Traditional Estimation Of Distribution Algorithms Research Articles

Estimation of Distribution Algorithm for Grammar-Guided Genetic Programming.

Genetic variation operators in grammar-guided genetic programming are fundamental to guide the evolutionary process in search and optimization problems. However, they show some limitations, mainly derived from an unbalanced exploration and local-search trade-off. This article presents an estimation of distribution algorithm for grammar-guided genetic programming to overcome this difficulty and thus increase the performance of the evolutionary algorithm. Our proposal employs an extended dynamic stochastic context-free grammar to encode and calculate the estimation of the distribution of the search space from some promising individuals in the population. Unlike traditional estimation of distribution algorithms, the proposed approach improves exploratory behavior by smoothing the estimated distribution model. Therefore, this algorithm is referred to as SEDA, smoothed estimation of distribution algorithm. Experiments have been conducted to compare overall performance using a typical genetic programming crossover operator, an incremental estimation of distribution algorithm, and the proposed approach after tuning their hyperparameters. These experiments involve challenging problems to test the local search and exploration features of the three evolutionary systems. The results show that grammar-guided genetic programming with SEDA achieves the most accurate solutions with an intermediate convergence speed.

Trade-offs in PMU and IED Deployment for Active Distribution State Estimation Using Multi-objective Evolutionary Algorithm

This paper proposes a new multi-objective optimization problem to find trade-offs in deployment of phasor measurement units (PMUs) and intelligent electronic devices (IEDs) for state estimation in active distribution networks. A new hybrid estimation of distribution algorithm (EDA) has been used to find the optimal number and location of measurement devices, such as PMU and IED, for accurate state estimation. The objective functions to be minimized in this optimization problem are the total cost of PMUs and IEDs, and the root mean square value of state estimation error. As the objectives are conflicting in nature, a multi-objective Pareto-based nondominated sorting (NDS) EDA algorithm is proposed. Moreover, to improve the local searching capability of the traditional EDA algorithm, the interior point method (IPM) is hybridized with EDA to get a near-global optimal solution. The hybridization of EDA with IPM brings a higher degree of balance between the exploration and exploitation capability of the traditional EDA during the search process. Furthermore, the random variation in loads and generations is also considered to check the reliability of the proposed meter placement technique. The viability of the proposed algorithm has been tested on the IEEE 69-bus system and Indian 85-bus system to validate the results. The obtained results have been compared with those of the conventional EDA algorithm, NDS genetic algorithm, and hybrid EDA-simulated annealing algorithm existing in the literature.

Variable Classification-based Co-estimation of Distribution Algorithm Assisted by a Cooperative Particle Swarm Optimizer

Since estimation of distribution algorithms (EDAs) were proposed, many methods have been made to improve EDAs’ performance. In this paper, a variable classification-based cooperative estimation of distribution algorithm (VC-CEDA) is proposed to balance the global and local searching ability of estimation of distribution algorithms. This study proposes a variable classification method to improve the efficiency and accuracy of probability model development. And a cooperative particle swarm optimizer that can improve the local searching ability is proposed. The VC-CEDA combines the advantages of traditional algorithm and cooperative operations. VC-CEDA shows significantly better performance on 10 test functions. In this study, the experimental results show that the VC-CEDA performs better than traditional EDAs.

Scaling Up Estimation of Distribution Algorithms for Continuous Optimization

Since estimation of distribution algorithms (EDAs) were proposed, many attempts have been made to improve EDAs' performance in the context of global optimization. So far, the studies or applications of multivariate probabilistic model-based EDAs in continuous domain are still mostly restricted to low-dimensional problems. Traditional EDAs have difficulties in solving higher dimensional problems because of the curse of dimensionality and rapidly increasing computational costs. However, scaling up continuous EDAs for large-scale optimization is still necessary, which is supported by the distinctive feature of EDAs: because a probabilistic model is explicitly estimated, from the learned model one can discover useful properties of the problem. Besides obtaining a good solution, understanding of the problem structure can be of great benefit, especially for black box optimization. We propose a novel EDA framework with model complexity control (EDA-MCC) to scale up continuous EDAs. By employing weakly dependent variable identification and subspace modeling, EDA-MCC shows significantly better performance than traditional EDAs on high-dimensional problems. Moreover, the computational cost and the requirement of large population sizes can be reduced in EDA-MCC. In addition to being able to find a good solution, EDA-MCC can also provide useful problem structure characterizations. EDA-MCC is the first successful instance of multivariate model-based EDAs that can be effectively applied to a general class of up to 500-D problems. It also outperforms some newly developed algorithms designed specifically for large-scale optimization. In order to understand the strengths and weaknesses of EDA-MCC, we have carried out extensive computational studies. Our results have revealed when EDA-MCC is likely to outperform others and on what kind of benchmark functions.

