A review of estimation of distribution algorithms in bioinformatics

Evolutionary search algorithms have become an essential asset in the algorithmic toolbox for solving high-dimensional optimization problems in across a broad range of bioinformatics problems. Genetic algorithms, the most well-known and representative evolutionary search technique, have been the subject of the major part of such applications. Estimation of distribution algorithms (EDAs) offer a novel evolutionary paradigm that constitutes a natural and attractive alternative to genetic algorithms. They make use of a probabilistic model, learnt from the promising solutions, to guide the search process. In this paper, we set out a basic taxonomy of EDA techniques, underlining the nature and complexity of the probabilistic model of each EDA variant. We review a set of innovative works that make use of EDA techniques to solve challenging bioinformatics problems, emphasizing the EDA paradigm's potential for further research in this domain.

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.

Multi-objective Estimation of Distribution Algorithm Based on Joint Modeling of Objectives and Variables

This paper proposes a new multi-objective estimation of distribution algorithm (EDA) based on joint modeling of objectives and variables. This EDA uses the multi-dimensional Bayesian network as its probabilistic model. In this way it can capture the dependencies between objectives, variables and objectives, as well as the dependencies learnt between variables in other Bayesian network-based EDAs. This model leads to a problem decomposition that helps the proposed algorithm to find better trade-off solutions to the multi-objective problem. In addition to Pareto set approximation, the algorithm is also able to estimate the structure of the multi-objective problem. To apply the algorithm to many-objective problems, the algorithm includes four different ranking methods proposed in the literature for this purpose. The algorithm is applied to the set of walking fish group (WFG) problems, and its optimization performance is compared with an evolutionary algorithm and another multi-objective EDA. The experimental results show that the proposed algorithm performs significantly better on many of the problems and for different objective space dimensions, and achieves comparable results on some compared with the other algorithms.

An Estimation of Distribution Algorithm for Nurse Scheduling

Schedules can be built in a similar way to a human scheduler by using a set of rules that involve domain knowledge. This paper presents an Estimation of Distribution Algorithm (EDA) for the nurse scheduling problem, which involves choosing a suitable scheduling rule from a set for the assignment of each nurse. Unlike previous work that used Genetic Algorithms (GAs) to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. we identify and mix building blocks directly. The EDA is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, a new rule string has been obtained. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems.

An Estimation of Distribution Algorithm for Nurse Scheduling

Schedules can be built in a similar way to a human scheduler by using a set of rules that involve domain knowledge. This paper presents an Estimation of Distribution Algorithm (EDA) for the nurse scheduling problem, which involves choosing a suitable scheduling rule from a set for the assignment of each nurse. Unlike previous work that used Genetic Algorithms (GAs) to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. we identify and mix building blocks directly. The EDA is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, a new rule string has been obtained. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems.

An Estimation of Distribution Algorithm for Nurse Scheduling

Schedules can be built in a similar way to a human scheduler by using a set of rules that involve domain knowledge. This paper presents an Estimation of Distribution Algorithm (EDA) for the nurse scheduling problem, which involves choosing a suitable scheduling rule from a set for the assignment of each nurse. Unlike previous work that used Genetic Algorithms (GAs) to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. we identify and mix building blocks directly. The EDA is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, a new rule string has been obtained. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems.

An Estimation of Distribution Algorithm with Intelligent Local Search for Rule-based Nurse Rostering

This paper proposes a new memetic evolutionary algorithm to achieve explicit learning in rule-based nurse rostering, which involves applying a set of heuristic rules for each nurse's assignment. The main framework of the algorithm is an estimation of distribution algorithm, in which an ant-miner methodology improves the individual solutions produced in each generation. Unlike our previous work (where learning is implicit), the learning in the memetic estimation of distribution algorithm is explicit, i.e. we are able to identify building blocks directly. The overall approach learns by building a probabilistic model, i.e. an estimation of the probability distribution of individual nurse-rule pairs that are used to construct schedules. The local search processor (i.e. the ant-miner) reinforces nurse-rule pairs that receive higher rewards. A challenging real world nurse rostering problem is used as the test problem. Computational results show that the proposed approach outperforms most existing approaches. It is suggested that the learning methodologies suggested in this paper may be applied to other scheduling problems where schedules are built systematically according to specific rules.

An Estimation of Distribution Algorithm with Intelligent Local Search for Rule-based Nurse Rostering

This paper proposes a new memetic evolutionary algorithm to achieve explicit learning in rule-based nurse rostering, which involves applying a set of heuristic rules for each nurse's assignment. The main framework of the algorithm is an estimation of distribution algorithm, in which an ant-miner methodology improves the individual solutions produced in each generation. Unlike our previous work (where learning is implicit), the learning in the memetic estimation of distribution algorithm is explicit, i.e. we are able to identify building blocks directly. The overall approach learns by building a probabilistic model, i.e. an estimation of the probability distribution of individual nurse-rule pairs that are used to construct schedules. The local search processor (i.e. the ant-miner) reinforces nurse-rule pairs that receive higher rewards. A challenging real world nurse rostering problem is used as the test problem. Computational results show that the proposed approach outperforms most existing approaches. It is suggested that the learning methodologies suggested in this paper may be applied to other scheduling problems where schedules are built systematically according to specific rules.

