The adoption of probabilistic models for the best individuals found so far is a powerful approach for evolutionary computation. Increasingly more complex models have been used by estimation of distribution algorithms (EDAs), which often result better effectiveness on finding the global optima for hard optimization problems. Supervised and unsupervised learning of Bayesian networks are very effective options, since those models are able to capture interactions of high order among the variables of a problem. Diversity preservation, through niching techniques, has also shown to be very important to allow the identification of the problem structure as much as for keeping several global optima. Recently, clustering was evaluated as an effective niching technique for EDAs, but the performance of simpler low-order EDAs was not shown to be much improved by clustering, except for some simple multimodal problems. This work proposes and evaluates a combination operator guided by a measure from information theory which allows a clustered low-order EDA to effectively solve a comprehensive range of benchmark optimization problems.
It was already shown that clustering improves the performance of some EDAs for certain classes of problems. For globally multimodal problems, for instance, clustering has revealed a promising approach @cite_1 . Such problems present several global optima or, in other words, several optimal solutions with the same fitness. Those problems may be very tricky for an evolutionary algorithm to solve, since slow convergence to one of the optima (genetic drift) often occurs. The retarded convergence is explained by the combination of solutions coming from different regions of the search space, which often results in poor solutions. The application of clustering in EDAs when solving globally multimodal problems can be described as the separation of the population in subpopulations (one for each cluster), and the subsequent learning of different probabilistic models for each subpopulation. Breeding generally involves no combination among different subpopulations. Clustering improves the performance of the evolutionary algorithm by such an interbreeding avoidance. However, this approach leads to a smaller exploration of the space, since combination from distant regions could be favorable.
@cite_1
2011699475 2022651954 2128859735 2116926066
The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. Observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate or compare them in some common space. A solution may consist in considering multiple clustering tasks independently for each modality. The main difficulty with such an approach is to guarantee that the unimodal clusterings are mutually consistent. In this letter, we show that multimodal clustering can be addressed within a novel framework: conjugate mixture models. These models exploit the explicit transformations that are often available between an unobserved parameter space (objects) and each of the observation spaces (sensors). We formulate the problem as a likelihood maximization task and derive the associated conjugate expectation-maximization algorithm. The convergence properties of the proposed algorithm are thoroughly investigated. Several local and global optimization techniques are proposed in order to increase its convergence speed. Two initialization strategies are proposed and compared. A consistent model selection criterion is proposed. The algorithm and its variants are tested and evaluated within the task of 3D localization of several speakers using both auditory and visual data. The discovery of evolving communities in dynamic networks is an important research topic that poses challenging tasks. Evolutionary clustering is a recent framework for clustering dynamic networks that introduces the concept of temporal smoothness inside the community structure detection method. Evolutionary-based clustering approaches try to maximize cluster accuracy with respect to incoming data of the current time step, and minimize clustering drift from one time step to the successive one. In order to optimize both these two competing objectives, an input parameter that controls the preference degree of a user towards either the snapshot quality or the temporal quality is needed. In this paper the detection of communities with temporal smoothness is formulated as a multiobjective problem and a method based on genetic algorithms is proposed. The main advantage of the algorithm is that it automatically provides a solution representing the best trade-off between the accuracy of the clustering obtained, and the deviation from one time step to the successive. Experiments on synthetic data sets show the very good performance of the method when compared with state-of-the-art approaches. We present a new method for clustering based on compression. The method does not use subject-specific features or background knowledge, and works as follows: First, we determine a parameter-free, universal, similarity distance, the normalized compression distance or NCD, computed from the lengths of compressed data files (singly and in pairwise concatenation). Second, we apply a hierarchical clustering method. The NCD is not restricted to a specific application area, and works across application area boundaries. A theoretical precursor, the normalized information distance, co-developed by one of the authors, is provably optimal. However, the optimality comes at the price of using the noncomputable notion of Kolmogorov complexity. We propose axioms to capture the real-world setting, and show that the NCD approximates optimality. To extract a hierarchy of clusters from the distance matrix, we determine a dendrogram (ternary tree) by a new quartet method and a fast heuristic to implement it. The method is implemented and available as public software, and is robust under choice of different compressors. To substantiate our claims of universality and robustness, we report evidence of successful application in areas as diverse as genomics, virology, languages, literature, music, handwritten digits, astronomy, and combinations of objects from completely different domains, using statistical, dictionary, and block sorting compressors. In genomics, we presented new evidence for major questions in Mammalian evolution, based on whole-mitochondrial genomic analysis: the Eutherian orders and the Marsupionta hypothesis against the Theria hypothesis. A key search mechanism in Evolutionary Algorithms is the mixing or juxtaposing of partial solutions present in the parent solutions. In this paper we look at the efficiency of mixing in genetic algorithms (GAs) and estimation-of-distribution algorithms (EDAs). We compute the mixing probabilities of two partial solutions and discuss the effect of the covariance build-up in GAs and EDas. Moreover, we propose two new Evolutionary Algorithms that maximize the juxtaposing of the partial solutions present in the parents: the Recombinative Optimal Mixing Evolutionary Algorithm (ROMEA) and the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA).