Covariance Matrix Self-adaptation Research Articles

An intelligent protection framework for intrusion detection in cloud environment based on covariance matrix self-adaptation evolution strategy and multi-criteria decision-making

The security defenses that are not comparable to sophisticated adversary tools, let the cloud as an open environment for attacks and intrusions. In this paper, an intelligent protection framework for intrusion detection in a cloud computing environment based on a covariance matrix self-adaptation evolution strategy (CMSA-ES) and multi-criteria decision-making (MCDM) is proposed. The proposed framework constructs an optimal intrusion detector by using CMSA-ES algorithm which adjusts the best parameter set for the attack detector. Moreover, the proposed framework uses a MEREC-VIKOR, a hybrid standardized evaluation technique. MEREC-VIKOR generates the own performance metrics (S, R, and Q) of the proposed framework which is a combination of multi-conflicting criteria. The proposed framework is evaluated for attack detection by using CICIDS 2017 dataset. The experiments show that the proposed framework can detect cloud attacks accurately with low S (utility), R (regret), and Q (integration between S and R). The proposed framework is analyzed with respect to several evolutionary algorithms such as GA, IGASAA, and CMA-ES. The performance analysis demonstrates that the proposed framework that depends on CMSA-ES converges faster than the other evolutionary algorithms such as GA, IGASAA, and CMA-ES. The outcomes also demonstrate that the proposed model is comparable to the state-of-the-art techniques.

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.

S-CoEA: Subproblems Co-Solving Evolutionary Algorithm for Uncertain Optimization.

Existing techniques on dealing with uncertain optimization problems (UOPs) mostly rely on the preference information of decision makers (DMs) or the knowledge involved in probability distributions on uncertainties. Actually, accurate preferences and distribution information of uncertainties are hard to obtain due to the lack of knowledge. Besides, it is risky to make assumptions on this information to handle uncertainties when DMs do not have sufficient knowledge about the problem. This article attempts to treat UOPs in an a posteriori manner and proposes a subproblem co-solving evolutionary algorithm (EA) for UOPs, namely, S-CoEA. It decomposes a UOP into a series of correlated subproblems by using the proposed decomposition strategy embedded with an original ordered weighted-sum (OWS) operator. These subproblems are formulated in different aggregation forms of sampled function values and represent different preferences on uncertainties. They are co-solved in parallel by using information from neighboring subproblems. The sampling strategy is used to gather the distribution information of uncertain functions and alleviate the detrimental effects of uncertainties. A sample-updating scheme based on historical information is presented to further improve the performance of S-CoEA. The proposed S-CoEA is compared with two state-of-the-art competitors, including the EA with the exponential sampling method (E-sampling) and the population-controlled covariance matrix self-adaptation evolution strategy (pcCMSA-ES). Numerical experiments are conducted on a series of test instances with various characteristics and different strength levels of uncertainties. Experimental results show that S-CoEA outperforms or performs competitively against competitors in the majority of 26 continuous test instances and four test cases of discrete redundancy allocation problems.

An improved water wave optimisation algorithm enhanced by CMA-ES and opposition-based learning

ABSTRACTWater Wave Optimisation algorithm (WWO) is a new swarm-based metaheuristic inspired by shallow wave models for global optimisation. In this paper, an enhanced WWO, which combines with multiple assistant strategies (EWWO), is proposed. First, the random opposition-based learning (ROBL) mechanism is introduced to generate the initial population with high quality. Second, a new modified operation is designed and embedded into propagation operation to balance the global exploration and the local exploitation. Third, the covariance matrix self-adaptation evolution strategy (CMA-ES) is employed by the refraction operation to further strengthen the local exploitation. Furthermore, the diversity of the population is maintained in the evolution process by using a crossover operator. The experiment results based on CEC 2017 benchmarks indicate that the EWWO outperforms the state-of-the-art variant algorithms of the WWO and the standard WWO.

A Covariance Matrix Self-Adaptation Evolution Strategy for Optimization Under Linear Constraints

This paper addresses the development of a covariance matrix self-adaptation evolution strategy (CMSA-ES) for solving optimization problems with linear constraints. The proposed algorithm is referred to as Linear Constraint CMSA-ES (lcCMSA-ES). It uses a specially built mutation operator together with repair by projection to satisfy the constraints. The lcCMSA-ES evolves itself on a linear manifold defined by the constraints. The objective function is only evaluated at feasible search points (interior point method). This is a property often required in application domains such as simulation optimization and finite element methods. The algorithm is tested on a variety of different test problems revealing considerable results.

