Probabilistic Model Building Based GAs in Permutation Domains Using Edge Histograms.

Estimation of distribution algorithm (EDA) is a new class of evolutionary algorithms with a wide range of real-world applications. However, it has been well known that the performance of EDA is not satisfactory enough if its population size is small. But to simply increase its population size may result in slow convergence. To the best knowledge of the authors', very few work has been done on improving the performance of EDA under small population size. This paper illustrates why EDA does not work well under small population size and proposes a novel approach termed as Over-Selection to boost EDA under small population size. Experimental results on several benchmark problems demonstrate that Over-Selection based EDA is often able to achieve a better solution without significantly increasing its time consumption when compared with the original version of EDA.

Estimation of distribution algorithms are a promising method in evolutionary computation. In the estimation of distribution algorithms, instead of using conventional crossover and mutation operations, probabilistic models are used to sample the genetic information in the next population. Although the use of probabilistic models enables EDAs to have several schema simultaneously, it sometimes causes worse performance due to converse schemata. In this paper, estimation of distribution algorithms with niche separation mechanism is proposed. Coexistence schemata are also newly introduced, where schemata at the same loci but converse information. The proposed method splits population into two subpopulations if such coexistence schemata are found. One of subpopulations is used to constitute the next generation while the probabilistic model of another subpopulation is enqueued. The queued probabilistic model is used if the current population is converged. The experimental results on max-sat problems and Ising spin glass problems show the effectiveness of the proposed method.

The compact Genetic Algorithm (cGA) is an Estimation of Distribution Algorithm that generates offspring population according to the estimated probabilistic model of the parent population instead of using traditional recombination and mutation operators. The cGA only needs a small amount of memory; therefore, it may be quite useful in memory-constrained applications. This paper introduces a theoretical framework for studying the cGA from the convergence point of view in which, we model the cGA by a Markov process and approximate its behavior using an Ordinary Differential Equation (ODE). Then, we prove that the corresponding ODE converges to local optima and stays there. Consequently, we conclude that the cGA will converge to the local optima of the function to be optimized.

The portfolio optimization/rebalancing problem is to determine a proportion-weighted combination in a portfolio in order to achieve certain investment targets. For this problem, many researchers have used various evolutionary methods and models such as genetic algorithms and simulated annealing. On the other hand, the portfolio optimization/rebalancing problem can be viewed as a multi-dimensional problem because its solution is a proportion-weighted combination for the given assets. The previous works, however, have not taken into account the multi-dimensional aspect of the problem. In order to approach this problem from the multi-dimensional aspect, we propose a model based on the probabilistic model-building genetic algorithm with narrower width histograms (PMBGA-NWH), and then apply it to optimize the constrained index funds with the given rebalancing cost in this paper. In the numerical experiments, we show that our model has better ability to make optimal index funds than the traditional genetic algorithm (GA).

A byproduct benefit of using probabilistic model-building genetic algorithms is the creation of cheap and accurate surrogate models. Learning classifier systems -- and genetics-based machine learning in general -- can greatly benefit from such surrogates which may replace the costly matching procedure of a rule against large data sets. In this paper we investigate the accuracy of such surrogate fitness functions when coupled with the probabilistic models evolved by the $\chi$-ary extended compact classifier system ($\chi$eCCS). To achieve such a goal, we show the need that the probabilistic models should be able to represent all the accurate basis functions required for creating an accurate surrogate. We also introduce a procedure to transform populations of rules based into dependency structure matrices (DSMs) which allows building accurate models of overlapping building blocks -- a necessary condition to accurately estimate the fitness of the evolved rules.

The Estimation of Distribution Algorithms (EDAs) is a novel class of evolutionary algorithms which is motivated by the idea of building probabilistic graphical model of promising solutions to represent linkage information between variables in chromosome. Through learning of and sampling from probabilistic graphical model, new population is generated and optimization procedure is repeated until the stopping criteria are met. In this paper, the mechanism of the Estimation of Distribution Algorithms is analyzed. Currently existing EDAs are surveyed and categorized according to the probabilistic model they used, then the strengths and weakness and the future perspective of EDAs are concluded.

