Multiorder neurons for evolutionary higher-order clustering and growth

This letter proposes to use multiorder neurons for clustering irregularly shaped data arrangements. Multiorder neurons are an evolutionary extension of the use of higher-order neurons in clustering. Higher-order neurons parametrically model complex neuron shapes by replacing the classic synaptic weight by higher-order tensors. The multiorder neuron goes one step further and eliminates two problems associated with higher-order neurons. First, it uses evolutionary algorithms to select the best neuron order for a given problem. Second, it obtains more information about the underlying data distribution by identifying the correct order for a given cluster of patterns. Empirically we observed that when the correlation of clusters found with ground truth information is used in measuring clustering accuracy, the proposed evolutionary multiorder neurons method can be shown to outperform other related clustering methods. The simulation results from the Iris, Wine, and Glass data sets show significant improvement when compared to the results obtained using self-organizing maps and higher-order neurons. The letter also proposes an intuitive model by which multiorder neurons can be grown, thereby determining the number of clusters in data.     

Using previous models to bias structural learning in the hierarchical BOA

Estimation of distribution algorithms (EDAs) are stochastic optimization techniques that explore the space of potential solutions by building and sampling explicit probabilistic models of promising candidate solutions. While the primary goal of applying EDAs is to discover the global optimum or at least its accurate approximation, besides this, any EDA provides us with a sequence of probabilistic models, which in most cases hold a great deal of information about the problem. Although using problem-specific knowledge has been shown to significantly improve performance of EDAs and other evolutionary algorithms, this readily available source of problem-specific information has been practically ignored by the EDA community. This paper takes the first step toward the use of probabilistic models obtained by EDAs to speed up the solution of similar problems in the future. More specifically, we propose two approaches to biasing model building in the hierarchical Bayesian optimization algorithm (hBOA) based on knowledge automatically learned from previous hBOA runs on similar problems. We show that the proposed methods lead to substantial speedups and argue that the methods should work well in other applications that require solving a large number of problems with similar structure.     

分布估计算法综述

分布估计算法是进化计算领域新兴起的一类随机优化算法，是当前国际进化计算领域的研究热点. 分布估计算法是遗传算法和统计学习的结合，通过统计学习的手段建立解空间内个体分布的概率模型，然后对概率模型随机采样产生新的群体，如此反复进行，实现群体的进化. 分布估计算法中没有传统的交叉、变异等遗传操作，是一种全新的进化模式；这种优化技术能够通过概率图模型对变量之间的关系进行建模，从而能有效的解决多变量相关的优化问题. 根据概率模型的复杂性，本文按照变量无关、双变量相关、多变量相关等三类分别介绍相应的分布估计算法. 作为一篇综述性文章，本文旨在全面系统的向国内读者介绍这一新技术，并总结分布估计算法的研究现状和未来的研究方向.     

Optimization based on phylogram analysis

Estimation of Distribution Algorithms (EDAs) is evolutionary algorithms with relevant performance in handling complex problems. Nevertheless, their efficiency and effectiveness directly depends on how accurate the deployed probabilistic models are, which in turn depend on methods of model building. Although the best models found in the literature are often built by computationally complex methods, whose corresponding EDAs require high running time, these methods may evaluate a lesser number of points in the search space. In order to find a better trade-off between running time (efficiency) and the number of evaluated points (effectiveness), this work uses probabilistic models built by algorithms of phylogenetic reconstruction, since some of them are able to efficiently produce accurate models. Then, an EDA, namely, Optimization based on Phylogram Analysis, and a new search technique, namely, Composed Exhaustive Search, are developed and proposed to find solutions for combinatorial optimization problems with different levels of difficulty. Experimental results show that the proposed new EDA features an interesting trade-off between running time and number of evaluated points, attaining solutions near to the best results found in the literature for each one of such performance measures.     

Learnable tabu search guided by estimation of distribution for maximum diversity problems

This paper presents a learnable tabu search (TS) guided by estimation of distribution algorithm (EDA), called LTS-EDA, for maximum diversity problem. The LTS-EDA introduces knowledge model and can extract knowledge during the search process of TS, and thus it adopts dual or cooperative evolution/search structure, consisting of probabilistic model space in clustered EDA and solution space searched by TS. The clustered EDA, as a learnable constructive method, is used to create a new starting solution, and the simple TS, as an improvement method, attempts to improve the solution created by the clustered EDA in the LTS-EDA. A distinguishing feature of the LTS-EDA is the usage of the clustered EDA with effective linkage learning to guide TS. In the clustered EDA, different clusters (models) focus on different substructures, and the combination of information from different clusters (models) effectively combines substructures. The LTS-EDA is tested on 50 large size benchmark problems with the size ranging from 2,000 to 5,000. Simulation results show that the LTS-EDA is better than the advanced algorithms proposed recently.     

