Rodney R. Saldanha

Improvements in genetic algorithms

This paper presents an exhaustive study of the Simple Genetic Algorithm (SGA), Steady State Genetic Algorithm (SSGA) and Replacement Genetic Algorithm (RGA). The performance of each method is analyzed in relation to several operators types of crossover, selection and mutation, as well as in relation to the probabilities of crossover and mutation with and without dynamic change of its values during the optimization process. In addition, the space reduction of the design variables and global elitism are analyzed. All GAs are effective when used with its best operations and values of parameters. For each GA, both sets of best operation types and parameters are found. The dynamic change of crossover and mutation probabilities, the space reduction and the global elitism during the evolution process show that great improvement can be achieved for all GA types. These GAs are applied to TEAM benchmark problem 22.

Electric distribution network multiobjective design using a problem-specific genetic algorithm

This paper presents a multiobjective approach for the design of electrical distribution networks. The objectives are defined as a monetary cost index (including installation cost and energy losses cost) and a system failure index. The true Pareto-optimal solutions are found with a multiobjective genetic algorithm that employs an efficient variable encoding scheme and some problem-specific mutation and crossover operators. Results based on 21- and 100-bus systems are presented. The information gained from the Pareto-optimal solution set is shown to be useful for the decision-making stage of distribution network evolution planning.

Improving generalization of MLPs with multi-objective optimization

Abstract This paper presents a new learning scheme for improving generalization of multilayer perceptrons. The algorithm uses a multi-objective optimization approach to balance between the error of the training data and the norm of network weight vectors to avoid overfitting. The results are compared with support vector machines and standard backpropagation.

Genetic algorithm coupled with a deterministic method for optimization in electromagnetics

In this paper, a hybrid technique for global optimization based on the genetic algorithm and a deterministic method is presented. A potential advantage of the hybrid method compared to the genetic algorithm is that global optimization can be performed more efficiently. An intrinsic problem of the hybrid techniques is related to the moment of stopping the stochastic routine to launch the deterministic one. This is investigated using some natural criteria for the commutation between the two methods. The results show that it is possible to gain in efficiency and in accuracy but the criterion is usually problem dependent. Finally, to show the solution of a real problem, the hybrid algorithm is coupled to a 2D code based on the boundary element method to optimize a connector of 145 kV GIS.

A Meshless Method for Electromagnetic Field Computation Based on the Multiquadric Technique

A meshless method for electromagnetic field computation is developed based on the multiquadric interpolation technique. A global approximation to the solution is built based only on the discretization of the domain in nodes and the differential equations describing the problem in the domain and its boundary. An attractive characteristic of the multiquadric solution is that it is continuous and it has infinitely continuous derivatives. This is particularly important to obtain field quantities in electromagnetic analysis. The method is also capable of dealing with physical discontinuities present at the interface between different materials. The formulation is presented in the Cartesian and polar coordinates, which can be extended to other systems. We applied the formulation in the analysis of an electrostatic micromotor and a microstrip. The results demonstrate good agreement with other numerical technique, showing the adequacy of the proposed methodology for electromagnetic analysis

A Multi-Objective Evolutionary Algorithm Based on Decomposition for Optimal Design of Yagi-Uda Antennas

This paper presents a multi-objective evolutionary algorithm based on decomposition (MOEA/D) to design broadband optimal Yagi-Uda antennas. A multi-objective problem is formulated to achieve maximum directivity, minimum voltage standing wave ratio and maximum front-to-back ratio. The algorithm was applied to the design of optimal 3 to 10 elements Yagi-Uda antennas, whose optimal Pareto fronts are provided in a single picture. The multi-objective problem is decomposed by Chebyshev decomposition, and it is solved by differential evolution (DE) and Gaussian mutation operators in order to provide a better approximation of the Pareto front. The results show that the implemented MOEA/D is efficient for designing Yagi-Uda antennas.

A Multiobjective Heuristic for Reconfiguration of the Electrical Radial Network

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.

A multiobjective proposal for the TEAM benchmark problem 22

The TEAM benchmark problem 22 is an important optimization problem in electromagnetic design, which can be formulated as a constrained mono-objective problem or a multiobjective one with two objectives. In this paper, we propose a multiobjective version with three objectives, whose third objective is related to the quench constraint and the better use of the superconducting material. The formulation proposed yields results that provide new alternatives to the designer. We solved the formulation proposed using the multiobjective clonal selection algorithm. After that, we selected a particular solution using a simple decision making procedure

Multicriteria optimization with a multiobjective golden section line search

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 new constrained ellipsoidal algorithm for nonlinear optimization with equality constraints

This paper presents a new algorithm for nonlinear optimization, the cone ellipsoidal algorithm (CEA), that is suitable for dealing with equality constraints and deterministically converges to the global solution in convex problems. The algorithm is based on the traditional ellipsoidal algorithm and on some new cone conditions. CEA simultaneously searches the objective function minimum and the problem feasible region. A case study is presented: the well-known TEAM 22 benchmark problem. The new algorithm finds a solution that is at least as good as the best solution that is known, with high computational efficiency.