A review on probabilistic graphical models in evolutionary computation

Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Evolutionary algorithms is one such discipline that has employed probabilistic graphical models to improve the search for optimal solutions in complex problems. This paper shows how probabilistic graphical models have been used in evolutionary algorithms to improve their performance in solving complex problems. Specifically, we give a survey of probabilistic model building-based evolutionary algorithms, called estimation of distribution algorithms, and compare different methods for probabilistic modeling in these algorithms

Multimodal estimation of distribution algorithms

Taking the advantage of estimation of distribution algorithms (EDAs) in preserving high diversity, this paper proposes a multimodal EDA. Integrated with clustering strategies for crowding and speciation, two versions of this algorithm are developed, which operate at the niche level. Then these two algorithms are equipped with three distinctive techniques: 1) a dynamic cluster sizing strategy; 2) an alternative utilization of Gaussian and Cauchy distributions to generate offspring; and 3) an adaptive local search. The dynamic cluster sizing affords a potential balance between exploration and exploitation and reduces the sensitivity to the cluster size in the niching methods. Taking advantages of Gaussian and Cauchy distributions, we generate the offspring at the niche level through alternatively using these two distributions. Such utilization can also potentially offer a balance between exploration and exploitation. Further, solution accuracy is enhanced through a new local search scheme probabilistically conducted around seeds of niches with probabilities determined self-adaptively according to fitness values of these seeds. Extensive experiments conducted on 20 benchmark multimodal problems confirm that both algorithms can achieve competitive performance compared with several state-of-the-art multimodal algorithms, which is supported by nonparametric tests. Especially, the proposed algorithms are very promising for complex problems with many local optima

Distributed Estimation of Distribution Algorithms for continuous optimization: how does the exchanged information influence their behavior?

One of the most promising areas in which probabilistic graphical models have shown an incipient activity is the field of heuristic optimization and, in particular, in Estimation of Distribution Algorithms. Due to their inherent parallelism, different research lines have been studied trying to improve Estimation of Distribution Algorithms from the point of view of execution time and/or accuracy. Among these proposals, we focus on the so-called distributed or island-based models. This approach defines several islands (algorithms instances) running independently and exchanging information with a given frequency. The information sent by the islands can be either a set of individuals or a probabilistic model. This paper presents a comparative study for a distributed univariate Estimation of Distribution Algorithm and a multivariate version, paying special attention to the comparison of two alternative methods for exchanging information, over a wide set of parameters and problems ? the standard benchmark developed for the IEEE Workshop on Evolutionary Algorithms and other Metaheuristics for Continuous Optimization Problems of the ISDA 2009 Conference. Several analyses from different points of view have been conducted to analyze both the influence of the parameters and the relationships between them including a characterization of the configurations according to their behavior on the proposed benchmark

Migrating Individuals and Probabilistic Models on DEDAS: a Comparison on Continuous Functions

One of the most promising areas in which probabilistic graphical models have shown an incipient activity is the field of heuristic optimization and, in particular, in the Estimation of Distribution Algorithms (EDAs). EDAs constitute a well-known family of Evolutionary Computation techniques, similar to Genetic Algorithms. Due to their inherent parallelism, different research lines have been studied trying to improve EDAs from the point of view of execution time and/or accuracy. Among these proposals, we focus on the so-called island-based models. This approach defines several islands (EDA instances) running independently and exchanging information with a given frequency. The information sent by the islands can be a set of individuals or a probabilistic model. This paper presents a comparative study of both information exchanging techniques for a univariate EDA (U M DAg) over a wide set of parameters and problems –the standard benchmark developed for the IEEE Workshop on Evolutionary Algorithms and other Metaheuristics for Continuous Optimization Problems of the ISDA 2009 Conference. The study concludes that the configurations based on migrating individuals obtain better result

On the evaluation of information exchange strategies in dEDAs

One of the most promising areas in which probabilistic graphical models have shown an incipient activity is the field of heuristic optimization and, in particular, in the Estimation of Distribution Algorithms (EDAs). EDAs constitute a well-known family of Evolutionary Computation techniques, similar to Genetic Algorithms. Due to their inherent parallelism, different research lines have tried to improve EDAs from the point of view of execution time and/or accuracy. Among these proposals, we focus on the so-called island-based models. This approach defines several islands (EDA instances) running independently and exchanging information with a given frequency. The information sent by the islands can be a set of individuals or a probabilistic model. This paper presents a comparative study of both information exchanging techniques for a univariate EDA (UMDAg) over a wide set of parameters and problems –the standard benchmark developed for the IEEE Workshop on Evolutionary Algorithms and other Metaheuristics for Continuous Optimization Problems of the ISDA 2009 Conference

