Predictive entropy search for efficient global optimization of black-box functions

We propose a novel information-theoretic approach for Bayesian optimization called Predictive Entropy Search (PES). At each iteration, PES selects the next evaluation point that maximizes the expected information gained with respect to the global maximum. PES codifies this intractable acquisition function in terms of the expected reduction in the differential entropy of the predictive distribution. This reformulation allows PES to obtain approximations that are both more accurate and efficient than other alternatives such as Entropy Search (ES). Furthermore, PES can easily perform a fully Bayesian treatment of the model hyperparameters while ES cannot. We evaluate PES in both synthetic and real-world applications, including optimization problems in machine learning, finance, biotechnology, and robotics. We show that the increased accuracy of PES leads to significant gains in optimization performance.

Improving sampling, optimization and feature extraction in Boltzmann machines

L’apprentissage supervisé de réseaux hiérarchiques à grande échelle connaît présentement un succès fulgurant. Malgré cette effervescence, l’apprentissage non-supervisé représente toujours, selon plusieurs chercheurs, un élément clé de l’Intelligence Artificielle, où les agents doivent apprendre à partir d’un nombre potentiellement limité de données. Cette thèse s’inscrit dans cette pensée et aborde divers sujets de recherche liés au problème d’estimation de densité par l’entremise des machines de Boltzmann (BM), modèles graphiques probabilistes au coeur de l’apprentissage profond. Nos contributions touchent les domaines de l’échantillonnage, l’estimation de fonctions de partition, l’optimisation ainsi que l’apprentissage de représentations invariantes. Cette thèse débute par l’exposition d’un nouvel algorithme d'échantillonnage adaptatif, qui ajuste (de fa ̧con automatique) la température des chaînes de Markov sous simulation, afin de maintenir une vitesse de convergence élevée tout au long de l’apprentissage. Lorsqu’utilisé dans le contexte de l’apprentissage par maximum de vraisemblance stochastique (SML), notre algorithme engendre une robustesse accrue face à la sélection du taux d’apprentissage, ainsi qu’une meilleure vitesse de convergence. Nos résultats sont présent ́es dans le domaine des BMs, mais la méthode est générale et applicable à l’apprentissage de tout modèle probabiliste exploitant l’échantillonnage par chaînes de Markov. Tandis que le gradient du maximum de vraisemblance peut-être approximé par échantillonnage, l’évaluation de la log-vraisemblance nécessite un estimé de la fonction de partition. Contrairement aux approches traditionnelles qui considèrent un modèle donné comme une boîte noire, nous proposons plutôt d’exploiter la dynamique de l’apprentissage en estimant les changements successifs de log-partition encourus à chaque mise à jour des paramètres. Le problème d’estimation est reformulé comme un problème d’inférence similaire au filtre de Kalman, mais sur un graphe bi-dimensionnel, où les dimensions correspondent aux axes du temps et au paramètre de température. Sur le thème de l’optimisation, nous présentons également un algorithme permettant d’appliquer, de manière efficace, le gradient naturel à des machines de Boltzmann comportant des milliers d’unités. Jusqu’à présent, son adoption était limitée par son haut coût computationel ainsi que sa demande en mémoire. Notre algorithme, Metric-Free Natural Gradient (MFNG), permet d’éviter le calcul explicite de la matrice d’information de Fisher (et son inverse) en exploitant un solveur linéaire combiné à un produit matrice-vecteur efficace. L’algorithme est prometteur: en terme du nombre d’évaluations de fonctions, MFNG converge plus rapidement que SML. Son implémentation demeure malheureusement inefficace en temps de calcul. Ces travaux explorent également les mécanismes sous-jacents à l’apprentissage de représentations invariantes. À cette fin, nous utilisons la famille de machines de Boltzmann restreintes “spike & slab” (ssRBM), que nous modifions afin de pouvoir modéliser des distributions binaires et parcimonieuses. Les variables latentes binaires de la ssRBM peuvent être rendues invariantes à un sous-espace vectoriel, en associant à chacune d’elles, un vecteur de variables latentes continues (dénommées “slabs”). Ceci se traduit par une invariance accrue au niveau de la représentation et un meilleur taux de classification lorsque peu de données étiquetées sont disponibles. Nous terminons cette thèse sur un sujet ambitieux: l’apprentissage de représentations pouvant séparer les facteurs de variations présents dans le signal d’entrée. Nous proposons une solution à base de ssRBM bilinéaire (avec deux groupes de facteurs latents) et formulons le problème comme l’un de “pooling” dans des sous-espaces vectoriels complémentaires.

