Covariance Matrix Adaptation Evolution Strategy Algorithm Research Articles

A Modification of the PBIL Algorithm Inspired by the CMA-ES Algorithm in Discrete Knapsack Problem

The subject of this paper is the comparison of two algorithms belonging to the class of evolutionary algorithms. The first one is the well-known Population-Based Incremental Learning (PBIL) algorithm, while the second one, proposed by us, is a modification of it and based on the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm. In the proposed Covariance Matrix Adaptation Population-Based Incremental Learning (CMA-PBIL) algorithm, the probability distribution of population is described by two parameters: the covariance matrix and the probability vector. The comparison of algorithms was performed in the discrete domain of the solution space, where we used the well-known knapsack problem in a variety of data correlations. The results obtained show that the proposed CMA-PBIL algorithm can perform better than standard PBIL in some cases. Therefore, the proposed algorithm can be a reasonable alternative to the PBIL algorithm in the discrete space domain.

Covariance matrix adaptation evolution strategy based optical phase control

In this letter, an investigation of the use of a covariance matrix adaptation evolution strategy (CMA-ES) algorithm is conducted as the phase-locking method for multi-channel coherent beam combining (CBC) for the first time. A comprehensive numerical analysis is carried out on the operational performances of the CMA-ES based phase-locking algorithm implemented into 7- and 19-channel CBC systems in a filled-aperture format. Through numerical simulations it can be verified that the CMA-ES algorithm can readily lead to over 0.90 of normalised beam combining efficiency with appropriate algorithm parameter sets, which can also be optimised by a combinatorial study. The proposed CMA-ES based phase-locking algorithm is a feasible option for novel phase-locking technique for a CBC system particularly when the local extremum issue becomes severe such as in CBC under turbulent atmospheric conditions.

Source mask optimization using the covariance matrix adaptation evolution strategy.

Source mask optimization (SMO) is one of the indispensable resolution enhancement techniques to guarantee the image fidelity and process robustness for the 2Xnm technology node and beyond. The optimization capacity and convergence efficiency of SMO are important, especially for full-chip SMO. An SMO method using the covariance matrix adaptation evolution strategy (CMA-ES), together with a new source representation method, is proposed in this paper. Based on the forward vector imaging formulation, the encoding and decoding methods of the source and the mask, and the constructed merit function, the source and the mask are optimized using the CMA-ES algorithm. The solution search space and the search step size are adaptively updated during the optimization procedure. Considering the sparsity of the optimal source, the source is represented by a set of ideal point sources with unit intensity and adjustable positions. The advantageous spatial frequency components of the source for imaging performance improvement are identified through the aggregation of the point sources. Simulations and comparisons verify the superior optimization capacity and convergence efficiency of the proposed method.

Retrieval of fractal dimension and size distribution of non-compact soot aggregates from relative intensities of multi-wavelength angular-resolved light scattering.

A new technique is developed to retrieve the fractal dimension and size distribution of soot aggregates simultaneously from the relative intensities of multi-wavelength angular-resolved light scattering. Compared with other techniques, the main advantage of this method is its independence of knowing complex refractive index, number density of aggregate, fractal prefactor and primary particle diameter. The forward light scattering procedure of soot aggregate is described by Rayleigh-Debye-Gans polydisperse fractal aggregate (RDG-PFA) scattering theory, and the retrieval process is performed by using the covariance matrix adaption-evolution strategy algorithm (CMA-ES). Three different measurement models, i.e. absolute scattering and transmittance, absolute scattering, relative scattering (RS), are investigated in present research. Numerical experiments have been performed to test the feasibility of the CMA-ES algorithm. Combined with the multi-wavelength RDG-PFA strategy, the retrieval accuracy of soot aggregate size distribution is proved to be more effectively by using the RS model. Satisfactory results under 10% Gaussian measurement noise have demonstrated the feasibility of the proposed method.

