Kiyoharu Tagawa

A statistical study of the Differential Evolution based on continuous generation model

Differentiation Evolution (DE) is an Evolutionary Algorithm (EA) for solving function optimization problems. In order to renew the population in EA, there are two generation models. The first one is “discrete generation model”, and the second one is “continuous generation model”. Conventional DEs have been based on the discrete generation model in which the current generations population is replaced by the next generations population at a time. In this paper, a novel DE based on the continuous generation model is described. Because a newborn excellent individual is added to an only population and can be used immediately to generate offspring in the continuous generation model, it can be expected that the novel DE converges faster than the conventional ones. Furthermore, by employing the continuous generation model, it becomes easy to introduce various survival selection methods into DE. Therefore, three survival selection methods are contrived for the novel DE based on the continuous generation model. Finally, the effects of the generation model, the survival selection method, the reproduction selection method, the population size and their interactions on the performance of DE are evaluated statistically by using the analysis of variance (ANOVA).

Distance based hybrid genetic algorithm: an application for the graph coloring problem

A hybrid genetic algorithm (GA) which combines the global search power of GA with the local search power of a local optimization algorithm is described for the graph coloring problem (GCP). Each solution of the GCP, which is called phenotype, is represented by a set of isomorphic genotypes conceptually. Then, a metric function between two phenotypes is defined by the least Hamming distance between the corresponding sets of isomorphic genotypes. The phenotypic distance is useful to analyze and control the behavior of genotypes in the search space from the view point of the problem space. A new crossover technique named harmonic crossover is proposed for the GCP. The phenotypic distance between two parents is considered in the harmonic crossover for preserving their common characteristics. Furthermore, the phenotypic distance between two parents is also used to predict promising regions in the problem space. In the proposed hybrid GA for the GCP, the local optimization algorithm is applied only in the most promising regions restrictedly and intensively. Consequently, the run of the local optimization algorithm does not hinder the performance of GA in its progress of global search.

An Imanishian genetic algorithm for the optimum design of surface acoustic wave filter

The frequency response characteristics of surface acoustic wave (SAW) filters are governed primarily by their geometrical structures, i.e., the configurations of interdigital transducers (IDTs) and reflectors arranged on piezoelectric substrates. We present an Imanishian genetic algorithm (GA), which is based on an evolutionary theory advocated by a Japanese ecologist, Kinji Imanishi, for the structural design of SAW filters. In the proposed Imanishian GA, each species is discriminated from others according to the distance between individuals. Then, the generation model tries to hold various species in the population as many as possible. In addition, a local search is used to improve respective individuals effectively. As a result, in comparison with traditional Darwinian GAs, the Imanishian GA is better at taking balance between exploration and exploitation. Computational experiments conducted on an optimum design of a resonator type SAW filter demonstrate the usefulness of the Imanishian GA.

Optimal design of three-IDT type SAW filter using local search

An optimal design approach for surface acoustic wave (SAW) filters is presented. First of all, the structural design of a three-IDT type SAW filter, which consists of three interdigital transducers (IDT) and two reflectors, is formulated as a combinatorial optimization problem. In order to simulate the frequency response of the SAW filter, the least equivalent circuit model of IDT is employed. Then, a new local search technique based on the k-degree-neighborhood is proposed and applied to the optimization problem successfully. The proposed local search is applicable generally to the structural design of various SAW devices.

Symbolic approach to the implementation of linearizing compensator for robotic manipulators

The authors propose a new method for practical implementation of linearizing compensators for robotic manipulators. A set of statements to compute inverse dynamics or outputs of the linearizing compensators is derived from closed-form symbolic equations generated using the algebraic computation system REDUCE. To remove redundant computations contained in closed-form symbolic equations, a factoring algorithm is proposed. Using a planar manipulator with two revolution joints, it is shown that the proposed method computes the inverse dynamics faster than the conventional method based on the recursive Newton-Euler formulation.<<ETX>>

A new metric function and harmonic crossover for symmetric and asymmetric traveling salesman problems

For the successful application of a genetic algorithm (GA) to the traveling salesman problem (TSP), a suitable distance between two Hamiltonian circuits on a complete graph is useful to estimate the problem landscape. This paper presents a new distance between two Hamiltonian circuits, or phenotypes. The phenotypic distance is defined by the least Hamming distance between isomorphic genotypes. Therefore, it is convenient to analyze and control the behavior of genotypes in the search space. In this paper, a new crossover technique based on the phenotypic distance is also proposed. The crossover technique works together the conventional crossovers arranged for the TSP such as partially mapped (PMX), order (OX) and cycle (CX) crossovers. Because a new child is sure to be located between two parents in the problem space, the local search performance of the conventional crossovers is enhanced with the proposed crossover technique.