A novel approach for solving constrained nonlinear optimization problems using neurofuzzy systems

A neural network model for solving constrained nonlinear optimization problems with bounded variables is presented in this paper. More specifically, a modified Hopfield network is developed and its internal parameters are completed using the valid-subspace technique. These parameters guarantee the convergence of the network to the equilibrium points. The network is shown to be completely stable and globally convergent to the solutions of constrained nonlinear optimization problems. A fuzzy logic controller is incorporated in the network to minimize convergence time. Simulation results are presented to validate the proposed approach.

A neural system to robust Nonlinear optimization subject to disjoint and constrained sets

The ability of neural networks to realize some complex nonlinear function makes them attractive for system identification. This paper describes a novel method using artificial neural networks to solve robust parameter estimation problems for nonlinear models with unknown-but-bounded errors and uncertainties. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the network convergence to the equilibrium points. A solution for the robust estimation problem with unknown-but-bounded error corresponds to an equilibrium point of the network. Simulation results are presented as an illustration of the proposed approach.

Problem-specific design of metaheuristics for constrained spanning tree problems

When designing metaheuristic optimization methods, there is a trade-off between application range and effectiveness. For large real-world instances of combinatorial optimization problems out-of-the-box metaheuristics often fail, and optimization methods need to be adapted to the problem at hand. Knowledge about the structure of high-quality solutions can be exploited by introducing a so called bias into one of the components of the metaheuristic used. These problem-specific adaptations allow to increase search performance. This thesis analyzes the characteristics of high-quality solutions for three constrained spanning tree problems: the optimal communication spanning tree problem, the quadratic minimum spanning tree problem and the bounded diameter minimum spanning tree problem. Several relevant tree properties, that should be explored when analyzing a constrained spanning tree problem, are identified. Based on the gained insights on the structure of high-quality solutions, efficient and robust solution approaches are designed for each of the three problems. Experimental studies analyze the performance of the developed approaches compared to the current state-of-the-art.

Duality in Constrained DC-Optimization via Toland’s Duality Approach

2000 Mathematics Subject Classification: 90C48, 49N15, 90C25

Nonholonomically Constrained Dynamics and Optimization of Rolling Isolation Systems

Rolling Isolation Systems provide a simple and effective means for protecting components from horizontal floor vibrations. In these systems a platform rolls on four steel balls which, in turn, rest within shallow bowls. The trajectories of the balls is uniquely determined by the horizontal and rotational velocity components of the rolling platform, and thus provides nonholonomic constraints. In general, the bowls are not parabolic, so the potential energy function of this system is not quadratic. This thesis presents the application of Gauss's Principle of Least Constraint to the modeling of rolling isolation platforms. The equations of motion are described in terms of a redundant set of constrained coordinates. Coordinate accelerations are uniquely determined at any point in time via Gauss's Principle by solving a linearly constrained quadratic minimization. In the absence of any modeled damping, the equations of motion conserve energy. This mathematical model is then used to find the bowl profile that minimizes response acceleration subject to displacement constraint.

Energy efficiency optimization in hardware-constrained large-scale MIMO systems

Large-scale multiple-input multiple-output (MIMO) communication systems can bring substantial improvement in spectral efficiency and/or energy efficiency, due to the excessive degrees-of-freedom and huge array gain. However, large-scale MIMO is expected to deploy lower-cost radio frequency (RF) components, which are particularly prone to hardware impairments. Unfortunately, compensation schemes are not able to remove the impact of hardware impairments completely, such that a certain amount of residual impairments always exists. In this paper, we investigate the impact of residual transmit RF impairments (RTRI) on the spectral and energy efficiency of training-based point-to-point large-scale MIMO systems, and seek to determine the optimal training length and number of antennas which maximize the energy efficiency. We derive deterministic equivalents of the signal-to-noise-and-interference ratio (SINR) with zero-forcing (ZF) receivers, as well as the corresponding spectral and energy efficiency, which are shown to be accurate even for small number of antennas. Through an iterative sequential optimization, we find that the optimal training length of systems with RTRI can be smaller compared to ideal hardware systems in the moderate SNR regime, while larger in the high SNR regime. Moreover, it is observed that RTRI can significantly decrease the optimal number of transmit and receive antennas.

