Aluizio F. R. Araújo

Identification and control of dynamical systems using the self-organizing map

In this paper, we introduce a general modeling technique, called vector-quantized temporal associative memory (VQTAM), which uses Kohonens self-organizing map (SOM) as an alternative to multilayer perceptron (MLP) and radial basis function (RBF) neural models for dynamical system identification and control. We demonstrate that the estimation errors decrease as the SOM training proceeds, allowing the VQTAM scheme to be understood as a self-supervised gradient-based error reduction method. The performance of the proposed approach is evaluated on a variety of complex tasks, namely: i) time series prediction; ii) identification of SISO/MIMO systems; and iii) nonlinear predictive control. For all tasks, the simulation results produced by the SOM are as accurate as those produced by the MLP network, and better than those produced by the RBF network. The SOM has also shown to be less sensitive to weight initialization than MLP networks. We conclude the paper by discussing the main properties of the VQTAM and their relationships to other well established methods for dynamical system identification. We also suggest directions for further work.

Growing Self-Reconstruction Maps

In this paper, we propose a new method for surface reconstruction based on growing self-organizing maps (SOMs), called growing self-reconstruction maps (GSRMs). GSRM is an extension of growing neural gas (GNG) that includes the concept of triangular faces in the learning algorithm and additional conditions in order to include and remove connections, so that it can produce a triangular two-manifold mesh representation of a target object given an unstructured point cloud of its surface. The main modifications concern competitive Hebbian learning (CHL), the vertex insertion operation, and the edge removal mechanism. The method proposed is able to learn the geometry and topology of the surface represented in the point cloud and to generate meshes with different resolutions. Experimental results show that the proposed method can produce models that approximate the shape of an object, including its concave regions, boundaries, and holes, if any.

Generalized immigration schemes for dynamic evolutionary multiobjective optimization

The insertion of atypical solutions (immigrants) in Evolutionary Algorithms populations is a well studied and successful strategy to cope with the difficulties of tracking optima in dynamic environments in single-objective optimization. This paper studies a probabilistic model, suggesting that centroid-based diversity measures can mislead the search towards optima, and presents an extended taxonomy of immigration schemes, from which three immigrants strategies are generalized and integrated into NSGA2 for Dynamic Multiobjective Optimization (DMO). The correlation between two diversity indicators and hypervolume is analyzed in order to assess the influence of the diversity generated by the immigration schemes in the evolution of non-dominated solutions sets on distinct continuous DMO problems under different levels of severity and periodicity of change. Furthermore, the proposed immigration schemes are ranked in terms of the observed offline hypervolume indicator.

Growing Self-Organizing Maps for Surface Reconstruction from Unstructured Point Clouds

This work introduces a new method for surface reconstruction based on Growing Self-organizing Maps, which learn 3D coordinates of each vertex in a mesh as well as they learn the topology of the input data set. Each map grows incrementally producing meshes of different resolutions, according to the application needs. Another highlight of the presented algorithm refers to the reconstruction time, which is independent from the size of the input data. Experimental results show that the proposed method can produce models that approximate the shape of an object, including its concave regions and holes, if any.

Growing self-organizing surface map: Learning a surface topology from a point cloud

The growing self-organizing surface map (GSOSM) is a novel map model that learns a folded surface immersed in a 3D space. Starting from a dense point cloud, the surface is reconstructed through an incremental mesh composed of approximately equilateral triangles. Unlike other models such as neural meshes (NM), the GSOSM builds a surface topology while accepting any sequence of sample presentation. The GSOSM model introduces a novel connection learning rule called competitive connection Hebbian learning (CCHL), which produces a complete triangulation. GSOSM reconstructions are accurate and often free of false or overlapping faces. This letter presents and discusses the GSOSM model. It also presents and analyzes a set of results and compares GSOSM with some other models.