Copula selection for graphical models in continuous Estimation of Distribution Algorithms

This paper presents the use of graphical models and copula functions in Estimation of Distribution Algorithms (EDAs) for solving multivariate optimization problems. It is shown in this work how the incorporation of copula functions and graphical models for modeling the dependencies among variables provides some theoretical advantages over traditional EDAs. By means of copula functions and two well known graphical models, this paper presents a novel approach for defining new EDAs. Either dependence is modeled by a copula function chosen from a predefined set of six functions that aim to cover a wide range of inter-relations. It is also shown how the use of mutual information in the learning of graphical models implies a natural way of employing copula entropies. The experimental results on separable and non-separable functions show that the two new EDAs, which adopt copula functions to model dependencies, perform better than their original version with Gaussian variables.

A block based estimation of distribution algorithm using bivariate model for scheduling problems

Recently, estimation of distribution algorithms (EDAs) have gradually attracted a lot of attention and have emerged as a prominent alternative to traditional evolutionary algorithms. In this paper, a block-based EDA using bivariate model is developed to solve combinatorial problems. Instead of generating a set of chromosomes, our approach generates a set of promising blocks using bivariate model and these blocks are reserved in an archive for future use. These blocks will be updated every other k generation. Then, two rules, i.e., AC1 and AC2, are developed to generate a new chromosome by combining the set of selected blocks and rest of genes. This block based approach is very efficient and effective when compared with the traditional EDAs. According to the experimental results, the block based EDA outperforms EDA, GA, ACO and other evolutionary approaches in solving benchmark permutation problems. The block based approach is a new concept and has a very promising result for other applications.

Subspace estimation of distribution algorithms: To perturb part of all variables in estimation of distribution algorithms

Abstract In the traditional estimation of distribution algorithms (EDAs), all the variables of candidate individuals are perturbed through sampling from a probability distribution of promising individuals. However, it may be unnecessary for the EDAs to perturb all variables of candidate individuals at each generation. This is because one variable may be dependent on another variable and all variables may have different saliences even if they are independent. Therefore, only a subset of all variables in EDAs really function at each generation. This paper proposes a novel class of EDAs, termed as subspace estimation of distribution algorithms (subEDAs), from a new perspective to reduce the space of variables for use in model building and model sampling based on EDAs’ performance. In subEDAs, only part of all variables of candidate individuals are perturbed at each generation. Three schemes are described in details to determine which variables should be perturbed at each generation: the random picking method (RP), the majority voting based on the similarity between high quality individuals (MVSH) and the majority voting based on the difference between high quality and low quality individuals (MVDHL). Then, subEDAs + RP, subEDAs + MVSH and subEDAs + MVDHL are tested on several benchmark functions and their algorithmic results are compared with those obtained by EDAs. Our experimental results indicate that subEDAs are able to obtain a comparative result using only a subset of problem variables in the model when compared with traditional EDAs.

Optimization by estimation of distribution with DEUM framework based on Markov random fields

This paper presents a Markov random field (MRF) approach to estimating and sampling the probability distribution in populations of solutions. The approach is used to define a class of algorithms under the general heading distribution estimation using Markov random fields (DEUM). DEUM is a subclass of estimation of distribution algorithms (EDAs) where interaction between solution variables is represented as an undirected graph and the joint probability of a solution is factorized as a Gibbs distribution derived from the structure of the graph. The focus of this paper will be on describing the three main characteristics of DEUM framework, which distinguishes it from the traditional EDA. They are: 1) use of MRF models, 2) fitness modeling approach to estimating the parameter of the model and 3) Monte Carlo approach to sampling from the model.