On the steady state analysis of covariance matrix self-adaptation evolution strategies on the noisy ellipsoid model

This paper addresses the analysis of covariance matrix self-adaptive Evolution Strategies (CMSA-ES) on a subclass of quadratic functions subject to additive Gaussian noise: the noisy ellipsoid model. To this end, it is demonstrated that the dynamical systems approach from the context of isotropic mutations can be transferred to ES that also control the covariance matrix. Theoretical findings such as the component-wise quadratic progress rate or the self-adaptation response function can thus be reused for the CMSA-ES analysis. By deriving the steady state quantities approached on the noisy ellipsoid model for constant population size, a detailed description of the asymptotic CMSA-ES behavior is obtained. By providing self-adaptive ES with a population control mechanism, despite noise disturbances, the algorithm is able to realize continuing progress towards the optimum. Regarding the population control CMSA-ES (pcCMSA-ES), the analytical findings allow to specify its asymptotic long-term behavior and to identify influencing parameters. The finally obtained convergence rate matches the theoretical lower bound of all comparison-based direct search algorithms.

Enhancing the performance of differential evolution with covariance matrix self-adaptation

Differential evolution (DE) is an efficient global optimizer, while the covariance matrix adaptation evolution strategy (CMA-ES) shows great power on local search. However, utilizing both of these advantages in one algorithm is difficult since the randomness introduced by DE may reduce the reliability of covariance matrix estimation. Moreover, the exploration ability of DE can be canceled out by CMA-ES because they use completely different mechanisms to control the search step. To take advantage of both DE and CMA-ES, we propose a novel DE variant with covariance matrix self-adaptation, named DECMSA. In DECMSA, a new mutation scheme named “DE/current-to-better/1” is implemented. This scheme uses a Gaussian distribution to guide the search and strengthens both exploration and exploitation capabilities of DE. The proposed algorithm has been tested on the CEC-13 benchmark suite. The experimental results demonstrate that DECMSA outperforms popular DE variants, and it is quite competitive with state-of-the-art CMA-ES variants such as IPOP-CMA-ES and BIPOP-CMA-ES. Moreover, equipped with a constraint handling method, DECMSA is able to produce better solutions than other comparative algorithms on three classic constrained engineering design problems.

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.

A Study on Performace of Levenberg-Marquardt and CMA-ES Optimization Methods for Atlas-based 2D/3D Reconstruction

Abstract: In this study, we compare the performance of our previously proposed deformable 2D/3D registration approach based on the Levenberg-Marquardt optimization with methods exploiting Covariance Matrix Adaptation (CMA) and Covariance Matrix Self Adaptation (CMSA) evolution strategies. The aim of the registration is to reconstruct a patient-specifc 3D bone model from a small set of plain 2D X-ray images what is achieved by ftting a deformable bone atlas onto the X-ray images. The comparison of diferent optimization methods is focused on both the robustness and the speed. The results were obtained using a large-scale data set of synthetic X-ray images. We show that our method is several times faster in comparison with the approaches based on evolution strategies while the robustness of the reconstruction is preserved. To speed-up the reconstruction process, certain parts of the registration pipeline are accelerated using graphics hardware. The median error of our proposed method was 1.12mm and the median reconstruction time was 7.2s. The median time reached by the CMA-ES and CMSA-ES methods was 48.5 s and 138.5 s respectively.

Evolution on trees: On the design of an evolution strategy for scenario-based multi-period portfolio optimization under transaction costs

Scenario-based optimization is a problem class often occurring in finance, planning and control. While the standard approach is usually based on linear stochastic programming, this paper develops an Evolution Strategy (ES) that can be used to treat nonlinear planning problems arising from Value at Risk (VaR)-constraints and not necessarily proportional transaction costs. Due to the VaR-constraints the optimization problem is generally of non-convex type and its decision version is already NP-complete. The developed ES is the first algorithm in the field of evolutionary and swarm intelligence that tackles this kind of optimization problem. The algorithm design is based on the covariance matrix self-adaptation ES (CMSA-ES). The optimization is performed on scenario trees where in each node specific constraints (balance equations) must be fulfilled. In order to evaluate the performance of the ES proposed, instances of increasing problem hardness are considered. The application to the general case with nonlinear node constraints shows not only the potential of the ES designed, but also its limitations. The latter are basically determined by the high dimensionalities of the search spaces defined by the scenario trees.

Erratum to “On the Design of Constraint Covariance Matrix Self-Adaptation Evolution Strategies Including a Cardinality Constraint” [Aug 12 578-596

In the above-named article [ibid., vol 16, no 4, pp. 578-596, Aug. 2012] an error occurred during the print production process that resulted in the incorrect display of Greek characters within many of the figures in the printed publication. However, the electronic PDF version available on IEEEXplore was not affected and all of the articles' figures appear correctly. Please visit http://ieeexplore. ieee.org/xpl/tocresult.jsp?isnumber=6249762p Fig. 6(a) vertical axis label incomplete, Greek rho missing; Fig. 9(a) vertical axis label incomplete, Greek rho missing; Fig. 9(c) vertical axis label incomplete, Greek sigma missing; Fig. 10(a) vertical axis label incomplete, Greek rho missing; Fig. 10(b) vertical axis label incomplete, Greek rho missing; Fig. 11(a) vertical axis label incomplete, Greek rho missing; Fig. 11(c) vertical axis label incomplete, Greek sigma missing; Fig. 12(a) vertical axis label incomplete, Greek rho missing; Fig. 12(c) vertical axis label incomplete, Greek sigma missing; Fig. 13(a) vertical axis label incomplete, Greek rho missing; Fig. 13(c) vertical axis label incomplete, Greek sigma missing; Fig. 14(a) and (b) vertical axis labels incomplete, Greek rho overlined (bar) missing; Fig. 17(a) and (b) horizontal axis labels, Greek kappa missing; Fig. 18 horizontal axis label, Greek kappa missing; Fig. 19(b) vertical axis label incomplete, Greek lambda missing; Fig. 21(a) and (b) horizontal axis labels, Greek kappa missing; Fig. 22(b) Delta before f and x missing; Fig. 24(a) and (b) horizontal axis labels, Greek lambda missing.

