Regularized continuous estimation of distribution algorithms

Karshenas, Hossein; Santana, Roberto; Bielza, Concha; Larrañaga, Pedro

doi:10.1016/j.asoc.2012.11.049

Cited by 29 publications

(16 citation statements)

References 41 publications

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“…It is obvious that for an easy problem, a small value of NP is sufficient, but for difficult problems, a large value of NP is recommended in order to avoid trapping to a local optimum. The large NP may provide better optimization with larger calculation [16]. However, it may vary from problem to problem.…”

Section: The Selection Of Np and Nbmentioning

confidence: 99%

“…There are many researches about the EDAs. Karshenas and Santana [16] adopt regularized method to improve the conventional EDA performance, which used some benchmarks with 100 dimensions for testing. Valdez and Hernández [17] adopt Gaussian model to approximate the Boltzmann distribution, which can analyze the minimization of the Kullback-Leibler divergence instead of computing the mean and variance of Gaussian model, and the test suite is up to 50 dimensions.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Learning Rate Elitism Estimation of Distribution Algorithm Combining Chaos Perturbation for Large Scale Optimization

Xu¹,

Zhang²,

Sun³

et al. 2016

Open Cyber

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Estimation of distribution algorithm (EDA) is a kind of EAs, which is based on the technique of probabilistic model and sampling. Large scale optimization problems are a challenge for the conventional EAs. This paper presents an adaptive learning rate elitism EDA combining chaos perturbation (ALREEDA) to improve the performance of traditional EDA to solve high dimensional optimization problems. The famous elitism strategy is introduced to maintain a good convergent performance of this algorithm. The learning rate of σ (a parameter of probabilistic model) is adaptive in the optimization to enhance the algorithm's global and local search ability, and the chaos perturbation strategy is used to improve the algorithm's local search ability. Some simulation experiments are conducted to verify the performance of ALREEDA by seven benchmarks of CEC'08 large scale optimization with dimensions 100, 500 and 1000. The results of ALREEDA are promising on majority of the testing problems, and it is comparable with other EDAs and some other improved EAs.

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Section: The Selection Of Np and Nbmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive Learning Rate Elitism Estimation of Distribution Algorithm Combining Chaos Perturbation for Large Scale Optimization

Xu¹,

Zhang²,

Sun³

et al. 2016

Open Cyber

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“…Yet, due to high dimensionality of a covariance matrix and limited number of samples, the WMLE estimate of the covariance matrix is an unreliable estimator with high variance. This over-fitted estimation of the covariance makes the upper-level policy highly biased to a specific region of the parameter space, which often causes premature convergence [7]. Instead, we can estimate only a diagonal covariance matrix with fewer parameters [8], yet, such a solution has a high bias and might result in a slow learning performance as we neglect the correlations between the parameters.…”

Section: Introductionmentioning

confidence: 99%

“…One other solution is using regularization techniques for estimating the covariance matrix. Standard regularization techniques such as covariance shrinkage [9], [7] are based on a convex combination of different estimators, e.g., the high variance estimator of the sample covariance matrix and the high bias estimator of the diagonal covariance matrix. Yet, policy search algorithms have a big advantage when estimating the covariance matrix.…”

Section: Introductionmentioning

confidence: 99%

Regularized covariance estimation for weighted maximum likelihood policy search methods

Abdolmaleki

Lau

Reis

et al. 2015

2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids)

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Abstract-Many episode-based (or direct) policy search algorithms, maintain a multivariate Gaussian distribution as search distribution over the parameter space of some objective function. One class of algorithms, such as episodic REPS, PoWER or PI 2 uses, a weighted maximum likelihood estimate (WMLE) to update the mean and covariance matrix of this distribution in each iteration. However, due to high dimensionality of covariance matrices and limited number of samples, the WMLE is an unreliable estimator. The use of WMLE leads to overfitted covariance estimates, and, hence the variance/entropy of the search distribution decreases too quickly, which may cause premature convergence. In order to alleviate this problem, the estimated covariance matrix can be regularized in different ways, for example by using a convex combination of the diagonal covariance estimate and the sample covariance estimate. In this paper, we propose a new covariance matrix regularization technique for policy search methods that uses the convex combination of the sample covariance matrix and the old covariance matrix used in last iteration. The combination weighting is determined by specifying the desired entropy of the new search distribution. With this mechanism, the entropy of the search distribution can be gradually decreased without damage from the maximum likelihood estimate.

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“…Other existing statistical methods have also been applied to control the amount of covariance/dependency modeling in EDAs. In [93], regularization techniques were adopted into EDAs. The resulting algorithm shows the ability to solve high dimensional problems with a comparable quality of solutions using much smaller populations.…”

Section: Issues Related To Edas and Their Remediesmentioning

confidence: 99%

Data-driven analysis of variables and dependencies in continuous optimization problems and estimation of distribution algorithms

Mishra¹

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Optimization problems occur widely in various domains and are of great practical importance. Better solutions to optimization problems translate into increased production or efficiency, or less waste or error. As a result, the development of optimization algorithms is a large and active area of research. Although there is a large amount of theory and techniques for solving optimization problems, there are also many open issues and questions in understanding the relationship between optimization algorithms and the problems that they are applied to.In any optimization problem, the influence of each solution variable on the objective function, as well as the interactions between variables are very important. For example, if the variables in a problem are independent, then it might be efficiently solved by decomposition. If important dependencies exist between variables, an algorithm that is able to capture these dependencies may be able to exploit them to find good solutions. Alternatively, if a variable has a strong influence on the objective function, then an algorithm may be better off focusing its search on this variable, compared with another variable that has very little influence on the objective function.Estimation of Distribution Algorithms (EDAs) are a class of black-box optimization algorithms that learn and sample from a probabilistic model over the solution variables to carry out the search process. The explicit model in an EDA clearly specifies how the algorithm handles problem variables during the search process. A major focus in EDA research has been the incorporation of dependency modeling using models of varying complexity (e.g. probabilistic graphical models). The intuition behind this work is that if the algorithm model is capable and successful at capturing the structure of the problem, it will produce good performance on that problem. Experimental results have confirmed this intuition, for example EDAs that model dependency information have outperformed EDAs that do not model dependencies on certain problems.While EDAs have shown good performance results, little work has analyzed the dynamics of EDA models in practice. In fact, it is not clear what kind of problem structure EDAs can successfully model, or to what extent it is necessary to successfully model problem structure in order to achieve good performance. To provide insight into these issues, a more detailed analysis of EDAs applied to specific problems is needed.In this thesis, an experimental methodology is proposed to analyze the features of variables in continuous optimization problems and continuous EDAs. The approach is based on sampling points from the problem fitness landscape and/or the history of points visited by an EDA during the search process. These samples are then analyzed in three different ways, to identify key structural variables, variable dependencies and important variables. The techniques are used to analyze a variety of test problems and EDAs optimizing the same problem set. The results confirm that the i...

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Regularized continuous estimation of distribution algorithms

Cited by 29 publications

References 41 publications

Adaptive Learning Rate Elitism Estimation of Distribution Algorithm Combining Chaos Perturbation for Large Scale Optimization

Adaptive Learning Rate Elitism Estimation of Distribution Algorithm Combining Chaos Perturbation for Large Scale Optimization

Regularized covariance estimation for weighted maximum likelihood policy search methods

Data-driven analysis of variables and dependencies in continuous optimization problems and estimation of distribution algorithms

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