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

Multivariate cauchy EDA optimisation

Abstract. We consider Black-Box continuous optimization by Estimation of Distribution Algorithms (EDA). In continuous EDA, the multivariate Gaussian distribution is widely used as a search operator, and it has the well-known ad-vantage of modelling the correlation structure of the search variables, which univariate EDA lacks. However, the Gaussian distribution as a search operator is prone to premature convergence when the population is far from the optimum. Recent work suggests that replacing the univariate Gaussian with a univariate Cauchy distribution in EDA holds promise in alleviating this problem because it is able to make larger jumps in the search space due to the Cauchy distribution's heavy tails. In this paper, we propose the use of a multivariate Cauchy distribu-tion to blend together the advantages of multivariate modelling with the ability of escaping early convergence to efficiently explore the search space. Experi-ments on 16 benchmark functions demonstrate the superiority of multivariate Cauchy EDA against univariate Cauchy EDA, and its advantages against multi-variate Gaussian EDA when the population lies far from the optimum

Preventing Premature Convergence in a Simple EDA Via Global Step Size Setting

When a simple real-valued estimation of distribution algorithm (EDA) with Gaussian model and maximum likelihood estimation of parameters is used, it converges prematurely even on the slope of the fitness function. The simplest way of preventing premature convergence by multiplying the variance estimate by a constant factor k each generation is studied. Recent works have shown that when increasing the dimensionality of the search space, such an algorithm becomes very quickly unable to traverse the slope and focus to the optimum at the same time. In this paper it is shown that when isotropic distributions with Gaussian or Cauchy distributed norms are used, the simple constant setting of k is able to ensure a reasonable behaviour of the EDA on the slope and in the valley of the fitness function at the same time

Truncation Selection and Gaussian EDA: Bounds for Sustainable Progress in High-Dimensional Spaces

In real-valued estimation-of-distribution algorithms, the Gaussian distribution is often used along with maximum likelihood (ML) estimation of its parameters. Such a process is highly prone to premature convergence. The simplest method for preventing premature convergence of Gaussian distribution is enlarging the maximum likelihood estimate of σ by a constant factor k each generation. Such a factor should be large enough to prevent convergence on slopes of the fitness function, but should not be too large to allow the algorithm converge in the neighborhood of the optimum. Previous work showed that for truncation selection such admissible k exists in 1D case. In this article it is shown experimentaly, that for the Gaussian EDA with truncation selection in high-dimensional spaces no admissible k exists

An Analysis of Phenotypic Diversity in Multi-Solution Optimization

In optimization methods that return diverse solution sets, three interpretations of diversity can be distinguished: multi-objective optimization which searches diversity in objective space, multimodal optimization which tries spreading out the solutions in genetic space, and quality diversity which performs diversity maintenance in phenotypic space. We introduce niching methods that provide more flexibility to the analysis of diversity and a simple domain to compare and provide insights about the paradigms. We show that multiobjective optimization does not always produce much diversity, quality diversity is not sensitive to genetic neutrality and creates the most diverse set of solutions, and multimodal optimization produces higher fitness solutions. An autoencoder is used to discover phenotypic features automatically, producing an even more diverse solution set. Finally, we make recommendations about when to use which approach