Genetic Learning Method Research Articles

Genetic Column Generation: Fast Computation of High-Dimensional Multimarginal Optimal Transport Problems

We introduce a simple, accurate, and extremely efficient method for numerically solving the multi-marginal optimal transport (MMOT) problems arising in density functional theory. The method relies on (i) the sparsity of optimal plans [for $N$ marginals discretized by $\ell$ gridpoints each, general Kantorovich plans require $\ell^N$ gridpoints but the support of optimizers is of size $O(\ell\cdot N)$ [FV18]], (ii) the method of column generation (CG) from discrete optimization which to our knowledge has not hitherto been used in MMOT, and (iii) ideas from machine learning. The well-known bottleneck in CG consists in generating new candidate columns efficiently; we prove that in our context, finding the best new column is an NP-complete problem. To overcome this bottleneck we use a genetic learning method tailormade for MMOT in which the dual state within CG plays the role of an adversary, in loose similarity to Wasserstein GANs. On a sequence of benchmark problems with up to 120 gridpoints and up to 30 marginals, our method always found the exact optimizers. Moreover, empirically the number of computational steps needed to find them appears to scale only polynomially when both $N$ and $\ell$ are simultaneously increased (while keeping their ratio fixed to mimic a thermodynamic limit of the particle system).

Optical fuzzy logic systems in problems of adaptive simulation of weakly formalized processes

A new class of optical fuzzy systems is considered. The class joins optical systems, fuzzy systems and genetic algorithms. Optical fuzzy systems are designed to solve a wide range of problems associated with fuzzy logical simulation of weakly formalized dynamic processes. Naturally integrating principles of spatially distributed optical computations, conventional computing technology and genetic learning methods, they allow realizing the potential of adaptive fuzzy logical real-time simulation of dynamic processes as fully as possible.

Genetic feature selection in a fuzzy rule-based classification system learning process for high-dimensional problems

Abstract The inductive learning of a fuzzy rule-based classification system (FRBCS) is made difficult by the presence of a large number of features that increases the dimensionality of the problem being solved. The difficulty comes from the exponential growth of the fuzzy rule search space with the increase in the number of features considered in the learning process. In this work, we present a genetic feature selection process that can be integrated in a multistage genetic learning method to obtain, in a more efficient way, FRBCSs composed of a set of comprehensible fuzzy rules with high-classification ability. The proposed process fixes, a priori, the number of selected features, and therefore, the size of the search space of candidate fuzzy rules. The experimentation carried out, using Sonar example base, shows a significant improvement on simplicity, precision and efficiency achieved by adding the proposed feature selection processes to the multistage genetic learning method or to other learning methods.

Darwinian Inheritance Genetic Learning Method of Neural Networks Under Dynamic Environment and its Application to Diagnostic System for Hepatobiliary Disorders

Darwinian Inheritance Genetic Learning Method of Neural Networks Under Dynamic Environment and its Application to Diagnostic System for Hepatobiliary Disorders