Seeking multiple solutions:an updated survey on niching methods and their applications

Multi-Modal Optimization (MMO) aiming to locate multiple optimal (or near-optimal) solutions in a single simulation run has practical relevance to problem solving across many fields. Population-based meta-heuristics have been shown particularly effective in solving MMO problems, if equipped with specificallydesigned diversity-preserving mechanisms, commonly known as niching methods. This paper provides an updated survey on niching methods. The paper first revisits the fundamental concepts about niching and its most representative schemes, then reviews the most recent development of niching methods, including novel and hybrid methods, performance measures, and benchmarks for their assessment. Furthermore, the paper surveys previous attempts at leveraging the capabilities of niching to facilitate various optimization tasks (e.g., multi-objective and dynamic optimization) and machine learning tasks (e.g., clustering, feature selection, and learning ensembles). A list of successful applications of niching methods to real-world problems is presented to demonstrate the capabilities of niching methods in providing solutions that are difficult for other optimization methods to offer. The significant practical value of niching methods is clearly exemplified through these applications. Finally, the paper poses challenges and research questions on niching that are yet to be appropriately addressed. Providing answers to these questions is crucial before we can bring more fruitful benefits of niching to real-world problem solving

On-line Search History-assisted Restart Strategy for Covariance Matrix Adaptation Evolution Strategy

Restart strategy helps the covariance matrix adaptation evolution strategy (CMA-ES) to increase the probability of finding the global optimum in optimization, while a single run CMA-ES is easy to be trapped in local optima. In this paper, the continuous non-revisiting genetic algorithm (cNrGA) is used to help CMA-ES to achieve multiple restarts from different sub-regions of the search space. The CMA-ES with on-line search history-assisted restart strategy (HR-CMA-ES) is proposed. The entire on-line search history of cNrGA is stored in a binary space partitioning (BSP) tree, which is effective for performing local search. The frequently sampled sub-region is reflected by a deep position in the BSP tree. When leaf nodes are located deeper than a threshold, the corresponding sub-region is considered a region of interest (ROI). In HR-CMA-ES, cNrGA is responsible for global exploration and suggesting ROI for CMA-ES to perform an exploitation within or around the ROI. CMA-ES restarts independently in each suggested ROI. The non-revisiting mechanism of cNrGA avoids to suggest the same ROI for a second time. Experimental results on the CEC 2013 and 2017 benchmark suites show that HR-CMA-ES performs better than both CMA-ES and cNrGA. A positive synergy is observed by the memetic cooperation of the two algorithms.Comment: 8 pages, 9 figure

Static and Dynamic Multimodal Optimization by Improved Covariance Matrix Self-Adaptation Evolution Strategy with Repelling Subpopulations

The covariance matrix self-adaptation evolution strategy with repelling subpopulations (RS-CMSA-ES) is one of the most successful multimodal optimization (MMO) methods currently available. However, some of its components may become inefficient in certain situations. This study introduces the second variant of this method, called RS-CMSA-ESII. It improves the adaptation schemes for the normalized taboo distances of the archived solutions and the covariance matrix of the subpopulation, the termination criteria for the subpopulations, and the way in which the infeasible solutions are treated. It also improves the time complexity of RS-CMSA-ES by updating the initialization procedure of a subpopulation and developing a more accurate metric for determining critical taboo regions. The effects of these modifications are illustrated by designing controlled numerical simulations. RS-CMSA-ESII is then compared with the most successful and recent niching methods for MMO on a widely adopted test suite. The results obtained reveal the superiority of RS-CMSA-ESII over these methods, including the winners of the competition on niching methods for MMO in previous years. Besides, this study extends RS-CMSA-ESII to dynamic MMO and compares it with a few recently proposed methods on the modified moving peak benchmark functions

Discovering the Elite Hypervolume by Leveraging Interspecies Correlation

Evolution has produced an astonishing diversity of species, each filling a different niche. Algorithms like MAP-Elites mimic this divergent evolutionary process to find a set of behaviorally diverse but high-performing solutions, called the elites. Our key insight is that species in nature often share a surprisingly large part of their genome, in spite of occupying very different niches; similarly, the elites are likely to be concentrated in a specific "elite hypervolume" whose shape is defined by their common features. In this paper, we first introduce the elite hypervolume concept and propose two metrics to characterize it: the genotypic spread and the genotypic similarity. We then introduce a new variation operator, called "directional variation", that exploits interspecies (or inter-elites) correlations to accelerate the MAP-Elites algorithm. We demonstrate the effectiveness of this operator in three problems (a toy function, a redundant robotic arm, and a hexapod robot).Comment: In GECCO 201

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

CMA-ES with Restarts for Solving CEC 2013 Benchmark Problems

This paper investigates the performance of 6 versions of Covariance Matrix Adaptation Evolution Strategy (CMAES) with restarts on a set of 28 noiseless optimization problems (including 23 multi-modal ones) designed for the special session on real-parameter optimization of CEC 2013. The experimental validation of the restart strategies shows that: i). the versions of CMA-ES with weighted active covariance matrix update outperform the original versions of CMA-ES, especially on illconditioned problems; ii). the original restart strategies with increasing population size (IPOP) are usually outperformed by the bi-population restart strategies where the initial mutation stepsize is also varied; iii). the recently proposed alternative restart strategies for CMA-ES demonstrate a competitive performance and are ranked first w.r.t. the proportion of function-target pairs solved after the full run on all 10-, 30- and 50-dimensional problems

Guiding evolutionary search towards innovative solutions

The main goal of this work is to develop a method that, operating on top of an Evolutionary Algorithm, increases its likeliness of finding innovative solutions. This likeliness is laid out to be increased with the diversity of the solutions found, provided that they are of sufficient quality. The developed method needs to be applicable in a scenario in which the search is required to be started from a single, fixed solution. Therefore, a scheme is envisioned in which the search is performed in a sequential fashion, zooming in on a locally-optimal solution, and then exploring for a new potentially high-quality region based on a memory of solutions encountered earlier in the search. Two exploration criteria, one using an archive of earlier solutions as memory and the other deriving from a surrogate model trained on earlier solutions, were established to be worthwhile for integration into quality-based search. The resulting schemes were applied to a real-world airfoil optimization task, showing both to perform better than the baseline method of multiple standard optimization runs. The model-based approach delivers the best results, in the sense that it finds more solutions, more diverse solutions, and better-quality solutions than the baseline method.Honda Research Institute Europe (HRI-EU)Algorithms and the Foundations of Software technolog