Evolutionary strategies as applied to shear strain effects in reinforced concrete beams

The reinforced concrete beams is a structural member that is widely used in all types of building and civil constructions. These beams are subjected to different external loads that, above a critical value, may cause the collapse of the whole structure, having devastating consequences for civilians. Therefore, the a priori simulation of the internal forces developed within a reinforced concrete beam, when it is subjected to external loads, is mandatory to figure out its progressive structural response, to provide integrated risk assessment for a wide range of constructions such as buildings, bridges, etc. In this paper, we provide a simulation framework to estimate the behavior of reinforced concrete beams when they are subjected to external loads. Of particular interest to us is the simulation of the particularly damaging internal force, called Shear force. Several techniques are under study such as regression analysis, Little Genetic Algorithm (LGA) and Covariance Matrix Adaptation Evolution Strategy (CMA-ES), along with different objective functions (lineal, polynomial and rational functions) to provide a solution that satisfies both the physical and computational constraints of the targeted problem. These techniques are empirically optimized by using different parameters and genetic operators such as elitism, penalization for unfeasible individuals, crossing by one point or by linear combination of two individuals, mutation by gen or by individual. Numerical results reveal that CMA-ES algorithm together with a proper objective function, elitism and penalization allows predicting, under a relative error less than 5% (compared to experimental data taken from a tested beam), the shear response of a reinforced concrete beam in the stages near to the structural collapse.

Design Of Multivariable Fractional Order Pid Controller Using Covariance Matrix Adaptation Evolution Strategy

Abstract This paper presents an automatic tuning of multivariable Fractional-Order Proportional, Integral and Derivative controller (FO-PID) parameters using Covariance Matrix Adaptation Evolution Strategy (CMAES) algorithm. Decoupled multivariable FO-PI and FO-PID controller structures are considered. Oustaloup integer order approximation is used for the fractional integrals and derivatives. For validation, two Multi-Input Multi- Output (MIMO) distillation columns described byWood and Berry and Ogunnaike and Ray are considered for the design of multivariable FO-PID controller. Optimal FO-PID controller is designed by minimizing Integral Absolute Error (IAE) as objective function. The results of previously reported PI/PID controller are considered for comparison purposes. Simulation results reveal that the performance of FOPI and FO-PID controller is better than integer order PI/PID controller in terms of IAE. Also, CMAES algorithm is suitable for the design of FO-PI / FO-PID controller.

Hybrid orthogonal CMAES for solving global optimization problems

In order to overcome the shortcomings of Covariance Matrix Adaptation Evolution Strategy(CMAES),such as premature convergence and low precision,when it is used in high-dimensional multimodal optimization,a hybrid algorithm combined CMAES with Orthogonal Design with Quantization(OD/Q) was proposed.Firstly,the small population CMAES was used to realize a fast searching.When orthogonal CMAES algorithm trapped in local extremum,base vectors for OD/Q were selected dynamically based on the position of current best solution.Then the entire solution space,including the field around extreme value,was explored by trial vectors generated by OD/Q.The proposed algorithm was guided by this process jumping out of the local optimum.The new approach was tested on six high-dimensional multimodal benchmark functions.Compared with other algorithms,the new algorithm has better searching precision,convergence speed and capacity of global search.

Static Loadabilty Assessment Using Covariance Matrix Adapted Evolution Strategy

This paper discusses application of Covariance Matrix Adapted Evolution Strategy (CMAES) algorithm for maximizing loadability margin of power system. CMAES is a class of continuous evolutionary algorithm that generates new population members by sampling from a probability distribution that is constructed during the optimization process. IEEE 14 bus , 30 bus and 118 bus systems are considered for simulation purpose. For comparison of the results, primal dual interior point (PDIP), continuation power flow (CPF), Particle swarm optimization algorithms are considered. Statistical performance of CMAES algorithm reveals that even the mean value of maximum loadability is better than maximum loadability obtained in other methods. Even though CMAES takes higher computation time due to the determination of covariance matrix, only this algorithm gives maximum loadability margin.

Application of covariance matrix adaptation–evolution strategy to optimal control of hepatitis B infection

To avoid the cirrhosis and liver cancer, antiviral treatment for chronic hepatitis is necessary. In the literature, several mathematical models have been used to describe the dynamics of viral infections. In addition, several control strategies have been reported in the literature to deal with optimal antiviral therapy problem of infectious diseases. In this paper, three controller structures with optimized parameters using covariance matrix adaptation–evolution strategy algorithm are proposed for optimal control of basic hepatitis B virus (HBV) infection dynamical system. The first structure is an optimized neural-type sigmoid-based closed-loop controller, which is a nonlinear feedback controller. The second structure is an optimized open-loop time-based fuzzy controller in which the control input is approximated using the mixture of Gaussian membership functions. Finally, an optimized closed-loop fuzzy controller is used as the third control structure. After designing the controllers, some parameters of the HBV infection model are considered to be unknown and the robustness of the controllers is studied. Experimental results show that the optimized neural-type sigmoid-based closed-loop controller has the best performance in terms of healthy hepatocytes and free HBVs concentration among the investigated controllers and the optimized closed-loop fuzzy controller is the best in terms of minimum mean control input signal that is the drug usage. Concerning the robustness, the optimized neural-type sigmoid-based closed-loop controller has the best performance.

