42 research outputs found

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

    Get PDF
    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

    A multi-tier adaptive grid algorithm for the evolutionary multi-objective optimisation of complex problems

    Get PDF
    The multi-tier Covariance Matrix Adaptation Pareto Archived Evolution Strategy (m-CMA-PAES) is an evolutionary multi-objective optimisation (EMO) algorithm for real-valued optimisation problems. It combines a non-elitist adaptive grid based selection scheme with the efficient strategy parameter adaptation of the elitist Covariance Matrix Adaptation Evolution Strategy (CMA-ES). In the original CMA-PAES, a solution is selected as a parent for the next population using an elitist adaptive grid archiving (AGA) scheme derived from the Pareto Archived Evolution Strategy (PAES). In contrast, a multi-tiered AGA scheme to populate the archive using an adaptive grid for each level of non-dominated solutions in the considered candidate population is proposed. The new selection scheme improves the performance of the CMA-PAES as shown using benchmark functions from the ZDT, CEC09, and DTLZ test suite in a comparison against the (Ī¼+Ī») Ī¼ Ī» Multi-Objective Covariance Matrix Adaptation Evolution Strategy (MO-CMA-ES). In comparison with MO-CMA-ES, the experimental results show that the proposed algorithm offers up to a 69 % performance increase according to the Inverse Generational Distance (IGD) metric

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

    Get PDF
    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 ā€“ Publicaties zonder aanstelling Universiteit Leide

    A new selection ratio for large population sizes

    Get PDF
    International audienceMotivated by parallel optimization, we study the Self-Adaptation algorithm for large population sizes. We ļ¬rst show that the current version of this algorithm does not reach the theoretical bounds, then we propose a very simple modiļ¬cation, in the selection part of the evolution process. We show that this simple modiļ¬cation leads to big improvement of the speed-up when the population size is large

    Adaptive Ranking Based Constraint Handling for Explicitly Constrained Black-Box Optimization

    Full text link
    A novel explicit constraint handling technique for the covariance matrix adaptation evolution strategy (CMA-ES) is proposed. The proposed constraint handling exhibits two invariance properties. One is the invariance to arbitrary element-wise increasing transformation of the objective and constraint functions. The other is the invariance to arbitrary affine transformation of the search space. The proposed technique virtually transforms a constrained optimization problem into an unconstrained optimization problem by considering an adaptive weighted sum of the ranking of the objective function values and the ranking of the constraint violations that are measured by the Mahalanobis distance between each candidate solution to its projection onto the boundary of the constraints. Simulation results are presented and show that the CMA-ES with the proposed constraint handling exhibits the affine invariance and performs similarly to the CMA-ES on unconstrained counterparts.Comment: 9 page

    A new selection ratio for large population sizes

    Get PDF
    International audienceMotivated by parallel optimization, we study the Self-Adaptation algorithm for large population sizes. We ļ¬rst show that the current version of this algorithm does not reach the theoretical bounds, then we propose a very simple modiļ¬cation, in the selection part of the evolution process. We show that this simple modiļ¬cation leads to big improvement of the speed-up when the population size is large

    Evolutionary Algorithms with Mixed Strategy

    Get PDF

    Using Optimisation Meta-Heuristics for the Roughness Estimation Problem in River Flow Analysis

    Get PDF
    Climate change threats make it difficult to perform reliable and quick predictions on floods forecasting. This gives rise to the need of having advanced methods, e.g., computational intelligence tools, to improve upon the results from flooding events simulations and, in turn, design best practices for riverbed maintenance. In this context, being able to accurately estimate the roughness coefficient, also known as Manningā€™s n coefficient, plays an important role when computational models are employed. In this piece of research, we propose an optimal approach for the estimation of ā€˜nā€™. First, an objective function is designed for measuring the quality of ā€˜candidateā€™ Manningā€™s coefficients relative to specif cross-sections of a river. Second, such function is optimised to return coefficients having the highest quality as possible. Five well-known meta-heuristic algorithms are employed to achieve this goal, these being a classic Evolution Strategy, a Differential Evolution algorithm, the popular Covariance Matrix Adaptation Evolution Strategy, a classic Particle Swarm Optimisation and a Bayesian Optimisation framework. We report results on two real-world case studies based on the Italian rivers ā€˜Pagliaā€™ and ā€˜Anieneā€™. A comparative analysis between the employed optimisation algorithms is performed and discussed both empirically and statistically. From the hydrodynamic point of view, the experimental results are satisfactory and produced within significantly less computational time in comparison to classic methods. This shows the suitability of the proposed approach for optimal estimation of the roughness coefficient and, in turn, for designing optimised hydrological models
    corecore