Globally Multimodal Problem Optimization Via an Estimation of Distribution Algorithm Based on Unsupervised Learning of Bayesian Networks

2005 ◽  
Vol 13 (1) ◽  
pp. 43-66 ◽  
Author(s):  
J. M. Peña ◽  
J. A. Lozano ◽  
P. Larrañaga
Keyword(s):  
Bayesian Networks ◽  
Unsupervised Learning ◽  
Genetic Drift ◽  
Optimization Problems ◽  
Estimation Of Distribution Algorithm ◽  
Estimation Of Distribution Algorithms ◽  
Estimation Of Distribution ◽  
Global Optima ◽  
Effectiveness And Efficiency ◽  
Distribution Algorithms

Many optimization problems are what can be called globally multimodal, i.e., they present several global optima. Unfortunately, this is a major source of difficulties for most estimation of distribution algorithms, making their effectiveness and efficiency degrade, due to genetic drift. With the aim of overcoming these drawbacks for discrete globally multimodal problem optimization, this paper introduces and evaluates a new estimation of distribution algorithm based on unsupervised learning of Bayesian networks. We report the satisfactory results of our experiments with symmetrical binary optimization problems.

Bayesian Networks Model for Estimation of Distribution Algorithms

2014 ◽  
Vol 926-930 ◽  
pp. 3594-3597
Author(s):  
Cai Chang Ding ◽  
Wen Xiu Peng ◽  
Wei Ming Wang
Keyword(s):  
Probability Distribution ◽  
Bayesian Networks ◽  
Evolutionary Computation ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Estimation Of Distribution Algorithms ◽  
Previous Generation ◽  
Mutation Operators ◽  
Estimation Of Distribution ◽  
Distribution Algorithms

Estimation of Distribution Algorithms (EDAs) are a set of algorithms that belong to the field of Evolutionary Computation. In EDAs there are neither crossover nor mutation operators. Instead, the new population of individuals is sampled from a probability distribution, which is estimated from a database that contains the selected individuals from the previous generation. Thus, the interrelations between the different variables that represent the individuals may be explicitly expressed through the joint probability distribution associated with the individuals selected at each generation.

The Limits of Estimation of Distribution Algorithms

2014 ◽  
Vol 926-930 ◽  
pp. 3294-3297
Author(s):  
Cai Chang Ding ◽  
Wen Xiu Peng ◽  
Wei Ming Wang
Keyword(s):  
Bayesian Networks ◽  
Probabilistic Model ◽  
Estimation Of Distribution Algorithms ◽  
Case Scenario ◽  
Learning Methods ◽  
Worst Case ◽  
Worst Case Scenario ◽  
Estimation Of Distribution ◽  
Distribution Algorithms

In this paper, we study the ability limit of EDAs to effectively solve problems in relation to the number of interactions among the variables. More in particular, we numerically analyze the learning limits that different EDA implementations encounter to solve problems on a sequence of additively decomposable functions (ADFs) in which new sub-functions are progressively added. The study is carried out in a worst-case scenario where the sub-functions are defined as deceptive functions. We argue that the limits for this type of algorithm are mainly imposed by the probabilistic model they rely on. Beyond the limitations of the approximate learning methods, the results suggest that, in general, the use of bayesian networks can entail strong computational restrictions to overcome the limits of applicability.

An Novel Estimation of Distribution Algorithm for TSP

2013 ◽  
Vol 373-375 ◽  
pp. 1089-1092
Author(s):  
Fa Hong Yu ◽  
Wei Zhi Liao ◽  
Mei Jia Chen
Keyword(s):  
Optimization Problem ◽  
Population Diversity ◽  
Combinatorial Optimization Problem ◽  
Estimation Of Distribution Algorithm ◽  
Traveling Salesman ◽  
Estimation Of Distribution Algorithms ◽  
Np Hard ◽  
Estimation Of Distribution ◽  
Np Hard Problem ◽  
Distribution Algorithms

Estimation of distribution algorithms (EDAs) is a method for solving NP-hard problem. But it is hard to find global optimization quickly for some problems, especially for traveling salesman problem (TSP) that is a classical NP-hard combinatorial optimization problem. To solve TSP effectively, a novel estimation of distribution algorithm (NEDA ) is provided, which can solve the conflict between population diversity and algorithm convergence. The experimental results show that the performance of NEDA is effective.

On the Taxonomy of Optimization Problems Under Estimation of Distribution Algorithms

2013 ◽  
Vol 21 (3) ◽  
pp. 471-495 ◽  
Author(s):  
Carlos Echegoyen ◽  
Alexander Mendiburu ◽  
Roberto Santana ◽  
Jose A. Lozano
Keyword(s):  
Probabilistic Model ◽  
Hamming Distance ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Search Space ◽  
Necessary Condition ◽  
Estimation Of Distribution Algorithms ◽  
Local Optima ◽  
Estimation Of Distribution ◽  
Distribution Algorithms

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 between functions it is possible to partition the space of problems in equivalence classes in which the algorithm has the same behavior. We show that only the probabilistic model is able to generate different partitions of the set of possible problems and hence, it predetermines the number of different behaviors that the algorithm can exhibit. As a natural consequence of our definitions, all the objective functions are in the same equivalence class when the algorithm does not impose restrictions to the probabilistic model. The taxonomy of problems, which is also valid for finite populations, is studied in depth for a simple EDA that considers independence among the variables of the problem. We provide the sufficient and necessary condition to decide the equivalence between functions and then we develop the operators to describe and count the members of a class. In addition, we show the intrinsic relation between univariate EDAs and the neighborhood system induced by the Hamming distance by proving that all the functions in the same class have the same number of local optima and that they are in the same ranking positions. Finally, we carry out numerical simulations in order to analyze the different behaviors that the algorithm can exhibit for the functions defined over the search space [Formula: see text].

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