, the length of the long run is based on a previously published scalability analysis 15 and allows 20×93.6× 1.81 evaluations where  is the number of parameters to optimize (7,803,795 evaluations for 25 grid points; 65,522,780 evaluations for 81 grid points). The short run is allowed only 1% of these evaluation budgets, implying a 100-fold speedup.…”

Niching an estimation-of-distribution algorithm by hierarchical Gaussian mixture learning

“…We refer to this niching algorithm as Clustered AMaLGaM, or CAMaLGaM. AMaLGaM was chosen as the core search algorithm partly because of its robust performance [6], but mainly because there are only few algorithmic parameters that need to be transferred over generations, making a rst implementation relatively straightforward, allowing us to focus on the design and impact of using HGML.…”

“…A crucial parameter in real-valued EDAs is the distribution multiplier, which prevents premature convergence due to limited diversity in the selection [6,10]. We have to keep track of this and other algorithmic parameters over di erent generations and transfer them from mixture components in one generation to mixture components in the next generation.…”

“…We have to keep track of this and other algorithmic parameters over di erent generations and transfer them from mixture components in one generation to mixture components in the next generation. In AMaLGaM, the set of algorithmic parameters η consist of three parameters: the distribution multiplier c; the no improvement stretch N nis , which is the number of generations without improvement, and the previous mean µ old of the mixture component to compute the anticipated mean shi [6].…”

“…e recommended population size for AMaLGaM, N AMaLGaM = 17 + 3d 1.5 from [6], is indicated by the blue line in the right column, which is about su cient for the two-peak problem, but is de nitely too small for the higher multi-modal landscapes with 10 or 40 peaks.…”