On the Design of Constraint Covariance Matrix Self-Adaptation Evolution Strategies Including a Cardinality Constraint

This paper describes the algorithm's engineering of a covariance matrix self-adaptation evolution strategy (CMSA-ES) for solving a mixed linear/nonlinear constrained optimization problem arising in portfolio optimization. While the feasible solution space is defined by the (probabilistic) simplex, the nonlinearity comes in by a cardinality constraint bounding the number of linear inequalities violated. This gives rise to a nonconvex optimization problem. The design is based on the CMSA-ES and relies on three specific techniques to fulfill the different constraints. The resulting algorithm is then thoroughly tested on a data set derived from time series data of the Dow Jones Index.

Covariance matrix self-adaptation evolution strategies and other metaheuristic techniques for neural adaptive learning

A covariance matrix self-adaptation evolution strategy (CMSA-ES) was compared with several metaheuristic techniques for multilayer perceptron (MLP)-based function approximation and classification. Function approximation was based on simulations of several 2D functions and classification analysis was based on nine cancer DNA microarray data sets. Connection weight learning by MLPs was carried out using genetic algorithms (GA–MLP), covariance matrix self-adaptation-evolution strategies (CMSA-ES–MLP), back-propagation gradient-based learning (MLP), particle swarm optimization (PSO–MLP), and ant colony optimization (ACO–MLP). During function approximation runs, input-side activation functions evaluated included linear, logistic, tanh, Hermite, Laguerre, exponential, and radial basis functions, while the output-side function was always linear. For classification, the input-side activation function was always logistic, while the output-side function was always regularized softmax. Self-organizing maps and unsupervised neural gas were used to reduce dimensions of original gene expression input features used in classification. Results indicate that for function approximation, use of Hermite polynomials for activation functions at hidden nodes with CMSA-ES–MLP connection weight learning resulted in the greatest fitness levels. On average, the most elite chromosomes were observed for MLP ($${\rm MSE}=0.4977$$ ), CMSA-ES–MLP (0.6484), PSO–MLP (0.7472), ACO–MLP (1.3471), and GA–MLP (1.4845). For classification analysis, overall average performance of classifiers used was 92.64% (CMSA-ES–MLP), 92.22% (PSO–MLP), 91.30% (ACO–MLP), 89.36% (MLP), and 60.72% (GA–MLP). We have shown that a reliable approach to function approximation can be achieved through application of MLP connection weight learning when the assumed function is unknown. In this scenario, the MLP architecture itself defines the equation used for solving the unknown parameters relating input and output target values. A major drawback of implementing CMSA-ES into an MLP is that when the number of MLP weights is large, the $${{\mathcal{O}}}(N^3)$$ Cholesky factorization becomes a bottleneck for performance. As an alternative, feature reduction using SOM and NG can greatly enhance performance of CMSA-ES–MLP by reducing $$N.$$ Future research into the speeding up of Cholesky factorization for CMSA-ES will be helpful in overcoming time complexity problems related to a large number of connection weights.

Evolutionary self-adaptation: a survey of operators and strategy parameters

The success of evolutionary search depends on adequate parameter settings. Ill conditioned strategy parameters decrease the success probabilities of genetic operators. Proper settings may change during the optimization process. The question arises if adequate settings can be found automatically during the optimization process. Evolution strategies gave an answer to the online parameter control problem decades ago: self-adaptation. Self-adaptation is the implicit search in the space of strategy parameters. The self-adaptive control of mutation strengths in evolution strategies turned out to be exceptionally successful. Nevertheless, for years self-adaptation has not achieved the attention it deserves. This paper is a survey of self-adaptive parameter control in evolutionary computation. It classifies self-adaptation in the taxonomy of parameter setting techniques, gives an overview of automatic online-controllable evolutionary operators and provides a coherent view on search techniques in the space of strategy parameters. Beyer and Sendhoff’s covariance matrix self-adaptation evolution strategy is reviewed as a successful example for self-adaptation and exemplarily tested for various concepts that are discussed.

Covariance Matrix Self-Adaptation and Kernel Regression - Perspectives of Evolutionary Optimization in Kernel Machines

Kernel based techniques have shown outstanding success in data mining and machine learning in the recent past. Many optimization problems of kernel based methods suffer from multiple local optima. ...