Covariance matrix adapted evolution strategy-based decentralised congestion management for multilateral transactions

This study proposes AC load flow-based decentralised model for congestion management in the forward markets using resource allocation technique. In this model, each transaction maximises its profit under the limits of transmission line capacities allocated by independent system operator. The voltage and reactive power impact of the system are also incorporated in the model. A covariance matrix adapted evolution strategy (CMAES) algorithm is used to solve decentralised congestion management problem for multilateral transactions. The proposed approach is tested on IEEE 30 bus, IEEE 118 bus and practical Indian utility 62 bus systems for three, six and two multilateral transactions, respectively, with smooth and non-smooth cost functions. The results obtained for decentralised model using CMAES algorithm is compared with particle swarm optimisation (PSO) algorithm and sequential quadratic programming (SQP) technique. The statistical performances of various algorithms such as best, worst, mean and standard deviations of social welfare for 20 independent trials are given. To prove the validity of the proposed improved decentralised model, the results obtained are also compared with centralised model. Simulation results clearly demonstrate the better performance of CMAES algorithm over PSO and SQP.

Covariance matrix adapted evolution strategy algorithm-based solution to dynamic economic dispatch problems

This article presents a covariance matrix adapted evolution strategy (CMAES) algorithm to solve dynamic economic dispatch (DED) problems. The DED is an extension of the conventional economic dispatch problem, in which optimal settings of generator units are determined with a predicted load demand over a period of time. In this article, the applicability and validity of the CMAES algorithm is demonstrated on three DED test systems with a sequential decomposition approach. The results obtained using the CMAES algorithm are compared with results obtained using the real-coded genetic algorithm, the Nelder–Mead simplex method, and other methods from the literature. To compare the performance of the various algorithms, statistical measures like best, mean, worst, standard deviation, and mean computation time over 20 independent runs are taken. The effect of population size on the performance of the CMAES algorithm is also investigated. The simulation experiments reveal that the CMAES algorithm performs better in terms of fuel cost and solution consistency. Karush–Kuhn–Tucker conditions are applied to the solutions obtained using the CMAES algorithm to verify optimality. It is found that the obtained results satisfy the Karush–Kuhn–Tucker conditions and confirm optimality.

Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm

The design of triangular fiber Bragg grating (TFBG) filters using covariance matrix adapted evolution strategy (CMAES) algorithm is presented. The TFBG filter can be used as a readout device in FBG-based sensor applications. Two different filter design problems are investigated. The first problem is the design of TFBG filter for a specified bandwidth. The other is maximizing the bandwidth of the TFBG filter for a given grating length and maximum index modulation of the FBG. A more practical asymmetrical triangular FBG filter design is also considered. The results show that for the same grating length and maximum index modulation, a larger bandwidth can be achieved with a chirped grating. The maximized bandwidth design can be used to achieve the maximum possible bandwidth for the specified grating length, maximum index modulation and chirp rate. The results obtained using CMAES algorithm (codes available at http://www.ntu.edu.sg/home/epnsugan) is compared with the results of PSO and other algorithms. Comparisons show that the CMAES algorithm is more consistent in obtaining the best solution with reduced computation time. Hence, the CMAES algorithm is effective for the design of TFBG filters for sensor applications.

Design of optimal length low-dispersion FBG filter using covariance matrix adapted evolution

The design of a low-dispersion fiber Bragg grating (FBG) with an optimal grating length using covariance matrix adapted evolution strategy (CMAES) is presented. A novel objective function formulation is proposed for the optimal grating length low-dispersion FBG design. The CMAES algorithm employs adaptive learning procedure to identify correlations among the design parameters. The design of a low-dispersion FBG filter with 25-GHz (or 0.2 nm in the 1550-nm band) bandwidth is considered. Simulation results, obtained using the codes available in public domain (the codes are available from the third author), show that the CMAES algorithm is more appropriate for the practical design of length optimized FBG-based filters when compared with the other optimization methods.