Douglas A. G. Vieira

Treating constraints as objectives in multiobjective optimization problems using niched Pareto genetic algorithm

In this paper, the constraints, in multiobjective optimization problems, are treated as objectives. The constraints are transformed in two new objectives: one is based on a penalty function and the other is made equal to the number of violated constraints. To ensure the convergence to a feasible Pareto optimal front, the constrained individuals are eliminated during the elitist process. The treatment of infeasible individuals required some relevant modifications in the standard Parks and Miller elitist technique. Analytical and electromagnetic problems are presented and the results suggest the effectiveness of the proposed approach.

The

This paper presents a novel approach for dealing with the structural risk minimization (SRM) applied to a general setting of the machine learning problem. The formulation is based on the fundamental concept that supervised learning is a bi-objective optimization problem in which two conflicting objectives should be minimized. The objectives are related to the empirical training error and the machine complexity. In this paper, one general Q-norm method to compute the machine complexity is presented, and, as a particular practical case, the minimum gradient method (MGM) is derived relying on the definition of the fat-shattering dimension. A practical mechanism for parallel layer perceptron (PLP) network training, involving only quasi-convex functions, is generated using the aforementioned definitions. Experimental results on 15 different benchmarks are presented, which show the potential of the proposed ideas.

Q

Abstract In this paper, both the architecture and learning procedure underlying the parallel layer perceptron is presented. This topology, different to the previous ones, uses parallel layers of perceptrons to map nonlinear input–output relationships. Comparisons between the parallel layer perceptron, multi-layer perceptron and ANFIS are included and show the effectiveness of the proposed topology.

-Norm Complexity Measure and the Minimum Gradient Method: A Novel Approach to the Machine Learning Structural Risk Minimization Problem

This paper proposes a new reconfiguration heuristic in order to reduce the total power loss and the maximum current of electrical radial networks. It is based on the branch-and-bound strategy, which is an implicit enumeration method that uses a tree structure and bounds to organize the searching process. The search tree in this paper is constructed by subdividing the feasible set using the branch-exchange technique in the networks. The constraints and the Pareto dominance are responsible for pruning the search tree. The heuristic also returns a feasible switching plan for each solution. The algorithm was successfully applied to medium- and large-scale problems.

Parallel layer perceptron

This work presents an algorithm for multiobjective optimization that is structured as: (i) a descent direction is calculated, within the cone of descent and feasible directions, and (ii) a multiobjective line search is conducted over such direction, with a new multiobjective golden section segment partitioning scheme that directly finds line-constrained efficient points that dominate the current one. This multiobjective line search procedure exploits the structure of the line-constrained efficient set, presenting a faster compression rate of the search segment than single-objective golden section line search. The proposed multiobjective optimization algorithm converges to points that satisfy the Kuhn-Tucker first-order necessary conditions for efficiency (the Pareto-critical points). Numerical results on two antenna design problems support the conclusion that the proposed method can solve robustly difficult nonlinear multiobjective problems defined in terms of computationally expensive black-box objective functions.

A Multiobjective Heuristic for Reconfiguration of the Electrical Radial Network

This paper investigates the characterization of inclusions in concrete structures, including the number of inclusions, their geometries, and electromagnetic properties. To solve this problem, a two phase algorithm that combines matched-filter-based reverse-time (MFBRT) migration algorithm with the particle swarm optimization (PSO) is employed. The first phase runs the MFBRT that can, robustly, define the number of inclusions and their centers; however, it cannot define the inclusion geometry and electromagnetic properties. Given the results obtained in the first phase, the PSO is launched in the second phase, in a parametric approach, to define the radii of the inclusions and their properties. Three types of inclusions were considered, water, air, and conductor. Results considering a nonhomogenous host medium having from one to three inclusions are presented showing the effectiveness of the proposed approach.

Multicriteria optimization with a multiobjective golden section line search

This paper presents a multiobjective shape optimization of an offset reflector antenna using the Cone of Efficient Directions Algorithm (CEDA), that includes a multiobjective line search. This algorithm features a monotone dominance convergence: the sequence of solution antennas occur in such a way that all the objectives are improved simultaneously. Given an area to be covered, the desired radiation pattern is the one with the maximum mean gain and uniformity, possibly weighted, inside it. These features are achieved by the definition of a single objective function, which must held in three different frequencies (a total of three conflicting objectives), in order to provide broad-band characteristics to the designed antenna

Inverse Algorithms for the GPR Assessment of Concrete Structures

This paper aims at detecting and characterizing inclusions in concrete structures by inverting ground-penetrating radar (GPR) data. First, the signal is preprocessed using the principal component analysis (PCA) and then used to train an artificial neural network (ANN). The GPR data consists of 1200 time steps. Using PCA, the data can be compressed to 286 dimensions without losing any information. Moreover, with 99.99% of the original variance the data needs only 139 dimensions. This dimensional reduction makes the ANN training easier and faster. The ANN were trained to find the buried inclusions characteristics-and-considering a nonhomogenous host medium by inverting the preprocessed data. The results show that the expected maximum error was kept under 1%, which is a remarkable result, since the host medium is nonhomogenous.

Multiobjective shape optimization of broad-band reflector antennas using the cone of efficient directions algorithm

This paper deals with the parallel layer perceptron (PLP) complexity control, bias and variance dilemma, using a multiobjective (MOBJ) training algorithm. To control the bias and variance the training process is rewritten as a bi-objective problem, considering the minimization of both training error and norm of the weight vector, which is a measure of the network complexity. This method is applied to regression and classification problems and compared with several other training procedures and topologies. The results show that the PLP MOBJ training algorithm presents good generalization results, outperforming traditional methods in the tested examples.

Characterization of Inclusions in a Nonhomogeneous GPR Problem by Artificial Neural Networks

This paper addresses the problem of extracting sensitivity information from a modified adaptive-network-based fuzzy inference system (ANFIS) topology, i.e., from a Parallel Layer Perceptron network. This topology was recently proposed and presents computational advantages if compared with the traditional ANFIS. The indirect extraction of gradient information is useful in optimization problems when a high computational effort is involved in the evaluation of the functions, for instance when finite element analysis is used to solve the electromagnetic field problem. An analytical and an electromagnetic optimization problem are discussed. The results show the effectiveness, i.e., simplicity, accuracy and saving in CPU time, of this novel topology for the extraction of sensitivity information.