A new multiobjective clustering technique based on the concepts of stability and symmetry

Most clustering algorithms operate by optimizing (either implicitly or explicitly) a single measure of cluster solution quality. Such methods may perform well on some data sets but lack robustness with respect to variations in cluster shape, proximity, evenness and so forth. In this paper, we have proposed a multiobjective clustering technique which optimizes simultaneously two objectives, one reflecting the total cluster symmetry and the other reflecting the stability of the obtained partitions over different bootstrap samples of the data set. The proposed algorithm uses a recently developed simulated annealing-based multiobjective optimization technique, named AMOSA, as the underlying optimization strategy. Here, points are assigned to different clusters based on a newly defined point symmetry-based distance rather than the Euclidean distance. Results on several artificial and real-life data sets in comparison with another multiobjective clustering technique, MOCK, three single objective genetic algorithm-based automatic clustering techniques, VGAPS clustering, GCUK clustering and HNGA clustering, and several hybrid methods of determining the appropriate number of clusters from data sets show that the proposed technique is well suited to detect automatically the appropriate number of clusters as well as the appropriate partitioning from data sets having point symmetric clusters. The performance of AMOSA as the underlying optimization technique in the proposed clustering algorithm is also compared with PESA-II, another evolutionary multiobjective optimization technique.     

基于数学形态学的聚类集成算法

提出了基于数学形态学的聚类集成算法CEOMM.它利用不同的结构元素的探针作用,对不同的结构元素探测出来的簇核心图进行集成,在集成所得到的簇核心基础上聚类.实验结果表明,算法CEOMM对有复杂类形状的数据集进行聚类时,效果比传统聚类算法更好,且能确定聚类数.而且由于采用了不同的结构元素进行探测,对于由不同形状的类构成的数据集其聚类效果很理想.     

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

Aims to study the advantages of using higher order statistics in estimation distribution of algorithms (EDAs). We study two EDAs with two-tournament selection for discrete optimization problems. One is the univariate marginal distribution algorithm (UMDA) using only first-order statistics and the other is the factorized distribution algorithm (FDA) using higher order statistics. We introduce the heuristic functions and the limit models of these two algorithms and analyze stability of these limit models. It is shown that the limit model of UMDA can be trapped at any local optimal solution for some initial probability models. However, degenerate probability density functions (pdfs) at some local optimal solutions are unstable in the limit model of FDA. In particular, the degenerate pdf at the global optimal solution is the unique asymptotically stable point in the limit model of FDA for the optimization of an additively decomposable function. Our results suggest that using higher order statistics could improve the chance of finding the global optimal solution.     

一种基于混合因子分析的分布估计算法

提出了一种基于混合因子分析的分布估计算法．首先用次胜者受罚的竞争学习算法对选出的最优个体集合聚类，然后对每个类用因子分析模型进行分布信息的估计．为了保持种群的多样性，算法保留那些具有较好适应值并且与所选的最优个体集合较远的个体，并利用聚类的参数来减少计算量．试验结果证实了算法的性能．     

Combinations of estimation of distribution algorithms and other techniques

This paper summaries our recent work on combining estimation of distribution algorithms (EDA) and other techniques for solving hard search and optimization problems:a) guided mutation,an offspring generator in which the ideas from EDAs and genetic algorithms are combined together,we have shown that an evolutionary algorithm with guided mutation outperforms the best GA for the maximum clique problem,b)evolutionary algorithms refining a heuristic,we advocate a strategy for solving a hard optimization problem with complicated data structure,and c) combination of two different local search techniques and EDA for numerical global optimization problems,its basic idea is that not all the new generated points are needed to be improved by an expensive local search.     

