Estimation of distribution algorithm

Eda mono-variant gauss iterations

Estimation of Distribution Algorithms (EDAs), sometimes known as Probabilistic Model-Building Genetic Algorithms (PMBGAs), are a class of evolutionary algorithms that guide the search for optimal solutions by building and sampling explicit probability distributions. EDAs represent a significant shift from traditional genetic algorithms (GAs) by replacing the crossover and mutation operators with the construction of a probability model of the selected individuals.

Overview

EDAs start with an initial population of candidate solutions to an optimization problem and iteratively update this population by generating new candidate solutions. The key difference from traditional GAs is in how these new candidates are generated. Instead of applying crossover and mutation to selected individuals, EDAs estimate the distribution of the best individuals and sample this distribution to generate new candidates. This approach allows EDAs to capture and exploit the interactions between variables more effectively.

Procedure

The general procedure of an EDA is as follows:

1. Initialization: Generate an initial population of solutions randomly.
2. Evaluation: Assess the quality of each solution using the objective function of the optimization problem.
3. Selection: Select a subset of the best solutions according to their fitness.
4. Model Building: Estimate the probability distribution of the selected solutions. This step involves identifying dependencies between variables and modeling these dependencies.
5. Sampling: Generate new solutions by sampling from the estimated distribution.
6. Replacement: Replace some or all of the old population with the new solutions.
7. Termination: Repeat steps 2-6 until a stopping criterion is met, such as a maximum number of generations or a satisfactory solution quality.

Types of EDAs

EDAs can be categorized based on the complexity of the probability models they use. Some common types include:

• Univariate EDAs, such as the Univariate Marginal Distribution Algorithm (UMDA), which assume that all variables are independent and model the distribution of each variable separately.
• Bivariate EDAs, such as the Mutual Information Maximization for Input Clustering (MIMIC), which capture pairwise interactions between variables.
• Multivariate EDAs, such as the Bayesian Optimization Algorithm (BOA), which model complex interactions between multiple variables using Bayesian networks.

Applications

EDAs have been successfully applied to a wide range of optimization problems, including combinatorial optimization, numerical optimization, and machine learning. Their ability to model complex variable interactions makes them particularly useful for problems where traditional GAs struggle.

Advantages and Disadvantages

Advantages:

• EDAs can efficiently solve problems with complex interactions between variables.
• They provide a more direct way of exploiting historical information to guide the search process.

Disadvantages:

• The model-building step can be computationally expensive, especially for multivariate EDAs.
• EDAs may require more parameters to be set compared to traditional GAs, such as the structure of the probability model.

Conclusion

Estimation of Distribution Algorithms represent a powerful and flexible approach to solving optimization problems. By building and sampling from probability models, they offer a novel way of exploring the search space that can be more effective than traditional genetic algorithms for certain types of problems.

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