scholarly journals Matrix Adaptation Evolution Strategy with Multi-Objective Optimization for Multimodal Optimization

Algorithms ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 56
Author(s):  
Wei Li
Keyword(s):  
Covariance Matrix ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Population Diversity ◽  
Evolution Strategy ◽  
Multimodal Optimization ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Covariance Matrix Adaptation ◽  
Adaptation Evolution

The standard covariance matrix adaptation evolution strategy (CMA-ES) is highly effective at locating a single global optimum. However, it shows unsatisfactory performance for solving multimodal optimization problems (MMOPs). In this paper, an improved algorithm based on the MA-ES, which is called the matrix adaptation evolution strategy with multi-objective optimization algorithm, is proposed to solve multimodal optimization problems (MA-ESN-MO). Taking advantage of the multi-objective optimization in maintaining population diversity, MA-ESN-MO transforms an MMOP into a bi-objective optimization problem. The archive is employed to save better solutions for improving the convergence of the algorithm. Moreover, the peaks found by the algorithm can be maintained until the end of the run. Multiple subpopulations are used to explore and exploit in parallel to find multiple optimal solutions for the given problem. Experimental results on CEC2013 test problems show that the covariance matrix adaptation with Niching and the multi-objective optimization algorithm (CMA-NMO), CMA Niching with the Mahalanobis Metric and the multi-objective optimization algorithm (CMA-NMM-MO), and matrix adaptation evolution strategy Niching with the multi-objective optimization algorithm (MA-ESN-MO) have overall better performance compared with the covariance matrix adaptation evolution strategy (CMA-ES), matrix adaptation evolution strategy (MA-ES), CMA Niching (CMA-N), CMA-ES Niching with Mahalanobis Metric (CMA-NMM), and MA-ES-Niching (MA-ESN).

Optimization Design of Trusses Based on Covariance Matrix Adaptation Evolution Strategy Algorithm

2012 ◽  
Vol 215-216 ◽  
pp. 133-137
Author(s):  
Guo Shao Su ◽  
Yan Zhang ◽  
Zhen Xing Wu ◽  
Liu Bin Yan
Keyword(s):  
Stochastic Optimization ◽  
Covariance Matrix ◽  
Optimization Problems ◽  
Fitness Function ◽  
Optimization Methods ◽  
Evolution Strategy ◽  
Covariance Matrix Adaptation ◽  
Study Results ◽  
Highly Nonlinear ◽  
Adaptation Evolution

Covariance matrix adaptation evolution strategy algorithm (CMA-ES) is a newly evolution algorithm. It has become a powerful tool for solving highly nonlinear multi-peak optimization problems. In many real-world optimization problems, the location of multiple optima is often required in a search space. In order to evaluate the solution, thousands of fitness function evaluations are involved that is a time consuming or expensive processes. Therefore, conventional stochastic optimization methods meet a special challenge for a very large number of problem function evaluations. Aiming to overcome the shortcoming of stochastic optimization methods in the high calculation cost, a truss optimal method based on CMA-ES algorithm is proposed and applied to solve the section and shape optimization problems of trusses. The study results show that the method is feasible and has the advantages of high accuracy, high efficiency and easy implementation.

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

2017 ◽  
Vol 25 (3) ◽  
pp. 439-471 ◽  
Author(s):  
Ali Ahrari ◽  
Kalyanmoy Deb ◽  
Mike Preuss
Keyword(s):  
Covariance Matrix ◽  
Optimization Problems ◽  
Search Space ◽  
Optimization Method ◽  
Evolution Strategy ◽  
Test Problems ◽  
Multimodal Optimization ◽  
Niching Methods ◽  
Self Adaptation ◽  
Adaptation Evolution

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.

scholarly journals Multi-objective simulation optimization for complex urban mass rapid transit systems

2019 ◽  
Author(s):  
David Schmaranzer ◽  
Roland Braune ◽  
Karl F. Doerner
Keyword(s):  
Covariance Matrix ◽  
Computational Study ◽  
Evolution Strategy ◽  
Rapid Transit ◽  
Two Phase ◽  
Transit Systems ◽  
Multi Objective ◽  
Covariance Matrix Adaptation ◽  
Adaptation Evolution ◽  
Mass Rapid Transit

Abstract In this paper, we present a multi-objective simulation-based headway optimization for complex urban mass rapid transit systems. Real-world applications often confront conflicting goals of cost versus service level. We propose a two-phase algorithm that combines the single-objective covariance matrix adaptation evolution strategy with a problem-specific multi-directional local search. With a computational study, we compare our proposed method against both a multi-objective covariance matrix adaptation evolution strategy and a non-dominated sorting genetic algorithm. The integrated discrete event simulation model has several stochastic elements. Fluctuating demand (i.e., creation of passengers) is driven by hourly origin-destination-matrices based on mobile phone and infrared count data. We also consider the passenger distribution along waiting platforms and within vehicles. Our two-phase optimization scheme outperforms the comparative approaches, in terms of both spread and the accuracy of the resulting Pareto front approximation.

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