809 research outputs found
Denoising Autoencoders for fast Combinatorial Black Box Optimization
Estimation of Distribution Algorithms (EDAs) require flexible probability
models that can be efficiently learned and sampled. Autoencoders (AE) are
generative stochastic networks with these desired properties. We integrate a
special type of AE, the Denoising Autoencoder (DAE), into an EDA and evaluate
the performance of DAE-EDA on several combinatorial optimization problems with
a single objective. We asses the number of fitness evaluations as well as the
required CPU times. We compare the results to the performance to the Bayesian
Optimization Algorithm (BOA) and RBM-EDA, another EDA which is based on a
generative neural network which has proven competitive with BOA. For the
considered problem instances, DAE-EDA is considerably faster than BOA and
RBM-EDA, sometimes by orders of magnitude. The number of fitness evaluations is
higher than for BOA, but competitive with RBM-EDA. These results show that DAEs
can be useful tools for problems with low but non-negligible fitness evaluation
costs.Comment: corrected typos and small inconsistencie
Spatial-photonic Boltzmann machines: low-rank combinatorial optimization and statistical learning by spatial light modulation
The spatial-photonic Ising machine (SPIM) [D. Pierangeli et al., Phys. Rev.
Lett. 122, 213902 (2019)] is a promising optical architecture utilizing spatial
light modulation for solving large-scale combinatorial optimization problems
efficiently. However, the SPIM can accommodate Ising problems with only
rank-one interaction matrices, which limits its applicability to various
real-world problems. In this Letter, we propose a new computing model for the
SPIM that can accommodate any Ising problem without changing its optical
implementation. The proposed model is particularly efficient for Ising problems
with low-rank interaction matrices, such as knapsack problems. Moreover, the
model acquires learning ability and can thus be termed a spatial-photonic
Boltzmann machine (SPBM). We demonstrate that learning, classification, and
sampling of the MNIST handwritten digit images are achieved efficiently using
SPBMs with low-rank interactions. Thus, the proposed SPBM model exhibits higher
practical applicability to various problems of combinatorial optimization and
statistical learning, without losing the scalability inherent in the SPIM
architecture.Comment: 7 pages, 5 figures (with a 3-page supplemental
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