On the Taxonomy of Optimization Problems Under Estimation of Distribution Algorithms

@article{Echegoyen2013OnTT,
  title={On the Taxonomy of Optimization Problems Under Estimation of Distribution Algorithms},
  author={Carlos Echegoyen and Alexander Mendiburu and Roberto Santana and Jos{\'e} Antonio Lozano},
  journal={Evolutionary Computation},
  year={2013},
  volume={21},
  pages={471-495}
}
Understanding the relationship between a search algorithm and the space of problems is a fundamental issue in the optimization field. In this paper, we lay the foundations to elaborate taxonomies of problems under estimation of distribution algorithms (EDAs). By using an infinite population model and assuming that the selection operator is based on the rank of the solutions, we group optimization problems according to the behavior of the EDA. Throughout the definition of an equivalence relation… 

Comprehensive characterization of the behaviors of estimation of distribution algorithms

Structural coherence of problem and algorithm: An analysis for EDAs on all 2-bit and 3-bit problems

TLDR
This work performs an exhaustive analysis of all 2 and 3 bit problems, grouped into classes based on mononotic invariance, and shows that each class has a minimal Walsh structure that can be used to solve the problem.

Extending distance-based ranking models in estimation of distribution algorithms

TLDR
This paper extends the use of distance-based ranking models in the framework of EDAs by introducing new distance metrics such as Cayley and Ulam, and shows that Mallows-Ulam EDA is the most stable algorithm among the studied proposals.

The role of Walsh structure and ordinal linkage in the optimisation of pseudo-Boolean functions under monotonicity invariance

TLDR
Insight is developed into the relationship between function structure and problem difficulty for optimisation, which may be used to direct the development of novel algorithms.

Customized Selection in Estimation of Distribution Algorithms

TLDR
This paper proposes to use different selection probabilities to learn the structural and parametric components of the probabilistic graphical models.

On the model updating operators in univariate estimation of distribution algorithms

TLDR
The role of the selection operation—that stochastically discriminate between individuals based on their merit—on the updating of the probability model in univariate estimation of distribution algorithms is investigated and a family of operators that generalize current model updating mechanisms is proposed.

Are we generating instances uniformly at random?

TLDR
In this paper, some aspects related to the random generation of artificial instances are studied, and the assumption that states that sampling uniformly at random in the space of parameters is equivalent to sampling uniformlyat random inThe space of functions is elaborated.

Gray-box optimization and factorized distribution algorithms: where two worlds collide

TLDR
The general question of using problem structure in EAs is analyzed focusing on confronting work done in gray-box optimization with related research accomplished in FDAs, and it is claimed that these two characterizations collide and compete at the time of providing a coherent framework to investigate this type of algorithms.

The Minimization of Public Facilities With Enhanced Genetic Algorithms Using War Elimination

TLDR
An enhanced version of the genetic algorithm based on war elimination and migration operations is presented, which overcomes the well-known shortcoming of GAs when the population becomes gradually more and more similar, which results in a diversity decrease which leads to a sub-optimal local minimum.

References

SHOWING 1-10 OF 41 REFERENCES

Drift and Scaling in Estimation of Distribution Algorithms

TLDR
This paper considers a phenomenon in Estimation of Distribution Algorithms (EDA) analogous to drift in population genetic dynamics, where any probability model which can generate only a single set of values with probability 1 can be an attractive fixed point of the algorithm.

On the limits of effectiveness in estimation of distribution algorithms

TLDR
This paper experimentally tests three different EDA implementations on a sequence of additively decomposable functions (ADFs) with an increasing number of interactions among binary variables and shows that the ability of EDAs to solve problems could be lost immediately when the degree of variable interaction is larger than a threshold.

Analysis of Computational Time of Simple Estimation of Distribution Algorithms

TLDR
This paper studies the computational time complexity of a simple EDA, i.e., the univariate marginal distribution algorithm (UMDA), and proves theoretically that the UMDA with margins can solve the BVLeadingOnes problem efficiently.

Toward Understanding EDAs Based on Bayesian Networks Through a Quantitative Analysis

TLDR
A methodology of analysis which provides new information about the behavior of EDAs by quantitatively analyzing the probabilistic models learned during the search, and allows us to discover common patterns of behavior in EDAs and propose new ideas in the development of this type of algorithms.

On stability of fixed points of limit models of univariate marginal distribution algorithm and factorized distribution algorithm

  • Qingfu Zhang
  • Mathematics
    IEEE Transactions on Evolutionary Computation
  • 2004
TLDR
It is shown that the limit model of UMDA can be trapped at any local optimal solution for some initial probability models, and it is suggested that using higher order statistics could improve the chance of finding the global optimal solution.

Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation

TLDR
This book presents an introduction to Evolutionary Algorithms, a meta-language for programming with real-time implications, and some examples of how different types of algorithms can be tuned for different levels of integration.

A comparison of predictive measures of problem difficulty in evolutionary algorithms

TLDR
This paper generalizes the reference classes of fitness distance correlation and epistasis variance, and constructs a new predictive measure that is insensitive to nonlinear fitness scaling, and investigates the relations between the reference Classes of the measures and a number of intuitively easy classes.

Ranking-Based Black-Box Complexity

TLDR
A ranking-based black-box algorithm is presented that has a runtime of Θ(n/logn), which shows that the OneMax problem does not become harder with the additional ranking- basedness restriction.

A review of estimation of distribution algorithms in bioinformatics

TLDR
A basic taxonomy of EDA techniques is set out, underlining the nature and complexity of the probabilistic model of each EDA variant, and emphasizing the EDA paradigm's potential for further research in this domain.

Schemata, Distributions and Graphical Models in Evolutionary Optimization

TLDR
For the test functions considered, the performance of FDA—in number of generations till convergence—is similar to that of a genetic algorithm for the OneMax function.