global optimization

We present a novel procedure for optimization based on the combination of efficient quantized tensor train representation and a generalized maximum matrix volume principle. We demonstrate the applicability of the new Tensor Train Optimizer (TTOpt) method for various tasks, ranging from minimization of multidimensional functions to reinforcement learning. Our algorithm compares favorably to popular gradient-free methods and outperforms them by the number of function evaluations or execution time, often by a significant margin.

The two dominant schemes for rule-learning, C4.5 and RIPPER, both operate in two stages. First they induce an initial rule set and then they refine it using a rather complex optimization stage that discards (C4.5) or adjusts (RIPPER) individual rules to make them work better together. In contrast, this paper shows how good rule sets can be learned one rule at a time, without any need for global optimization. We present an algorithm for inferring rules by repeatedly generating partial decision trees, thus combining the two major paradigms for rule generation—creating rules from decision trees and the separate-and-conquer rule-learning technique. The algorithm is straightforward and elegant: despite this, experiments on standard datasets show that it produces rule sets that are as accurate as and of similar size to those generated by C4.5, and more accurate than RIPPER's. Moreover, it operates efficiently, and because it avoids postprocessing, does not suffer the extremely slow performance on pathological example sets for which the C4.5 method has been criticized.

Flower pollination is an intriguing process in the natural world. Its evolutionary characteristics can be used to design new optimization algorithms. In this paper, we propose a new algorithm, namely, flower pollination algorithm, inspired by the pollination process of flowers. We first use ten test functions to validate the new algorithm, and compare its performance with genetic algorithms and particle swarm optimization. Our simulation results show the flower algorithm is more efficient than both GA and PSO. We also use the flower algorithm to solve a nonlinear design benchmark, which shows the convergence rate is almost exponential.

We present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition. This algorithm is derived by minimizing a generalized Bayes/MDL criterion using the variational principle. The algorithm is guaranteed to converge to a local minimum and combines aspects of snakes/balloons and region growing. Indeed the classic snakes/balloons and region growing algorithms can be directly derived from our approach. We provide theoretical analysis of region competition including accuracy of boundary location, criteria for initial conditions, and the relationship to edge detection using filters. It is straightforward to generalize the algorithm to multi-band segmentation and we demonstrate it on grey level images, color images and texture images. The novel color model allows us to eliminate intensity gradients and shadows, thereby obtaining segmentation based on the albedos of objects. It also helps detect highlight regions.

Bayesian optimization is an approach to optimizing objective functions that take a long time (minutes or hours) to evaluate. It is best-suited for optimization over continuous domains of less than 20 dimensions, and tolerates stochastic noise in function evaluations. It builds a surrogate for the objective and quantifies the uncertainty in that surrogate using a Bayesian machine learning technique, Gaussian process regression, and then uses an acquisition function defined from this surrogate to decide where to sample. In this tutorial, we describe how Bayesian optimization works, including Gaussian process regression and three common acquisition functions: expected improvement, entropy search, and knowledge gradient. We then discuss more advanced techniques, including running multiple function evaluations in parallel, multi-fidelity and multi-information source optimization, expensive-to-evaluate constraints, random environmental conditions, multi-task Bayesian optimization, and the inclusion of derivative information. We conclude with a discussion of Bayesian optimization software and future research directions in the field. Within our tutorial material we provide a generalization of expected improvement to noisy evaluations, beyond the noise-free setting where it is more commonly applied. This generalization is justified by a formal decision-theoretic argument, standing in contrast to previous ad hoc modifications.

We propose several means for improving the performance and training of neural networks for classification. We use crossvalidation as a tool for optimizing network parameters and architecture. We show further that the remaining residual “generalization” error can be reduced by invoking ensembles of similar networks.

Metaheuristic algorithms such as particle swarm optimization, firefly algorithm and harmony search are now becoming powerful methods for solving many tough optimization problems. In this paper, we propose a new metaheuristic method, the Bat Algorithm, based on the echolocation behaviour of bats. We also intend to combine the advantages of existing algorithms into the new bat algorithm. After a detailed formulation and explanation of its implementation, we will then compare the proposed algorithm with other existing algorithms, including genetic algorithms and particle swarm optimization. Simulations show that the proposed algorithm seems much superior to other algorithms, and further studies are also discussed.