. The direct application of statistics to stochastic optimization based on iterated density estimation has become more important and present in evolutionary computation over the last few years. The estimation of densities over selected samples and the sampling from the resulting distributions, is a combination of the recombination and mutation steps used in evolutionary algorithms. We introduce the framework named IDEA to formalize this notion. By combining continuous probability theory with techniques from existing algorithms, this framework allows us to dene new continuous evolutionary optimization algorithms. 1 Introduction Algorithms in evolutionary optimization guide their search through statistics based on a vector of samples, often called a population. By using this stochastic information, non{deterministic induction is performed in order to attempt to use the structure of the search space and thereby aid the search for the optimal solution. In order to perform induct...

This paper shows how the Gaussian network paradigm can be used to solve optimization problems in continuous domains. Some methods of structure learning from data and simulation of Gaussian networks are applied in the Estimation of Distribution Algorithm (EDA) as well as new methods based on information theory are proposed. Experimental results are also presented. 1 Estimation of Distribution Algorithms approaches in continuous domains Figure 1 shows a schematic of the EDA approach for continuous domains. We will use x = (x 1 ; : : : ; xn ) to denote individuals, and D l to denote the population of N individuals in the l-th generation. Similarly, D Se l will represent the population of the selected Se individuals from D l . In the EDA [9] our interest will be to estimate f(x j D Se ), that is, the joint probability density function over one individual x being among the selected individuals. We denote as f l (x) = f l (x j D Se l 1 ) the joint density of the l-th genera...

This paper shows how the Bayesian network paradigm can be used in order to solve combinatorial optimization problems. To do it some methods of structure learning from data and simulation of Bayesian networks are inserted inside Estimation of Distribution Algorithms (EDA). EDA are a new tool for evolutionary computation in which populations of individuals are created by estimation and simulation of the joint probability distribution of the selected individuals. We propose new approaches to EDA for combinatorial optimization based on the theory of probabilistic graphical models. Experimental results are also presented.

In this paper, we propose an evolutionary algorithm using marginal histograms to model the parent population in a continuous domain. We propose two types of marginal histogram models: the fixed-width histogram (FWH) and the fixed-height histogram (FHH). The results showed that both models worked fairly well on test functions with no or weak interactions among variables. Especially, FHH could find the global optimum with very high accuracy effectively and showed good scale-up with the problem size.

This paper presents a theoretical study of the behaviour of the Univariate Marginal Distribution Algorithm for continuous domains (UMDAc ) in dimension n. To this end, the algorithm with tournament selection is modelled mathematically, assuming an infinite number of tournaments. The mathematical model is then used to study the algorithm's behaviour in the minimization of linear functions L(x) = a0 + i=1 a i x i and quadratic function Q(x) = i , with x = (x1 , . . . , xn ) and a i IR, i = 0, 1, . . . , n. Linear functions are used to model the algorithm when far from the optimum, while quadratic function is used to analyze the algorithm when near the optimum. The analysis shows that the algorithm performs poorly in the linear function L1 (x) = i=1 x i . In the case of quadratic function Q(x) the algorithm 's behaviour was analyzed for certain particular dimensions. After taking into account some simplifications we can conclude that when the algorithm starts near the optimum, UMDAc is able to reach it. Moreover the speed of convergence to the optimum decreases as the dimension increases.

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Evolutionary optimization based on proba- bilistic models has so far been limited to the use of factorizations in the case of continuous representations. Furthermore, a maximum complexity parameter n was required previously to construct factorizations to prevent unnecessary complexity to be introduced in the factorization. In this paper, we advance these techniques by using clustering and the EM algorithm to allow for mixture distributions.

The development of Estimation of Distribution Algorithms (EDAs) has largely been driven by using more and more complex statistical models to approximate the structure of search space. However, there are still problems that are difficult for EDAs even with models capable of capturing high order dependences. In this paper, we show that diversity maintenance plays an important role in the performance of EDAs. A continuous EDA based on the Cholesky decomposition is tested on some well-known difficult benchmark problems to demonstrate how different diversity maintenance approaches could be applied to substantially improve its performance.

Abstract. Recently, there has been a growing interest in developing evolutionary algorithms based on probabilistic modeling. In this scheme, the offspring population is generated according to the estimated probability density model of the parent instead of using recombination and mutation operators. In this paper, we have proposed probabilistic model-building genetic algorithms (PMBGAs) in permutation representation domain using edge histogram based sampling algorithms (EHBSAs). Two types of sampling algorithms, without template (EHBSA/WO) and with template (EHBSA/WT), are presented. The results were tested in the TSP and showed EHBSA/WT worked fairly well with a small population size in the test problems used. It also worked better than well-known traditional two-parent recombination operators. 1

We propose an algorithm for multi-objective optimization using a mixture-based iterated density estimation evolutionary algorithm (M IDE A). The M IDE A algorithm is a probabilistic model building evolutionary algorithm that constructs at each generation a mixture of factorized probability distributions.