Multicast routing using genetic algorithm seen as a permutation problem

Classical approaches of multicast routing consider a tree path whose computational cost entails high use of resources such time and memory in the optimization process. This paper presents a genetic algorithm model applied to the multicast routing problem, in which no tree is built. The solution aims to maximize common paths in source-destinations routes and to minimize the route sizes. New options of fitness functions, variation and selection operators were proposed to increase the ability to generate feasible routes. The simulations were performed in two networks: the 33-node European GEANT WAN network to assess the capacity to find viable solutions and a 100-node network to test the capacity to handle larger networks. The results suggest promising performance for this approach.

Correlation between diversity and hypervolume in evolutionary multiobjective optimization

This paper reports a study of the influence of diversity in the convergence dynamics of Multiobjective Evolutionary Algorithms (MOEAs) towards the Pareto Front (PF). By varying mutation and crossover parameters, several scenarios of exploration and exploitation are considered, in which each of them is analysed in order to assess the role of diversity levels on the evolution of high quality sets of non-dominated solutions, in terms of the Hypervolume indicator. For this task, the application of the NSGA2 algorithm for approximating the PF in five ZDT benchmark problems is considered. The results not only indicate that there are significant statistical correlations between several diversity metrics and the observed maximum Hypervolume levels on the evolved populations, but also suggest that there are predictable temporal patterns of correlation when the evolutionary process is portrayed generation wise.

Improving NSGA-II with an adaptive mutation operator

The performance of a Multiobjective Evolutionary Algorithm (MOEA) is crucially dependent on the parameter setting of the operators. The most desired control of such parameters presents the characteristic of adaptiveness, i.e., the capacity of changing the value of the parameter, in distinct stages of the evolutionary process, using feedbacks from the search for determining the direction and/or magnitude of changing. Given the great popularity of the algorithm NSGA-II, the objective of this research is to create adaptive controls for each parameter existing in this MOEA. With these controls, we expect to improve even more the performance of the algorithm. In this work, we propose an adaptive mutation operator that has an adaptive control which uses information about the diversity of candidate solutions for controlling the magnitude of the mutation. A number of experiments considering different problems suggest that this mutation operator improves the ability of the NSGA-II for reaching the Pareto optimal Front and for getting a better diversity among the final solutions.

MulRoGA: A Multicast Routing Genetic Algorithm approach considering multiple objectives

We solve a multicast routing problem by means of a genetic algorithm (GA) without using multicast trees. The source-destination routes need to fulfill two conflicting objectives: maximization of the common links and minimization of the route sizes. The proposed GA can be characterized by its representation of network links and routes in a variable size multi-chromosome problem; local viability restrictions in order to generate the initial population and define variation operators; selection operators in order to choose the most promising individuals thus preserving diversity, and the fitness function in order to handle the conflicting multiple objectives. The proposed model is called a Multicast Routing Genetic Algorithm (MulRoGA). The model was tested on the 33-node European GÉANT WAN network backbone and three other networks (66-node, 100-node and 200-node) randomly generated using the Waxman model on a network topology generator BRITE. On considering each network, a number of solutions were found for changes in the size and node members of the multicast groups, and the source node. The results of the MulRoGA operation suggest a consistent and robust performance in the various cases including comparisons with the methods of unicast shortest path routing, shortest path tree routing (SPT), and simulated annealing (SA) heuristic.

Diversity-based model reference for genetic algorithms in dynamic environment

Preservation of diversity in the evolutionary process is crucial to solve problems considering dynamic environments. This work proposes an adaptive evolutionary algorithm to control the population diversity based on a diversity function. The evolutionary process searches for the optimum while the diversity is controlled to track the diversity function. To control the population diversity, the proposed method creates a selection mechanism to adjust the fitnesses of a part of the population based on a fitness penalty. The proposed adaptive method uses the model-reference adaptive system as the control strategy to adjust the fitness penalty parameter. The proposed method is called diversity-reference adaptive control (DRAC). The performance of DRAC method was evaluated for multimodal and dynamic test functions. The results show that DRAC method often reached the optimum area, following environment changes, faster than SGA.