Adaptive algorithms for history matching and uncertainty quantification

Numerical reservoir simulation models are the basis for many decisions in regard to predicting, optimising, and improving production performance of oil and gas reservoirs. History matching is required to calibrate models to the dynamic behaviour of the reservoir, due to the existence of uncertainty in model parameters. Finally a set of history matched models are used for reservoir performance prediction and economic and risk assessment of different development scenarios. Various algorithms are employed to search and sample parameter space in history matching and uncertainty quantification problems. The algorithm choice and implementation, as done through a number of control parameters, have a significant impact on effectiveness and efficiency of the algorithm and thus, the quality of results and the speed of the process. This thesis is concerned with investigation, development, and implementation of improved and adaptive algorithms for reservoir history matching and uncertainty quantification problems. A set of evolutionary algorithms are considered and applied to history matching. The shared characteristic of applied algorithms is adaptation by balancing exploration and exploitation of the search space, which can lead to improved convergence and diversity. This includes the use of estimation of distribution algorithms, which implicitly adapt their search mechanism to the characteristics of the problem. Hybridising them with genetic algorithms, multiobjective sorting algorithms, and real-coded, multi-model and multivariate Gaussian-based models can help these algorithms to adapt even more and improve their performance. Finally diversity measures are used to develop an explicit, adaptive algorithm and control the algorithm’s performance, based on the structure of the problem. Uncertainty quantification in a Bayesian framework can be carried out by resampling of the search space using Markov chain Monte-Carlo sampling algorithms. Common critiques of these are low efficiency and their need for control parameter tuning. A Metropolis-Hastings sampling algorithm with an adaptive multivariate Gaussian proposal distribution and a K-nearest neighbour approximation has been developed and applied

On the application of estimation of distribution algorithms to multi-marker tagging SNP selection

This paper presents an algorithm for the automatic selection of a minimal subset of tagging single nucleotide polymorphisms (SNPs) using an estimation of distribution algorithm (EDA). The EDA stochastically searches the constrained space of possible feasible solutions and takes advantage of the underlying topological structure defined by the SNP correlations to model the problem interactions. The algorithm is evaluated across the HapMap reference panel data sets. The introduced algorithm is effective for the identification of minimal multi-marker SNP sets, which considerably reduce the dimension of the tagging SNP set in comparison with single-marker sets. New reduced tagging sets are obtained for all the HapMap SNP regions considered. We also show that the information extracted from the interaction graph representing the correlations between the SNPs can help to improve the efficiency of the optimization algorithm. keywords: SNPs, tagging SNP selection, multi-marker selection, estimation of distribution algorithms, HapMap

UMDA/S: An Effective Iterative Compilation Algorithm for Parameter Search

The search process is critical for iterative compilation because the large size of the search space and the cost of evaluating the candidate implementations make it infeasible to find the true optimal value of the optimization parameter by brute force. Considering it as a nonlinear global optimization problem, this paper introduces a new hybrid algorithm -- UMDA/S: Univariate Marginal Distribution Algorithm with Nelder-Mead Simplex Search, which utilizes the optimization space structure and parameter dependency to find the near optimal parameter. Elitist preservation, weighted estimation and mutation are proposed to improve the performance of UMDA/S. Experimental results show the ability of UMDA/S to locate more excellent parameters, as compared to existing static methods and search algorithms

Improving the efficiency of Bayesian Network Based EDAs and their application in Bioinformatics

Estimation of distribution algorithms (EDAs) is a relatively new trend of stochastic optimizers which have received a lot of attention during last decade. In each generation, EDAs build probabilistic models of promising solutions of an optimization problem to guide the search process. New sets of solutions are obtained by sampling the corresponding probability distributions. Using this approach, EDAs are able to provide the user a set of models that reveals the dependencies between variables of the optimization problems while solving them. In order to solve a complex problem, it is necessary to use a probabilistic model which is able to capture the dependencies. Bayesian networks are usually used for modeling multiple dependencies between variables. Learning Bayesian networks, especially for large problems with high degree of dependencies among their variables is highly computationally expensive which makes it the bottleneck of EDAs. Therefore introducing efficient Bayesian learning algorithms in EDAs seems necessary in order to use them for large problems. In this dissertation, after comparing several Bayesian network learning algorithms, we propose an algorithm, called CMSS-BOA, which uses a recently introduced heuristic called max-min parent children (MMPC) in order to constrain the model search space. This algorithm does not consider a fixed and small upper bound on the order of interaction between variables and is able solve problems with large numbers of variables efficiently. We compare the efficiency of CMSS-BOA with the standard Bayesian network based EDA for solving several benchmark problems and finally we use it to build a predictor for predicting the glycation sites in mammalian proteins