Combination of Evolutionary Algorithms with Experimental Design, Traditional Optimization and Machine Learning

Evolutionary algorithms alone cannot solve optimization problems very efficiently since there are many random (not very rational) decisions in these algorithms. Combination of evolutionary algorithms and other techniques have been proven to be an efficient optimization methodology. In this talk, I will explain the basic ideas of our three algorithms along this line (1): Orthogonal genetic algorithm which treats crossover/mutation as an experimental design problem, (2) Multiobjective evolutionary algorithm based on decomposition (MOEA/D) which uses decomposition techniques from traditional mathematical programming in multiobjective optimization evolutionary algorithm, and (3) Regular model based multiobjective estimation of distribution algorithms (RM-MEDA) which uses the regular property and machine learning methods for improving multiobjective evolutionary algorithms.

Evolutionary computation of forests with Degree- and Role-Constrained Minimum Spanning Trees

Finding the degree-constrained minimum spanning tree (DCMST) of a graph is a widely studied NP-hard problem. One of its most important applications is network design. Here we deal with a new variant of the DCMST problem, which consists of finding not only the degree- but also the role-constrained minimum spanning tree (DRCMST), i.e., we add constraints to restrict the role of the nodes in the tree to root, intermediate or leaf node. Furthermore, we do not limit the number of root nodes to one, thereby, generally, building a forest of DRCMSTs. The modeling of network design problems can benefit from the possibility of generating more than one tree and determining the role of the nodes in the network. We propose a novel permutation-based representation to encode these forests. In this new representation, one permutation simultaneously encodes all the trees to be built. We simulate a wide variety of DRCMST problems which we optimize using eight different evolutionary computation algorithms encoding individuals of the population using the proposed representation. The algorithms we use are: estimation of distribution algorithm, generational genetic algorithm, steady-state genetic algorithm, covariance matrix adaptation evolution strategy, differential evolution, elitist evolution strategy, non-elitist evolution strategy and particle swarm optimization. The best results are for the estimation of distribution algorithms and both types of genetic algorithms, although the genetic algorithms are significantly faster.

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.

Regularized model learning in EDAs for continuous and multi-objective optimization

Probabilistic modeling is the de�ning characteristic of estimation of distribution algorithms (EDAs) which determines their behavior and performance in optimization. Regularization is a well-known statistical technique used for obtaining an improved model by reducing the generalization error of estimation, especially in high-dimensional problems. `1-regularization is a type of this technique with the appealing variable selection property which results in sparse model estimations. In this thesis, we study the use of regularization techniques for model learning in EDAs. Several methods for regularized model estimation in continuous domains based on a Gaussian distribution assumption are presented, and analyzed from di�erent aspects when used for optimization in a high-dimensional setting, where the population size of EDA has a logarithmic scale with respect to the number of variables. The optimization results obtained for a number of continuous problems with an increasing number of variables show that the proposed EDA based on regularized model estimation performs a more robust optimization, and is able to achieve signi�cantly better results for larger dimensions than other Gaussian-based EDAs. We also propose a method for learning a marginally factorized Gaussian Markov random �eld model using regularization techniques and a clustering algorithm. The experimental results show notable optimization performance on continuous additively decomposable problems when using this model estimation method. Our study also covers multi-objective optimization and we propose joint probabilistic modeling of variables and objectives in EDAs based on Bayesian networks, speci�cally models inspired from multi-dimensional Bayesian network classi�ers. It is shown that with this approach to modeling, two new types of relationships are encoded in the estimated models in addition to the variable relationships captured in other EDAs: objectivevariable and objective-objective relationships. An extensive experimental study shows the e�ectiveness of this approach for multi- and many-objective optimization. With the proposed joint variable-objective modeling, in addition to the Pareto set approximation, the algorithm is also able to obtain an estimation of the multi-objective problem structure. Finally, the study of multi-objective optimization based on joint probabilistic modeling is extended to noisy domains, where the noise in objective values is represented by intervals. A new version of the Pareto dominance relation for ordering the solutions in these problems, namely �-degree Pareto dominance, is introduced and its properties are analyzed. We show that the ranking methods based on this dominance relation can result in competitive performance of EDAs with respect to the quality of the approximated Pareto sets. This dominance relation is then used together with a method for joint probabilistic modeling based on `1-regularization for multi-objective feature subset selection in classi�cation, where six di�erent measures of accuracy are considered as objectives with interval values. The individual assessment of the proposed joint probabilistic modeling and solution ranking methods on datasets with small-medium dimensionality, when using two di�erent Bayesian classi�ers, shows that comparable or better Pareto sets of feature subsets are approximated in comparison to standard methods.

Population-based continuous optimization, probabilistic modelling and mean shift

Evolutionary algorithms perform optimization using a population of sample solution points. An interesting development has been to view population-based optimization as the process of evolving an explicit, probabilistic model of the search space. This paper investigates a formal basis for continuous, population-based optimization in terms of a stochastic gradient descent on the Kullback-Leibler divergence between the model probability density and the objective function, represented as an unknown density of assumed form. This leads to an update rule that is related and compared with previous theoretical work, a continuous version of the population-based incremental learning algorithm, and the generalized mean shift clustering framework. Experimental results are presented that demonstrate the dynamics of the new algorithm on a set of simple test problems.