Indicator-based differential evolution using exclusive hypervolume approximation and parallelization for multi-core processors

A new Multi-Objective Evolutionary Algorithm (MOEA) based on Differential Evolution (DE), i.e., Indicator-Based DE (IBDE) is proposed. IBDE employs a strategy of DE for generating a series of offspring. In order to evaluate the quality of each individual in the population, IBDE uses the exclusive hypervolume as an indicator function. A fast algorithm called Incremental Hypervolume by Slicing Objectives (IHSO) has been reported for calculating the exclusive hypervolume. However, the computational time spent by IHSO increases exponentially with the number of objectives and considered individuals. Therefore, an exclusive hypervolume approximation, in which IHSO can be also used effectively, is proposed. Furthermore, it is proven that the proposed exclusive hypervolume approximation gives an upper bound of the accurate exclusive hypervolume. The procedure of IHSO is parallelized by using the multiple threads of the Java language. By using the parallelized IHSO, not only the exclusive hypervolume but also the exclusive hypervolume approximation can be calculated concurrently on a multi-core processor. By the results of numerical experiments and statistical tests conducted on test problems, the usefulness of the proposed approach is demonstrated.

Robust optimum design of SAW filters with the Taguchi method and a memetic algorithm

This paper presents a robust optimum design approach to tackle the structural design of surface acoustic wave (SAW) filters. The frequency response characteristics of SAW filters are governed primarily by their geometrical structures: the configurations of inter-digital transducers (IDTs) and grating reflectors fabricated on piezoelectric substrates. For deciding an optimal structure of SAW filters based on the computer simulation, the equivalent circuit model of IDT, which includes several uncertain parameters, has to be utilized. In order to cope well with the designing imperfections caused by the inevitable dispersion of these uncertain parameters, the quality engineering technique, or the Taguchi method, is employed. First of all, according to the Taguchi method, the signal to noise ratio (SNR) of SAW filters is defined to evaluate their robustness. Then, for increasing the SNR of SAW filters as much as possible without losing their specified functions, the robust optimum design of SAW filters is formulated as a constrained optimization problem. Furthermore, a memetic algorithm combining an evolutionary algorithm based on the penalty function method with a local search is proposed. Finally, the memetic algorithm is effectively applied to the robust optimum design of a resonator type SAW filter. Computational experiments show that the proposed memetic algorithm not only can find a feasible solution of the constrained optimization problem, or a desirable structure of objective SAW filter, but also can drastically improve the robustness of the SAW filter.

Many-hard-objective optimization using differential evolution based on two-stage constraint-handling

This paper focus on the Many-Hard-objective Optimization Problem (MHOP) in which a lot of objectives are limited by a goal point. In order to obtain an approximation of Pareto-optimal feasible solution set for MHOP, a new algorithm called Differential Evolution for Many-Hard-objective Optimization (DEMHO) is proposed. For sorting non dominated solutions, DEMHO uses Pairwise Exclusive Hypervolume (PEH) with a newly proposed fast calculation algorithm. Besides, for handing the infeasible solutions of MHOP, a new two-stage truncation method is employed. Through the numerical experiment and the statistical test conducted on some instances of MHOP, the performance of DEMHO is assessed. As a case study, the usefulness of DEMHO is also demonstrated on an optimum design of SAW duplexer.

Optimum design of balanced SAW filters using multi-objective differential evolution

Three Multi-Objective Differential Evolutions (MODEs) that differ in their selection schemes are applied to a real-world application, i.e., the multi-objective optimum design of the balanced Surface Acoustic Wave (SAW) filter used in cellular phones. In order to verify the optimality of the Pareto-optimal solutions obtained by the best MODE, those solutions are also compared with the solutions obtained by the weighted sum method. Besides, from the Principal Component Analysis (PCA) of the Pareto-optimal solutions, an obvious relationship between the objective function space and the design parameter space is disclosed.