Recent trends of the most used metaheuristic techniques for distribution network reconfiguration

Distribution network reconfiguration (DNR) continues to be a good option to reduce technical losses in a distribution power grid. However, this non-linear combinatorial problem is not easy to assess by exact methods when solving for large distribution networks, which requires large computational times. For solving this type of problem, some researchers prefer to use metaheuristic techniques due to convergence speed, near-optimal solutions, and simple programming. Some literature reviews specialize in topics concerning the optimization of power network reconfiguration and try to cover most techniques. Nevertheless, this does not allow detailing properly the use of each technique, which is important to identify the trend. The contributions of this paper are three-fold. First, it presents the objective functions and constraints used in DNR with the most used metaheuristics. Second, it reviews the most important techniques such as particle swarm optimization (PSO), genetic algorithm (GA), simulated annealing (SA), ant colony optimization (ACO), immune algorithms (IA), and tabu search (TS). Finally, this paper presents the trend of each technique from 2011 to 2016. This paper will be useful for researchers interested in knowing the advances of recent approaches in these metaheuristics applied to DNR in order to continue developing new best algorithms and improving solutions for the topi

Optimization in Networks

The recent surge in the network modeling of complex systems has set the stage for a new era in the study of fundamental and applied aspects of optimization in collective behavior. This Focus Issue presents an extended view of the state of the art in this field and includes articles from a large variety of domains where optimization manifests itself, including physical, biological, social, and technological networked systems.Comment: Opening article of the CHAOS Focus Issue "Optimization in Networks", available at http://link.aip.org/link/?CHA/17/2/htmlto

Finding community structure in networks using the eigenvectors of matrices

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as "modularity" over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.Comment: 22 pages, 8 figures, minor corrections in this versio

On the Analysis of Trajectories of Gradient Descent in the Optimization of Deep Neural Networks

Theoretical analysis of the error landscape of deep neural networks has garnered significant interest in recent years. In this work, we theoretically study the importance of noise in the trajectories of gradient descent towards optimal solutions in multi-layer neural networks. We show that adding noise (in different ways) to a neural network while training increases the rank of the product of weight matrices of a multi-layer linear neural network. We thus study how adding noise can assist reaching a global optimum when the product matrix is full-rank (under certain conditions). We establish theoretical foundations between the noise induced into the neural network - either to the gradient, to the architecture, or to the input/output to a neural network - and the rank of product of weight matrices. We corroborate our theoretical findings with empirical results.Comment: 4 pages + 1 figure (main, excluding references), 5 pages + 4 figures (appendix