copulaedas: An R Package for Estimation of Distribution Algorithms Based on Copulas

The use of copula-based models in EDAs (estimation of distribution algorithms) is currently an active area of research. In this context, the copulaedas package for R provides a platform where EDAs based on copulas can be implemented and studied. The package offers complete implementations of various EDAs based on copulas and vines, a group of well-known optimization problems, and utility functions to study the performance of the algorithms. Newly developed EDAs can be easily integrated into the package by extending an S4 class with generic functions for their main components. This paper presents copulaedas by providing an overview of EDAs based on copulas, a description of the implementation of the package, and an illustration of its use through examples. The examples include running the EDAs defined in the package, implementing new algorithms, and performing an empirical study to compare the behavior of different algorithms on benchmark functions and a real-world problem

TEDA: A Targeted Estimation of Distribution Algorithm

This thesis discusses the development and performance of a novel evolutionary algorithm, the Targeted Estimation of Distribution Algorithm (TEDA). TEDA takes the concept of targeting, an idea that has previously been shown to be effective as part of a Genetic Algorithm (GA) called Fitness Directed Crossover (FDC), and introduces it into a novel hybrid algorithm that transitions from a GA to an Estimation of Distribution Algorithm (EDA). Targeting is a process for solving optimisation problems where there is a concept of control points, genes that can be said to be active, and where the total number of control points found within a solution is as important as where they are located. When generating a new solution an algorithm that uses targeting must first of all choose the number of control points to set in the new solution before choosing which to set. The hybrid approach is designed to take advantage of the ability of EDAs to exploit patterns within the population to effectively locate the global optimum while avoiding the tendency of EDAs to prematurely converge. This is achieved by initially using a GA to effectively explore the search space before transitioning into an EDA as the population converges on the region of the global optimum. As targeting places an extra restriction on the solutions produced by specifying their size, combining it with the hybrid approach allows TEDA to produce solutions that are of an optimal size and of a higher quality than would be found using a GA alone without risking a loss of diversity. TEDA is tested on three different problem domains. These are optimal control of cancer chemotherapy, network routing and Feature Subset Selection (FSS). Of these problems, TEDA showed consistent advantage over standard EAs in the routing problem and demonstrated that it is able to find good solutions faster than untargeted EAs and non evolutionary approaches at the FSS problem. It did not demonstrate any advantage over other approaches when applied to chemotherapy. The FSS domain demonstrated that in large and noisy problems TEDA’s targeting derived ability to reduce the size of the search space significantly increased the speed with which good solutions could be found. The routing domain demonstrated that, where the ideal number of control points is deceptive, both targeting and the exploitative capabilities of an EDA are needed, making TEDA a more effective approach than both untargeted approaches and FDC. Additionally, in none of the problems was TEDA seen to perform significantly worse than any alternative approaches

Regularized model learning in EDAs for continuous and multi-objective optimization

Probabilistic modeling is the de�ning characteristic of estimation of distribution algorithms (EDAs) which determines their behavior and performance in optimization. Regularization is a well-known statistical technique used for obtaining an improved model by reducing the generalization error of estimation, especially in high-dimensional problems. `1-regularization is a type of this technique with the appealing variable selection property which results in sparse model estimations. In this thesis, we study the use of regularization techniques for model learning in EDAs. Several methods for regularized model estimation in continuous domains based on a Gaussian distribution assumption are presented, and analyzed from di�erent aspects when used for optimization in a high-dimensional setting, where the population size of EDA has a logarithmic scale with respect to the number of variables. The optimization results obtained for a number of continuous problems with an increasing number of variables show that the proposed EDA based on regularized model estimation performs a more robust optimization, and is able to achieve signi�cantly better results for larger dimensions than other Gaussian-based EDAs. We also propose a method for learning a marginally factorized Gaussian Markov random �eld model using regularization techniques and a clustering algorithm. The experimental results show notable optimization performance on continuous additively decomposable problems when using this model estimation method. Our study also covers multi-objective optimization and we propose joint probabilistic modeling of variables and objectives in EDAs based on Bayesian networks, speci�cally models inspired from multi-dimensional Bayesian network classi�ers. It is shown that with this approach to modeling, two new types of relationships are encoded in the estimated models in addition to the variable relationships captured in other EDAs: objectivevariable and objective-objective relationships. An extensive experimental study shows the e�ectiveness of this approach for multi- and many-objective optimization. With the proposed joint variable-objective modeling, in addition to the Pareto set approximation, the algorithm is also able to obtain an estimation of the multi-objective problem structure. Finally, the study of multi-objective optimization based on joint probabilistic modeling is extended to noisy domains, where the noise in objective values is represented by intervals. A new version of the Pareto dominance relation for ordering the solutions in these problems, namely �-degree Pareto dominance, is introduced and its properties are analyzed. We show that the ranking methods based on this dominance relation can result in competitive performance of EDAs with respect to the quality of the approximated Pareto sets. This dominance relation is then used together with a method for joint probabilistic modeling based on `1-regularization for multi-objective feature subset selection in classi�cation, where six di�erent measures of accuracy are considered as objectives with interval values. The individual assessment of the proposed joint probabilistic modeling and solution ranking methods on datasets with small-medium dimensionality, when using two di�erent Bayesian classi�ers, shows that comparable or better Pareto sets of feature subsets are approximated in comparison to standard methods