Estimation of Distribution Algorithms
Encyclopedia
Estimation of Distribution Algorithms (EDA), sometimes called Probabilistic Model-Building Genetic Algorithms (PMBGA), are an outgrowth of genetic algorithms. In a genetic algorithm, a population of candidate solutions to a problem is maintained as part of the search for an optimum solution. This population is typically represented explicitly as an array of objects. Depending on the specifics of the GA, the objects might be bit strings, vectors of real numbers, LISP
style S expressions or some custom representation. In an EDA, this explicit representation of the population is replaced with a probability distribution over the choices available at each position in the vector that represents a population member.
For example, if the population is represented by bit strings of length 4, the EDA for the populations would be a single vector of four probabilities (p1, p2, p3, p4) where each p is the probability of that position being a 1. Using this probability vector it is possible to create an arbitrary number of candidate solutions.
In evolutionary computation
new candidate solutions are often generated by combining and modifying existing solutions in a stochastic way. The underlying probability distribution of new solutions over the space of possible solutions is usually not explicitly specified. In EDAs a population may be approximated with a probability distribution and new candidate solutions can be obtained by sampling this distribution. This may have several advantages, including avoiding premature convergence
and being a more compact representation.
Better-known EDAs include
The model may be found to fit an existing population or take on the role of the population entirely. Once the model is obtained, it can be sampled to produce more candidate solutions which are then used to adapt or regenerate the model. EDAs are typically classified according to the level of variable interaction that their probabilistic model includes - they can be classed as univariate
(no interactions), bivariate (interactions between pairs of variables) or multivariate (interactions between more than two variables) (Pelikan, 1999).
Lisp
A lisp is a speech impediment, historically also known as sigmatism. Stereotypically, people with a lisp are unable to pronounce sibilants , and replace them with interdentals , though there are actually several kinds of lisp...
style S expressions or some custom representation. In an EDA, this explicit representation of the population is replaced with a probability distribution over the choices available at each position in the vector that represents a population member.
For example, if the population is represented by bit strings of length 4, the EDA for the populations would be a single vector of four probabilities (p1, p2, p3, p4) where each p is the probability of that position being a 1. Using this probability vector it is possible to create an arbitrary number of candidate solutions.
In evolutionary computation
Evolutionary computation
In computer science, evolutionary computation is a subfield of artificial intelligence that involves combinatorial optimization problems....
new candidate solutions are often generated by combining and modifying existing solutions in a stochastic way. The underlying probability distribution of new solutions over the space of possible solutions is usually not explicitly specified. In EDAs a population may be approximated with a probability distribution and new candidate solutions can be obtained by sampling this distribution. This may have several advantages, including avoiding premature convergence
Premature convergence
In genetic algorithms, the term of premature convergence means that a population for an optimization problem converged too early, resulting in being suboptimal. In this context, the parental solutions, through the aid of genetic operators, are not able to generate offsprings that are superior to...
and being a more compact representation.
Better-known EDAs include
- Population-based incremental learningPopulation-based incremental learningIn computer science and machine learning, population-based incremental learning is an optimization algorithm, and an estimation of distribution algorithm. This is a type of genetic algorithm where the genotype of an entire population is evolved rather than individual members. The algorithm is...
(PBIL) - Hill Climbing with Learning (HCwL)
- Compact Genetic Algorithm (cGA)
- Univariate Marginal Distribution Algorithm (UMDA)
- Estimation of Multivariate Normal Algorithm (EMNA)
- Mutual Information Maxminization for Input Clustering (MIMIC)
- Bivariate Marginal Distribution Algorithm (BMDA)
- Extended Compact Genetic Algorithm (ECGA)
- Bayesian Optimization Algorithm (BOA)
- Estimation of Bayesian Networks Algorithm (EBNA)
- Stochastic hill climbing with learning by vectors of normal distributions (SHCLVND)
- Real-coded PBIL
- Probabilistic Incremental Program Evolution (PIPE)
- Estimation of Gaussian Networks Algorithm (EGNA)
The model may be found to fit an existing population or take on the role of the population entirely. Once the model is obtained, it can be sampled to produce more candidate solutions which are then used to adapt or regenerate the model. EDAs are typically classified according to the level of variable interaction that their probabilistic model includes - they can be classed as univariate
Univariate
In mathematics, univariate refers to an expression, equation, function or polynomial of only one variable. Objects of any of these types but involving more than one variable may be called multivariate...
(no interactions), bivariate (interactions between pairs of variables) or multivariate (interactions between more than two variables) (Pelikan, 1999).