The True Destination of EGO is Multi-local Optimization

Efficient global optimization is a popular algorithm for the optimization of expensive multimodal black-box functions. One important reason for its popularity is its theoretical foundation of global convergence. However, as the budgets in expensive optimization are very small, the asymptotic properties only play a minor role and the algorithm sometimes comes off badly in experimental comparisons. Many alternative variants have therefore been proposed over the years. In this work, we show experimentally that the algorithm instead has its strength in a setting where multiple optima are to be identified

Niching an estimation-of-distribution algorithm by hierarchical Gaussian mixture learning

Estimation-of-Distribution Algorithms (EDAs) have been applied with quite some success when solving real-valued optimization problems, especially in the case of Black Box Optimization (BBO). Generally, the performance of an EDA depends on the match between its driving probability distribution and the landscape of the problem being solved. Because most well-known EDAs, including CMA-ES, NES, and AMaLGaM, use a uni-modal search distribution, they have a high risk of getting trapped in local optima when a problem is multi-modal with a (moderate) number of relatively comparable modes. This risk could potentially be mitigated using niching methods that define multiple regions of interest where separate search distributions govern sub-populations. However, a key question is how to determine a suitable number of niches, especially in BBO. In this paper, we present a novel, adaptive niching approach that determines the niches through hierarchical clustering based on the correlation between the probability densities and fitness values of solutions. We test the performance of a combination of this niching approach with AMaLGaM on both new and well-known niching benchmark problems and ind that the new approach properly identifies multiple landscape modes, leading to much beter performance on multi-modal problems than with a non-niched, uni-modal EDA

Multimodal Optimization by Covariance Matrix Self-Adaptation Evolution Strategy with Repelling Subpopulations

During the recent decades, many niching methods have been proposed and empirically verified on some available test problems. They often rely on some particular assumptions associated with the distribution, shape, and size of the basins, which can seldom be made in practical optimization problems. This study utilizes several existing concepts and techniques, such as taboo points, normalized Mahalanobis distance, and the Ursem's hill-valley function in order to develop a new tool for multimodal optimization, which does not make any of these assumptions. In the proposed method, several subpopulations explore the search space in parallel. Offspring of a subpopulation are forced to maintain a sufficient distance to the center of fitter subpopulations and the previously identified basins, which are marked as taboo points. The taboo points repel the subpopulation to prevent convergence to the same basin. A strategy to update the repelling power of the taboo points is proposed to address the challenge of basins of dissimilar size. The local shape of a basin is also approximated by the distribution of the subpopulation members converging to that basin. The proposed niching strategy is incorporated into the covariance matrix self-adaptation evolution strategy (CMSA-ES), a potent global optimization method. The resultant method, called the covariance matrix self-adaptation with repelling subpopulations (RS-CMSA), is assessed and compared to several state-of-the-art niching methods on a standard test suite for multimodal optimization. An organized procedure for parameter setting is followed which assumes a rough estimation of the desired/expected number of minima available. Performance sensitivity to the accuracy of this estimation is also studied by introducing the concept of robust mean peak ratio. Based on the numerical results using the available and the introduced performance measures, RS-CMSA emerges as the most successful method when robustness and efficiency are considered at the same time.FWN – Publicaties zonder aanstelling Universiteit Leide

Otimização multimodal para domínio contínuo com heurísticas de agrupamento adaptativo

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Ciência da Computação, Florianópolis, 2015.O crescente interesse nos métodos de otimização multimodal se deve a uma característica, quase que geral, dos problemas reais - a multimodalidade. Essa característica implica que o problema possui mais de uma solução ótima. Encontrar um conjunto de soluções ótimas é o objetivo dos métodos de otimização multimodal. O método apresentado neste trabalho, Estratégia de Evolução Multimodal baseada em Multi-população, ou NMESIS como será chamado devido a sua tradução para a língua inglesa Niching Multi-population Evolution Strategy with Improved Search, é um algoritmo de niching paralelo e explícito que utiliza como base a Adaptação da Matriz de Covariância. O método representa cada população como uma distribuição normal, o que permite utilizar técnicas destinadas à modelos de misturas gaussianas. Essa escolha ajuda a simplificar a parametrização, enquanto facilita o desenvolvimento de operadores robustos para troca de informação entre os nichos. O NMESIS foi avaliado através de um benchmark, utilizado em competições de algoritmos de niching, que contêm 20 problemas de teste, especialmente concebidos para avaliação de métodos de otimização multimodal, e seu desempenho foi comparado a outros métodos no estado da arte como NMMSO, dADE e NEA2 (último vencedor do CEC 2013). Os resultados apresentados mostram que o NMESIS conseguiu encontrar mais soluções que os concorrentes. Outro fator positivo foi a consistência dos resultados, mesmo com o aumento da precisão.Abstract : The growing interest in multimodal optimization methods is motivated by an characteristic commonly found in real problems --- multimodality. Find a set of optimal solutions is the target of multimodal optimization research. The method presented in this work, called Niching Multi-population Evolution Strategy with Improved Search (NMESIS), is a parallel niching method which is also explicit. Each niche is maintained by a CMA-ES instance. NMESIS abstracts the niche population as a Gaussian Mixture Model, allowing to use methods that are developed for classification and clustering. This helps to create robust operators to detect overlaps. Also, the abstraction allows a better communication mechanism between niches (migration). We apply a benchmark of 20 test functions, specially designed for multimodal optimization evaluation, and compare the performance with state-of- the-art methods. Finally we discuss the results and show that the proposed approach can reach better and stable results even in high-dimensional spaces

Illuminating meaningful diversity in complex feature spaces through adaptive grid-based genetic algorithms

In many fields there exist problems for which multiple solutions of suitably high performance may be found across distinct regions of the search space. Optimisation of the search towards including these distinct solutions is important not only to understanding these spaces but also to avoiding local optima. This is the goal of a type of genetic algorithms called illumination algorithms. In Chapter 2, we demonstrate the use of an illumination algorithm in the exploration of networks sharing only a given set of structural features (valid networks). This method produces a population of valid networks that are more diverse than those produced using state of the art methods, however, it was found to be too inefficient to be usable in real-world problems. Additionally, setting an appropriate resolution of the search requires some amount of prior knowledge of the space of solutions. Addressing this problem is the focus of Chapter 3, in which we develop three extensions to the method: a) an exact method of mutation whereby only valid networks are explored, b) an adaptive mechanism for setting the resolution of the search, c) a principle for tuning mutations parameters to the search’ s resolution. We show that with these additions our method is able to increase the diversity of solutions found in significantly fewer iterations. Finally, in Chapter 4 we expand our method for use in more general problem spaces. We benchmark it against the state of the art. In all tested landscapes, we show that our method is able to identify more meaningful niches in the spaces in the same number of iterations. We conclude by highlighting the limits of our framework and discuss further directions