Thermodynamic modeling of the LiF-YF3 phase diagram

A thermodynamic optimization of the LiF-YF3 binary phase diagram was performed by fitting the Gibbs energy functions to experimental data that were taken from the literature, as well as from own thermoanalytic measurements (DTA and DSC) on HF-treated samples. The Gibbs energy functions for the end member compounds were taken from the literature. Excess energy terms, which describe the effect of interaction between the two fluoride compounds in the liquid phase, were expressed by the Redlich-Kister polynomial function. The calculated phase diagram and thermodynamic properties for the unique formed compound, LiYF4, are in reasonable agreement with the experimental data.Comment: 4 pages, 3 figure

An analysis of the local optima storage capacity of Hopfield network based fitness function models

A Hopfield Neural Network (HNN) with a new weight update rule can be treated as a second order Estimation of Distribution Algorithm (EDA) or Fitness Function Model (FFM) for solving optimisation problems. The HNN models promising solutions and has a capacity for storing a certain number of local optima as low energy attractors. Solutions are generated by sampling the patterns stored in the attractors. The number of attractors a network can store (its capacity) has an impact on solution diversity and, consequently solution quality. This paper introduces two new HNN learning rules and presents the Hopfield EDA (HEDA), which learns weight values from samples of the fitness function. It investigates the attractor storage capacity of the HEDA and shows it to be equal to that known in the literature for a standard HNN. The relationship between HEDA capacity and linkage order is also investigated

Dependency structure matrix, genetic algorithms, and effective recombination

In many different fields, researchers are often confronted by problems arising from complex systems. Simple heuristics or even enumeration works quite well on small and easy problems; however, to efficiently solve large and difficult problems, proper decomposition is the key. In this paper, investigating and analyzing interactions between components of complex systems shed some light on problem decomposition. By recognizing three bare-bones interactions-modularity, hierarchy, and overlap, facet-wise models arc developed to dissect and inspect problem decomposition in the context of genetic algorithms. The proposed genetic algorithm design utilizes a matrix representation of an interaction graph to analyze and explicitly decompose the problem. The results from this paper should benefit research both technically and scientifically. Technically, this paper develops an automated dependency structure matrix clustering technique and utilizes it to design a model-building genetic algorithm that learns and delivers the problem structure. Scientifically, the explicit interaction model describes the problem structure very well and helps researchers gain important insights through the explicitness of the procedure.This work was sponsored by Taiwan National Science Council under grant NSC97- 2218-E-002-020-MY3, U.S. Air Force Office of Scientific Research, Air Force Material Command, USAF, under grants FA9550-06-1-0370 and FA9550-06-1-0096, U.S. National Science Foundation under CAREER grant ECS-0547013, ITR grant DMR-03-25939 at Materials Computation Center, grant ISS-02-09199 at US National Center for Supercomputing Applications, UIUC, and the Portuguese Foundation for Science and Technology under grants SFRH/BD/16980/2004 and PTDC/EIA/67776/2006

The Univariate Marginal Distribution Algorithm Copes Well With Deception and Epistasis

In their recent work, Lehre and Nguyen (FOGA 2019) show that the univariate marginal distribution algorithm (UMDA) needs time exponential in the parent populations size to optimize the DeceptiveLeadingBlocks (DLB) problem. They conclude from this result that univariate EDAs have difficulties with deception and epistasis. In this work, we show that this negative finding is caused by an unfortunate choice of the parameters of the UMDA. When the population sizes are chosen large enough to prevent genetic drift, then the UMDA optimizes the DLB problem with high probability with at most $\lambda(\frac{n}{2} + 2 e \ln n)$ fitness evaluations. Since an offspring population size $\lambda$ of order $n \log n$ can prevent genetic drift, the UMDA can solve the DLB problem with $O(n^2 \log n)$ fitness evaluations. In contrast, for classic evolutionary algorithms no better run time guarantee than $O(n^3)$ is known (which we prove to be tight for the ${(1+1)}$ EA), so our result rather suggests that the UMDA can cope well with deception and epistatis. From a broader perspective, our result shows that the UMDA can cope better with local optima than evolutionary algorithms; such a result was previously known only for the compact genetic algorithm. Together with the lower bound of Lehre and Nguyen, our result for the first time rigorously proves that running EDAs in the regime with genetic drift can lead to drastic performance losses

A review on probabilistic graphical models in evolutionary computation

Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Evolutionary algorithms is one such discipline that has employed probabilistic graphical models to improve the search for optimal solutions in complex problems. This paper shows how probabilistic graphical models have been used in evolutionary algorithms to improve their performance in solving complex problems. Specifically, we give a survey of probabilistic model building-based evolutionary algorithms, called estimation of distribution algorithms, and compare different methods for probabilistic modeling in these algorithms

Symmetry breaking perturbations and strange attractors

The asymmetrically forced, damped Duffing oscillator is introduced as a prototype model for analyzing the homoclinic tangle of symmetric dissipative systems with \textit{symmetry breaking} disturbances. Even a slight fixed asymmetry in the perturbation may cause a substantial change in the asymptotic behavior of the system, e.g. transitions from two sided to one sided strange attractors as the other parameters are varied. Moreover, slight asymmetries may cause substantial asymmetries in the relative size of the basins of attraction of the unforced nearly symmetric attracting regions. These changes seems to be associated with homoclinic bifurcations. Numerical evidence indicates that \textit{strange attractors} appear near curves corresponding to specific secondary homoclinic bifurcations. These curves are found using analytical perturbational tools

Advancing Model-Building for Many-Objective Optimization Estimation of Distribution Algorithms

Proceedings of: 3rd European Event on Bio-Inspired Algorithms for Continuous Parameter Optimisation (EvoNUM 2010) [associated to: EvoApplications 2010. European Conference on the Applications of Evolutionary Computation]. Istambul, Turkey, April 7-9, 2010In order to achieve a substantial improvement of MOEDAs regarding MOEAs it is necessary to adapt their model-building algorithms. Most current model-building schemes used so far off-the-shelf machine learning methods. These methods are mostly error-based learning algorithms. However, the model-building problem has specific requirements that those methods do not meet and even avoid. In this work we dissect this issue and propose a set of algorithms that can be used to bridge the gap of MOEDA application. A set of experiments are carried out in order to sustain our assertionsThis work was supported by projects CICYT TIN2008-06742-C02-02/TSI, CICYT TEC2008-06732-C02-02/TEC, SINPROB, CAM CONTEXTS S2009/TIC-1485 and DPS2008-07029-C02-0Publicad