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**11 - 18**of**18**### Combining Search Space Diagnostics and

"... Abstract—Stochastic optimisers such as Evolutionary Algorithms outperform random search due to their ability to exploit gradients in the search landscape, formed by the algorithm’s search operators in combination with the objective function. Research into the suitability of algorithmic approaches to ..."

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Abstract—Stochastic optimisers such as Evolutionary Algorithms outperform random search due to their ability to exploit gradients in the search landscape, formed by the algorithm’s search operators in combination with the objective function. Research into the suitability of algorithmic approaches to problems has been made more tangible by the direct study and characterisation of the underlying fitness landscapes. Authors have devised metrics, such as the autocorrelation length, to help define these landscapes. In this work, we contribute the Predictive Diagnostic Optimisation method, a new local-searchbased algorithm which provides knowledge about the search space while it searches for the global optimum of a problem. It is a contribution to a less researched area which may be named Diagnostic Optimisation. I.

### Network EDAs: An Empirical Study

, 2012

"... Learning a good model structure is important to the efficient solving of problems by estimation of distribution algorithms. In this paper we present the results of a series of experiments, applying a structure learning algorithm for undirected probabilistic graphical models based on statistical depe ..."

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Learning a good model structure is important to the efficient solving of problems by estimation of distribution algorithms. In this paper we present the results of a series of experiments, applying a structure learning algorithm for undirected probabilistic graphical models based on statistical dependency tests to three fitness functions with different selection operators, proportions and pressures. The number of spurious interactions found by the algorithm are measured and reported. Truncation selection, and its complement (selecting only low fitness solutions) prove quite robust, resulting in a similar number of spurious dependencies regardless of selection pressure. In contrast, tournament and fitness proportionate selection are strongly affected by the selection proportion and pressure.

### Modeling with Copulas and Vines in Estimation of Distribution Algorithms

"... The aim of this work is studying the use of copulas and vines in the optimization with Estimation of Distribution Algorithms (EDAs). Two EDAs are built around the multivariate product and normal copulas, and other two are based on pair-copula decom-position of vine models. Empirically we study the e ..."

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The aim of this work is studying the use of copulas and vines in the optimization with Estimation of Distribution Algorithms (EDAs). Two EDAs are built around the multivariate product and normal copulas, and other two are based on pair-copula decom-position of vine models. Empirically we study the effect of both marginal distributions and dependence structure separately, and show that both aspects play a crucial role in the success of the optimization. The results show that the use of copulas and vines opens new opportunities to a more appropriate modeling of search distributions in EDAs. 1

### A Posteriori Pareto Front Diversification Using a Copula-Based Estimation of Distribution Algorithm

"... Distribution Algorithm, to increase the size, achieve high diversity and convergence of optimal solutions for a multiobjective optimization problem. The algorithm exploits the statistical properties of Copulas to produce new solutions from the existing ones through the estimation of their distributi ..."

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Distribution Algorithm, to increase the size, achieve high diversity and convergence of optimal solutions for a multiobjective optimization problem. The algorithm exploits the statistical properties of Copulas to produce new solutions from the existing ones through the estimation of their distribution. CEDA starts by taking initial solutions provided by any MOEA (Multi Objective Evolutionary Algorithm), construct Copulas to estimate their distribution, and uses the constructed Copulas to generate new solutions. This design saves CEDA the need of running an MOEA every time alternative solutions are requested by a Decision Maker when the found solutions are not satisfactory. CEDA was tested on a set of benchmark problems traditionally used by the community, namely UF1, UF2,..., UF10 and CF1, CF2,..., CF10. CEDA used along with SPEA2 and NSGA2 as two examples of MOEA thus resulting in two variants CEDA-SPEA2 and CEDA-NSGA2 and compare them with SPEA2 and NSGA2. The results of The experiments show that, with both variants of CEDA, new solutions can be generated in a significantly smaller without compromising quality compared to those found SPEA2 and NSGA2.

### Combining Search Space Diagnostics and

"... Abstract—Stochastic optimisers such as Evolutionary Algo-rithms outperform random search due to their ability to exploit gradients in the search landscape, formed by the algorithm’s search operators in combination with the objective function. Research into the suitability of algorithmic approaches t ..."

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Abstract—Stochastic optimisers such as Evolutionary Algo-rithms outperform random search due to their ability to exploit gradients in the search landscape, formed by the algorithm’s search operators in combination with the objective function. Research into the suitability of algorithmic approaches to prob-lems has been made more tangible by the direct study and characterisation of the underlying fitness landscapes. Authors have devised metrics, such as the autocorrelation length, to help define these landscapes. In this work, we contribute the Predictive Diagnostic Optimisation method, a new local-search-based algorithm which provides knowledge about the search space while it searches for the global optimum of a problem. It is a contribution to a less researched area which may be named Diagnostic Optimisation. I.

### Distance-based Bias . . . Decomposable Problems

, 2012

"... For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the dependencies between variables that are closer to each other wi ..."

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For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the dependencies between variables that are closer to each other with respect to the metric are expected to be stronger than the dependencies between variables that are further apart. The purpose of this paper is to describe a method that combines such a problem-specific distance metric with information mined from probabilistic models obtained in previous runs of estimation of distribution algorithms with the goal of solving future problem instances of similar type with increased speed, accuracy and reliability. While the focus of the paper is on additively decomposable problems and the hierarchical Bayesian optimization algorithm, it should be straightforward to generalize the approach to other model-directed optimization techniques and other problem classes. Compared to other techniques for learning from experience put forward in the past, the proposed technique is both more practical and more broadly applicable.

### Research Article A Fast Elitism Gaussian Estimation of Distribution Algorithm and Application for PID Optimization

"... which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Estimation of distribution algorithm (EDA) is an intelligent optimization algorithm based on the probability statistics theory. A fast elitism Gaussian estimation of distributi ..."

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which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Estimation of distribution algorithm (EDA) is an intelligent optimization algorithm based on the probability statistics theory. A fast elitism Gaussian estimation of distribution algorithm (FEGEDA) is proposed in this paper. The Gaussian probability model is used tomodel the solution distribution.The parameters of Gaussian come from the statistical information of the best individuals by fast learning rule. A fast learning rule is used to enhance the efficiency of the algorithm, and an elitism strategy is used to maintain the convergent performance.The performances of the algorithm are examined based upon several benchmarks. In the simulations, a one-dimensional benchmark is used to visualize the optimization process and probability model learning process during the evolution, and several two-dimensional and higher dimensional benchmarks are used to testify the performance of FEGEDA.The experimental results indicate the capability of FEGEDA, especially in the higher dimensional problems, and the FEGEDA exhibits a better performance than some other algorithms and EDAs. Finally, FEGEDA is used in PID controller optimization of PMSM and compared with the classical-PID and GA. 1.