Shude Zhou

Histogram-Based Estimation of Distribution Algorithm: A Competent Method for Continuous Optimization

Designing efficient estimation of distribution algorithms for optimizing complex continuous problems is still a challenging task. This paper utilizes histogram probabilistic model to describe the distribution of population and to generate promising solutions. The advantage of histogram model, its intrinsic multimodality, makes it proper to describe the solution distribution of complex and multimodal continuous problems. To make histogram model more efficiently explore and exploit the search space, several strategies are brought into the algorithms: the surrounding effect reduces the population size in estimating the model with a certain number of the bins and the shrinking strategy guarantees the accuracy of optimal solutions. Furthermore, this paper shows that histogram-based EDA (Estimation of distribution algorithm) can give comparable or even much better performance than those predominant EDAs based on Gaussian models.

Optimizing continuous problems using estimation of distribution algorithm based on histogram model

In the field of estimation of distribution algorithms, choosing probabilistic model for optimizing continuous problems is still a challenging task. This paper proposes an improved estimation of distribution algorithm (HEDA) based on histogram probabilistic model. By utilizing both historical and current population information, a novel learning method – accumulation strategy – is introduced to update the histogram model. In the sampling phase, mutation strategy is used to increase the diversity of population. In solving some well-known hard continuous problems, experimental results support that HEDA behaves much better than the conventional histogram-based implementation both in convergence speed and scalability. Compared with UMDA-Gaussian, SGA and CMA-ES, the proposed algorithms exhibit excellent performance in the test functions.

Reducing computational complexity of estimating multivariate histogram-based probabilistic model

In continuous domain, how to efficiently learn the complex probabilistic graphical model is a bottleneck problem for estimation of distribution algorithms (EDAs). The predominant researches focus on Gaussian probabilistic model instead of histogram distribution model because of its comparative superiority in the computational complexity. In this paper, however, we find that using the histogram model does not necessarily bring into exponential computational complexity. Based on the fact many bins are zero-height, we propose a novel method that can learn the multivariate- dependency histogram based probabilistic graphical model with acceptable polynomial computational complexity. Several strategies previously used in the HEDA are combined into the new algorithm to improve the convergence and diversity. Experiments showed the superior performance of the new algorithm on several continuous problems compared with UMDAc IDEA-G and sur-shr-HEDA.

Detecting the epistatic structure of generalized embedded landscape

Working under the premise that most optimizable functions are of bounded epistasis, this paper addresses the problem of discovering the linkage structure of a black-box function with a domain of arbitrary-cardinality under the assumption of bounded epistasis. To model functions of bounded epistasis, we develop a generalization of the mathematical model of “embedded landscapes” over domains of cardinality M. We then generalize the Walsh transform as a discrete Fourier transform, and develop algorithms for linkage learning of epistatically bounded GELs. We propose Generalized Embedding Theorem that models the relationship between the underlying decomposable structure of GEL and its Fourier coefficients. We give a deterministic algorithm to exactly calculate the Fourier coefficients of GEL with bounded epistasis. Complexity analysis shows that the epistatic structure of epistatically bounded GEL can be obtained after a polynomial number of function evaluations. Finally, an example experiment of the algorithm is presented.

Marginal probability distribution estimation in characteristic space of covariance-matrix

Marginal probability distribution has been widely used as the probabilistic model in EDAs because of its simplicity and efficiency. However, the obvious shortcoming of the kind of EDAs lies in its incapability of taking the correlation between variables into account. This paper tries to solve the problem from the point view of space transformation. As we know, it seems a default rule that the probabilistic model is usually constructed directly from the selected samples in the space defined by the problem. In the algorithm CM-MEDA, instead, we first transform the sampled data from the initial coordinate space into the characteristic space of covariance-matrix and then the marginal probabilistic model is constructed in the new space. We find that the marginal probabilistic model in the new space can capture the variable linkages in the initial space quite well. The relationship of CM-MEDA with Covariance-Matrix estimation and principal component analysis is also analyzed in this paper. We implement CM-MEDA in continuous domain based on both Gaussian and histogram models. The experimental results verify the effectiveness of our idea.

Optimal motion generation of flexible macro-micro manipulator systems using estimation of distribution algorithm

In this paper, a new approach for motion generation and optimization of the flexible macro-micro manipulator system is proposed based on Estimation of Distribution Algorithm (EDA). The macro-micro manipulator system is a redundant system, of which inverse kinematics remains challenging, with no generic solution to date. Here, the manipulator system configurations, or the optimal joint motions, are generated using the EDA algorithm base on Gaussian probability model. Compared with simple genetic algorithms (SGA), this approach uses fewer parameters and the time for motion optimization is remarkably reduced. The proposed approach shows excellent performance on motion generation and optimization of a flexible macro-micro manipulator system, as demonstrated by the simulation results.

A Bayesian view on the polynomial distribution model in estimation of distribution algorithms

Estimation of distribution algorithms(EDA) are a class of recently-developed evolutionary algorithms in which the probabilistic model are used to explicitly characterize the distribution of the population and to generate new individuals. The polynomial distribution is applied by discrete EDAs and continuous EDAs based on discretization of the domain such as histogram-based EDA. We can unify those kinds of EDA from their distribution and call them PolyEDA. In this paper, we theoretically analyze PolyEDA from a Bayesian analysis view. Our analysis is based on the assumption that the prior distribution of the parameters satisfies a Dirichlet distribution, because under this assumption the formulation can be analytically solved. Furthermore, we notice that the prior distribution is always overlooked by previous algorithms, so we follow this way and propose some strategies to improve the PolyEDA. The experimental results show that these new strategies can help the polynomial model based estimation of distribution algorithms achieve better convergence and diversity.

Generalized embedded landscape and its decomposed representation

In this paper, embedded landscapes are extended to a non-binary discrete domain. Generalized embedded landscapes (GEL) are a class of additive decomposable problems where the representation can be expressed as a simple sum of subfunctions over subsets of the representation domain. The paper proposes a Generalized Embedding Theorem that reveals the close relationship between the underlying structure and the Walsh coefficients. Theoretical inductions show that the Walsh coefficients of any GEL with bounded difficulty can be calculated with a polynomial number of function evaluations. A deterministic algorithm is proposed to construct the decomposed representation of GEL. It offers an efficient way to detect the decomposable structure of the search space.