Protein Folding in Simplified Models With Estimation of Distribution Algorithms

Simplified lattice models have played an important role in protein structure prediction and protein folding problems. These models can be useful for an initial approximation of the protein structure, and for the investigation of the dynamics that govern the protein folding process. Estimation of distribution algorithms (EDAs) are efficient evolutionary algorithms that can learn and exploit the search space regularities in the form of probabilistic dependencies. This paper introduces the application of different variants of EDAs to the solution of the protein structure prediction problem in simplified models, and proposes their use as a simulation tool for the analysis of the protein folding process. We develop new ideas for the application of EDAs to the bidimensional and tridimensional (2-d and 3-d) simplified protein folding problems. This paper analyzes the rationale behind the application of EDAs to these problems, and elucidates the relationship between our proposal and other population-based approaches proposed for the protein folding problem. We argue that EDAs are an efficient alternative for many instances of the protein structure prediction problem and are indeed appropriate for a theoretical analysis of search procedures in lattice models. All the algorithms introduced are tested on a set of difficult 2-d and 3-d instances from lattice models. Some of the results obtained with EDAs are superior to the ones obtained with other well-known population-based optimization algorithms.     

基于全局性分裂算子的进化K-means算法

进化算法可以有效地克服K means对初始聚类中心敏感的缺陷,提高了聚类性能。在进化K means聚类算法 (F-EAC)的基础上,针对其变异操作——簇分裂算子的随机性与局部性,提出了两个全局性分裂算子。结合最大最小距离的思想,利用待分裂簇的周边簇信息来指导簇分裂初始点的选择,使簇的分裂更有利于全局划分,以进一步提高进化聚类的有效性。实验结果表明,基于全局性分裂算子的算法在类数发现及聚类精度方面均优于F EAC。     

Automatic clustering algorithm based on multi-objective Immunized PSO to classify actions of 3D human models

Multi-objective clustering algorithms are preferred over its conventional single objective counterparts as they incorporate additional knowledge on properties of data in the from of objectives to extract the underlying clusters present in many datasets. Researchers have recently proposed some standardized multi-objective evolutionary clustering algorithms based on genetic operations, particle swarm optimization, clonal selection principles, differential evolution and simulated annealing, etc. In many cases it is observed that hybrid evolutionary algorithms provide improved performance compared to that of individual algorithm. In this paper an automatic clustering algorithm MOIMPSO (Multi-objective Immunized Particle Swarm Optimization) is proposed, which is based on a recently developed hybrid evolutionary algorithm Immunized PSO. The proposed algorithm provides suitable Pareto optimal archive for unsupervised problems by automatically evolving the cluster centers and simultaneously optimizing two objective functions. In addition the algorithm provides a single best solution from the Pareto optimal archive which mostly satisfy the users' requirement. Rigorous simulation studies on 11 benchmark datasets demonstrate the superior performance of the proposed algorithm compared to that of the standardized automatic clustering algorithms such as MOCK, MOPSO and MOCLONAL. An interesting application of the proposed algorithm has also been demonstrated to classify the normal and aggressive actions of 3D human models.     

Environment identification-based memory scheme for estimation of distribution algorithms in dynamic environments

In estimation of distribution algorithms (EDAs), the joint probability distribution of high-performance solutions is presented by a probability model. This means that the priority search areas of the solution space are characterized by the probability model. From this point of view, an environment identification-based memory management scheme (EI-MMS) is proposed to adapt binary-coded EDAs to solve dynamic optimization problems (DOPs). Within this scheme, the probability models that characterize the search space of the changing environment are stored and retrieved to adapt EDAs according to environmental changes. A diversity loss correction scheme and a boundary correction scheme are combined to counteract the diversity loss during the static evolutionary process of each environment. Experimental results show the validity of the EI-MMS and indicate that the EI-MMS can be applied to any binary-coded EDAs. In comparison with three state-of-the-art algorithms, the univariate marginal distribution algorithm (UMDA) using the EI-MMS performs better when solving three decomposable DOPs. In order to understand the EI-MMS more deeply, the sensitivity analysis of parameters is also carried out in this paper.     

Hierarchical evolving Dirichlet processes for modeling nonlinear evolutionary traces in temporal data

Clustering analysis aims to group a set of similar data objects into the same cluster. Topic models, which belong to the soft clustering methods, are powerful tools to discover latent clusters/topics behind large data sets. Due to the dynamic nature of temporal data, clusters often exhibit complicated patterns such as birth, branch and death. However, most existing temporal clustering models assume that clusters evolve as a linear chain, and they cannot model and detect branching of clusters. In this paper, we present evolving Dirichlet processes (EDP for short) to model nonlinear evolutionary traces behind temporal data, especially for temporal text collections. In the setting of EDP, temporal collections are divided into epochs. In order to model cluster branching over time, EDP allows each cluster in an epoch to form Dirichlet processes (DP) and uses a combination of the cluster-specific DPs as the prior for cluster distributions in the next epoch. To model hierarchical temporal data, such as online document collections, we propose a new class of evolving hierarchical Dirichlet processes (EHDP for short) which extends the hierarchical Dirichlet processes (HDP) to model evolving temporal data. We design an online learning framework based on Gibbs sampling to infer the evolutionary traces of clusters over time. In experiments, we validate that EDP and EHDP can capture nonlinear evolutionary traces of clusters on both synthetic and real-world text collections and achieve better results than its peers.     

