Jaime A. Ramírez

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.

A clonal selection algorithm for optimization in electromagnetics

This paper proposes the real-coded clonal selection algorithm (RCSA) for use in electromagnetic design optimization. Some features of the algorithm, such as the number of clones, mutation range, and the fraction of the population selected each generation are discussed. The TEAM Workshop problem 22 is investigated, in order to illustrate the performance of the algorithm in a real electromagnetic problem. The results obtained, a set of optimal solutions representing a broader range of options for the designer, are compared with those achieved by a genetic algorithm, showing the efficiency of the RCSA in practical optimization problems.

A multiobjective methodology for evaluating genetic operators

This paper is concerned with the problem of evaluating genetic algorithm (GA) operator combinations. Each GA operator, like crossover or mutation, can be implemented according to several different formulations. This paper shows that: 1) the performances of different operators are not independent and 2) different merit figures for measuring a GA performance are conflicting. In order to account for this problem structure, a multiobjective analysis methodology is proposed. This methodology is employed for the evaluation of a new crossover operator (real-biased crossover) that is shown to bring a performance enhancement. A GA that was found by the proposed methodology is applied in an electromagnetic (EM) benchmark problem.

A modified immune network algorithm for multimodal electromagnetic problems

Some optimization algorithms based on theories from immunology have the feature of finding an arbitrary number of optima, including the global solution. However, this advantage comes at the cost of a large number of objective function evaluations, in most cases, prohibitive in electromagnetic design. This paper proposes a modified version of the artificial immune network algorithm (opt-AINet) for electromagnetic design optimization. The objective of this modified AINet (m-AINet) is to reduce the computational effort required by the algorithm, while keeping or improving the convergence characteristics. Another improvement proposed is to make it more suitable for constrained problems through the utilization of a specific constraint-handling technique. The results obtained over an analytical problem and the design of an electromagnetic device show the applicability of the proposed algorithm

Optimization of Cost Functions Using Evolutionary Algorithms with Local Learning and Local Search

Evolutionary algorithms can benefit from their association with local search operators, giving rise to hybrid or memetic algorithms. The cost of the local search may be prohibitive, particularly when dealing with computationally expensive functions. We propose the use of local approximations in the local search phase of memetic algorithms for optimization of cost functions. These local approximations are generated using only information already collected by the algorithm during the evolutionary process, requiring no additional evaluations. The local search improves some individuals of the population, hence speeding up the overall optimization process. We investigate the design of a loudspeaker magnet with seven variables. The results show the improvement achieved by the proposed combination of local learning and search within evolutionary algorithms

Multiobjective approaches for robust electromagnetic design

Robust optimization problems are inherently multiobjective, because the designer searches for compromise solutions between the mathematical model and possible uncertainties when constructing the physical device. We propose a novel formulation that consists of the employment of a multiobjective approach for robust design. The proposed methodology is applied to two practical problems: the design of a loudspeaker and the design of a superconducting magnetic storage device. The results provide more alternatives to the decision maker, confirming the usefulness and benefit of the approach

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

Pareto cone ε-dominance: improving convergence and diversity in multiobjective evolutionary algorithms

Relaxed forms of Pareto dominance have been shown to be the most effective way in which evolutionary algorithms can progress towards the Pareto-optimal front with a widely spread distribution of solutions. A popular concept is the e-dominance technique, which has been employed as an archive update strategy in some multiobjective evolutionary algorithms. In spite of the great usefulness of the e-dominance concept, there are still difficulties in computing an appropriate value of e that provides the desirable number of nondominated points. Additionally, several viable solutions may be lost depending on the hypergrid adopted, impacting the convergence and the diversity of the estimate set. We propose the concept of cone e-dominance, which is a variant of the e-dominance, to overcome these limitations. Cone e-dominance maintains the good convergence properties of e-dominance, provides a better control over the resolution of the estimated Pareto front, and also performs a better spread of solutions along the front. Experimental validation of the proposed cone e-dominance shows a significant improvement in the diversity of solutions over both the regular Pareto-dominance and the e-dominance.

A Distributed Clonal Selection Algorithm for Optimization in Electromagnetics

This paper proposes the real-coded distributed clonal selection algorithm (DCSA) for use in electromagnetic design optimization. This algorithm employs different types of probability distributions for the mutation of the clones. In order to illustrate the efficiency of this algorithm in practical optimization problems, we compare the results obtained by DCSA with other immune and genetic algorithms over analytical problems and for the TEAM Workshop Problem 22 for the 3 and 8 variables versions. The results indicate that the DCSA is a suitable optimization tool in terms of accuracy and performance.

Multiobjective Memetic Algorithms With Quadratic Approximation-Based Local Search for Expensive Optimization in Electromagnetics

We describe a local search procedure for multiobjective genetic algorithms that employs quadratic approximations for all nonlinear functions involved in the optimization problem. The samples obtained by the algorithm during the evolutionary process are used to fit these quadratic approximations in the neighborhood of the point selected for local search, implying that no extra cost of function evaluations is required. After that, a locally improved solution is easily estimated from the associated quadratic problem. We demonstrate the hybridization of our procedure with the well-known multiobjective genetic algorithm. This methodology can also be coupled with other multiobjective evolutionary algorithms. The results show that the proposed procedure is suitable for time-demanding black-box optimization problems.