Hajime Igarashi

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.

On convergence of ICCG applied to finite-element equation for quasi-static fields

This paper discusses convergence of the incomplete Cholesky conjugate gradient method (ICCG) which solves edge-based finite-element equations for quasi-static electromagnetic fields. It has been observed in numerical computations that convergence of ICCG for the A-V method is faster than that for the A method. This phenomenon is found to be explained by the fact that, in the A-V method, the preconditioning eliminates the small singular values which deteriorate the condition number while they remain after the preconditioning in the case of the A method.

Optimization of Inductors Using Evolutionary Algorithms and Its Experimental Validation

This paper presents parameter and topology optimization of inductor shapes using evolutionary algorithms. The goal of the optimization is to reduce the size of inductors satisfying the specifications on inductance values under weak and strong bias-current conditions. The inductance values are computed from the finite-element (FE) method taking magnetic saturation into account. The result of the parameter optimization, which leads to significant reduction in the volume, is realized for test, and the dependence of inductance on bias currents is experimentally measured, which is shown to agree well with the computed values. Moreover, novel methods are introduced for topology optimization to obtain inductor shapes with homogeneous ferrite cores suitable for mass production.

On the property of the curl-curl matrix in finite element analysis with edge elements

This paper discusses properties of the curl-curl matrix in the finite element formulation with edge elements. Moreover, the observed deceleration in convergence of the CG and ICCG methods applied to magnetostatic problems through the tree-cotree gauging is explained on the basis of the eigenvalue separation property. From the eigenvalue separation property it follows that neither minimum nonzero eigenvalue of the curl-curl matrix nor maximum one increase through the tree-cotree gauging. Hence it is concluded that the condition number of the curl-curl matrix tends to grow by its definition. Moreover, the maximum eigenvalue tends to keep constant whereas the minimum nonzero eigenvalue reduces. This property also makes the condition number worse.

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

Estimation of effective permeability of magnetic composite materials

This paper describes a method to estimate effective permeability of magnetic composite materials for static field. In the present method, the structures of the composite materials are assumed to be periodic, and the unit cell is defined. The effective permeability is determined on the basis of magnetic energy balance in the unit cell. The present method considers magnetic interaction between inclusions of the composite materials, and is more accurate and useful. Therefore, the present method can be more widely applied than conventional models, for example, the Maxwell-Garnett formula and the Bruggeman formula. Validity of the present method is confirmed by numerical analyses. This approach can be applied also to nonlinear magnetic composite materials.

Analysis of magnetic shielding effect of layered shields based on homogenization

This paper describes a nonlinear analysis of magnetic field based on homogenization. The analysis of a magnetic field is time-consuming when the problem includes magnetic substance with fine structure. Simplification of the fine structure by homogenization makes it possible to analyze them efficiently. The authors have introduced a homogenization method to estimate effective permeability of magnetic composite structure for a static field. This method can be applied not only for linear problems but also nonlinear ones. In this paper, the magnetic shielding effect of layered nonlinear material is analyzed by using the homogenization method, and the applicability of this method is discussed

Overview of artificial immune systems for multi-objective optimization

Evolutionary algorithms have become a very popular approach for multiobjective optimization in many fields of engineering. Due to the outstanding performance of such techniques, new approaches are constantly been developed and tested to improve convergence, tackle new problems, and reduce computational cost. Recently, a new class of algorithms, based on ideas from the immune system, have begun to emerge as problem solvers in the evolutionary multiobjective optimization field. Although all these immune algorithms present unique, individual characteristics, there are some trends and common characteristics that, if explored, can lead to a better understanding of the mechanisms governing the behavior of these techniques. In this paper we propose a common framework for the description and analysis of multiobjective immune algorithms.

Model Reduction of Three-Dimensional Eddy Current Problems Based on the Method of Snapshots

The model reduction based on the method of snapshots is applied to the finite element analysis of three-dimensional transient eddy current problems. It is known that accuracy of the reduced model highly depends on the number of snapshots. In this paper, we introduce a novel method which determines the adequate number of snapshots automatically. It is shown that the computational time can be reduced when using the model reduction based on the present method.