Regularized continuous estimation of distribution algorithms

Regularization is a well-known technique in statistics for model estimation which is used to improve the generalization ability of the estimated model. Some of the regularization methods can also be used for variable selection that is especially useful in high-dimensional problems. This paper studies the use of regularized model learning in estimation of distribution algorithms (EDAs) for continuous optimization based on Gaussian distributions. We introduce two approaches to the regularized model estimation and analyze their effect on the accuracy and computational complexity of model learning in EDAs. We then apply the proposed algorithms to a number of continuous optimization functions and compare their results with other Gaussian distribution-based EDAs. The results show that the optimization performance of the proposed RegEDAs is less affected by the increase in the problem size than other EDAs, and they are able to obtain significantly better optimization values for many of the functions in high-dimensional settings.     

Initial approaches to the application of islands-based parallel EDAs in continuous domains

Estimation of distribution algorithms (EDAs) are a wide-ranging family of evolutionary algorithms whose common feature is the way they evolve by learning a probability distribution from the best individuals in a population and sampling it to generate the next one. Although they have been widely applied to solve combinatorial optimization problems, there are also extensions that work with continuous variables. In this paper [this paper is an extended version of delaOssa et al. Initial approaches to the application of islands-based parellel EDAs in continuous domains, in: Proceedings of the 34th International Conference on Parallel Processing Workshops (ICPP 2005 Workshops), Oslo, 2005, pp. 580–587] we focus on the solution of the latter by means of island models. Besides evaluating the performance of traditional island models when applied to EDAs, our main goal consists in achieving some insight about the behavior and benefits of the migration of probability models that this framework allow.     

Continuous probabilistic model building genetic network programming using reinforcement learning

Recently, a novel probabilistic model-building evolutionary algorithm (so called estimation of distribution algorithm, or EDA), named probabilistic model building genetic network programming (PMBGNP), has been proposed. PMBGNP uses graph structures for its individual representation, which shows higher expression ability than the classical EDAs. Hence, it extends EDAs to solve a range of problems, such as data mining and agent control. This paper is dedicated to propose a continuous version of PMBGNP for continuous optimization in agent control problems. Different from the other continuous EDAs, the proposed algorithm evolves the continuous variables by reinforcement learning (RL). We compare the performance with several state-of-the-art algorithms on a real mobile robot control problem. The results show that the proposed algorithm outperforms the others with statistically significant differences.     

基于密度可达的多密度聚类算法

为对多密度数据集聚类,提出一种基于密度可达的多密度聚类算法。使用网格划分技术来提高计算每个点密度值的效率,每次聚类都是从最高密度点开始,根据密度可达的概念和广度优先的策略逐步向外扩展进行聚类。实验表明,该算法能够有效地对任意形状、大小的均匀数据集和多密度数据集进行聚类,并能较好地识别出孤立点和噪声,其精度和效率优于SNN算法。     

Inexact graph matching by means of estimation of distribution algorithms

Estimation of distribution algorithms (EDAs) are a quite recent topic in optimization techniques. They combine two technical disciplines of soft computing methodologies: probabilistic reasoning and evolutionary computing. Several algorithms and approaches have already been proposed by different authors, but up to now there are very few papers showing their potential and comparing them to other evolutionary computational methods and algorithms such as genetic algorithms (GAs). This paper focuses on the problem of inexact graph matching which is NP-hard and requires techniques to find an approximate acceptable solution. This problem arises when a nonbijective correspondence is searched between two graphs. A typical instance of this problem corresponds to the case where graphs are used for structural pattern recognition in images. EDA algorithms are well suited for this type of problems.

This paper proposes to use EDA algorithms as a new approach for inexact graph matching. Also, two adaptations of the EDA approach to problems with constraints are described as two techniques to control the generation of individuals, and the performance of EDAs for inexact graph matching is compared with the one of GAs.