In the last few years there has been a growing interest in the field of Estimation of Distribution Algorithms (EDAs), where crossover and mutation genetic operators are replaced by probability estimation and sampling techniques. The Bayesian Optimization Algorithm incorporates methods for learning Bayesian networks and uses these to model the promising solutions and generate new ones. The aim of this paper is to propose the parallel version of this algorithm, where the optimization time decreases linearly with the number of processors. During the parallel construction of network, the explicit topological ordering of variables is used to keep the model acyclic. The performance of the optimization process seems to be not affected by this constraint and our version of algorithm was successfully tested for the discrete combinatorial problem represented by graph partitioning as well as for deceptive functions.

Communities are basic units of complex networks and understanding of their structure help us to understand the structure of a network. Communities are groups of nodes that have many links inside and few links outside them. Community detection in a network can be modeled as an optimization problem. We can use some measures such as Modularity and Community Score for evaluating the quality of a partition of nodes. In this paper, we present a new algorithm for detecting communities in networks based on an Estimation of Distribution Algorithm (EDA) with the assumption that the problem variables are independent. EDAs are those evolutionary algorithms that build and sample the probabilistic models of selected solutions instead of using crossover and mutation operators. In this paper, we assess our algorithm by synthetic and real data sets and compare it with other community detection algorithms.

The layout positioning problem of facilities on a straight line is known as Single Row Facility Layout Problem (SRFLP). The objective of SRFLP, categorized as NP-Complete problem, is to arrange the layout such that the sum of distances between all facilities’ pairs can be minimized. Extended Artificial Chromosome Genetic Algorithm (eACGA) is a promising algorithm that has been proposed recently. eACGA extends the probabilistic model in Estimation of Distribution Algorithms (EDAs) and then hybridize it with Genetic Algorithms (GAs). eACGA is proven to produce an excellent solution for scheduling problem. In this paper, we modify the eACGA to solve SRFLP. Computational results on benchmark problems show the effectiveness of eACGA for solving SRFLP. Key Words: single row facility layout, estimation distribution algorithm, genetic algorithm.

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 UMDA <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> , IDEA-G and sur-shr-HEDA.

DE/EDA: A new evolutionary algorithm for global optimization

Model reference adaptive search (MRAS) for solving global optimization problems works with a parameterized probabilistic model on the solution space and generates at each iteration a group of candidate solutions. These candidate solutions are then used to update the parameters associated with the probabilistic model in such a way that the future search will be biased toward the region containing high-quality solutions. The parameter updating procedure in MRAS is guided by a sequence of implicit probabilistic models we call reference models. We provide a particular algorithm instantiation of the MRAS method, where the sequence of reference models can be viewed as the generalized probability distribution models for estimation of distribution algorithms (EDAs) with proportional selection scheme. In addition, we show that the model reference framework can also be used to describe the recently proposed cross-entropy (CE) method for optimization and to study its properties. Hence, this paper can also be seen as a study on the effectiveness of combining CE and EDAs. We prove global convergence of the proposed algorithm in both continuous and combinatorial domains, and we carry out numerical studies to illustrate the performance of the algorithm.

The Estimation of Distribution Algorithms(EDAs) is a new paradigm for Evolutionary Computation. This new class of algorithms generalizes Genetic Algorithms(GAs) by replacing the crossover and mutation operators by learning and sampling the probability distribution of the best individuals of the population at each iteration of the algorithm. In this paper, we review the EDAs for the solution of combinatorial optimization problems and optimization in continuous domains. The paper gives a brief overview of the multiobjective problems(MOP) and estimation of distribution algorithms(EDAs). We introduce a representative algorithm called RMMEDA (Regularity Model Based Multi-objective Estimation of Distribution Algorithm). In order to improve the convergence performance of the algorithm, we improve the traditional RM-MEDA. The improvement we make is using part of the parent population with better performance instead of the entire parent population to establish a more accurate manifold model, and the RM-MEDA based on elitist strategy theory is proposed. Experimental results show that the improved RM-MEDA performs better on the convergence metric and the algorithm runtime than the original one.KeywordsEDARMMEDAElitist Strategy

Estimation of Distribution Algorithms (EDAs) are a set of algorithms that belong to the field of Evolutionary Computation. In EDAs there are neither crossover nor mutation operators. Instead, the new population of individuals is sampled from a probability distribution, which is estimated from a database that contains the selected individuals from the previous generation. Thus, the interrelations between the different variables that represent the individuals may be explicitly expressed through the joint probability distribution associated with the individuals selected at each generation.

A comparative study of hybrid estimation distribution algorithms in solving the facility layout problem