Development and optimization of fluoxetine orally disintegrating tablets using Box-Behnken design

Purpose: To develop and optimise some variables that influence fluoxetine orally disintegrating tablets (ODTs) formulation. Methods: Fluoxetine ODTs tablets were prepared using direct compression method. Three-factor, 3- level Box-Behnken design was used to optimize and develop fluoxetine ODT formulation. The design suggested 15 formulations of different lubricant concentration (X1), lubricant mixing time (X2), and compression force (X3) and then their effect was monitored on tablet weight (Y1), thickness (Y2), hardness (Y3), % friability (Y4), and disintegration time (Y5). Results: All powder blends showed acceptable flow properties, ranging from good to excellent. The disintegration time (Y5) was affected directly by lubricant concentration (X1). Lubricant mixing time (X2) had a direct effect on tablet thickness (Y2) and hardness (Y3), while compression force (X3) had a direct impact on tablet hardness (Y3), % friability (Y4) and disintegration time (Y5). Accordingly, Box-Behnken design suggested an optimized formula of 0.86 mg (X1), 15.3 min (X2), and 10.6 KN (X3). Finally, the prediction error percentage responses of Y1, Y2, Y3, Y4, and Y5 were 0.31, 0.52, 2.13, 3.92 and 3.75 %, respectively. Formula 4 and 8 achieved 90 % of drug release within the first 5 min of dissolution test. Conclusion: Fluoxetine ODT formulation has been developed and optimized successfully using Box- Behnken design and has also been manufactured efficiently using direct compression technique.

A hybrid genetic algorithm for the optimal constrained web service selection problem in web service composition

Web service composition is an important problem in web service based systems. It is about how to build a new value-added web service using existing web services. A web service may have many implementations, all of which have the same functionality, but may have different QoS values. Thus, a significant research problem in web service composition is how to select a web service implementation for each of the web services such that the composite web service gives the best overall performance. This is so-called optimal web service selection problem. There may be mutual constraints between some web service implementations. Sometimes when an implementation is selected for one web service, a particular implementation for another web service must be selected. This is so called dependency constraint. Sometimes when an implementation for one web service is selected, a set of implementations for another web service must be excluded in the web service composition. This is so called conflict constraint. Thus, the optimal web service selection is a typical constrained ombinatorial optimization problem from the computational point of view. This paper proposes a new hybrid genetic algorithm for the optimal web service selection problem. The hybrid genetic algorithm has been implemented and evaluated. The evaluation results have shown that the hybrid genetic algorithm outperforms other two existing genetic algorithms when the number of web services and the number of constraints are large.

A review of optimization techniques used in the design of fibre composite structures for civil engineering applications

Fibre composite structures have become the most attractive candidate for civil engineering applications. Fibre reinforced plastic polymer (FRP) composite materials have been used in the rehabilitation and replacement of the old degrading traditional structures or build new structures. However, the lack of design standards for civil infrastructure limits their structural applications. The majority of the existing applications have been designed based on the research and guidelines provided by the fibre composite manufacturers or based on the designer’s experience. It has been a tendency that the final structure is generally over-designed. This paper provides a review on the available studies related to the design optimization of fibre composite structures used in civil engineering such as; plate, beam, box beam, sandwich panel, bridge girder, and bridge deck. Various optimization methods are presented and compared. In addition, the importance of using the appropriate optimization technique is discussed. An improved methodology, which considering experimental testing, numerical modelling, and design constrains, is proposed in the paper for design optimization of composite structures.

An Introduction to Constrained Control

An ubiquitous problem in control system design is that the system must operate subject to various constraints. Although the topic of constrained control has a long history in practice, there have been recent significant advances in the supporting theory. In this chapter, we give an introduction to constrained control. In particular, we describe contemporary work which shows that the constrained optimal control problem for discrete-time systems has an interesting geometric structure and a simple local solution. We also discuss issues associated with the output feedback solution to this class of problems, and the implication of these results in the closely related problem of anti-windup. As an application, we address the problem of rudder roll stabilization for ships.

On optimal control of constrained linear systems with imperfect state information and stochastic disturbances

We address the problem of finite horizon optimal control of discrete-time linear systems with input constraints and uncertainty. The uncertainty for the problem analysed is related to incomplete state information (output feedback) and stochastic disturbances. We analyse the complexities associated with finding optimal solutions. We also consider two suboptimal strategies that could be employed for larger optimization horizons.