This paper proposes a new approach to solve Chance Constrained Optimization Problems (CCOPs). The stochastic objective and constraint values in CCOP are evaluated efficiently by using an approximation of Cumulative Distribution Function (CDF) instead of the primitive Monte Carlo simulation. In order to approximate CDF from samples, a technique of the computational statistics called Empirical CDF (ECDF) is widely known. In this paper, an improved version of ECDF named Weighted Empirical CDF (W ECDF) is used. Then, for solving CCOP, a modified Differential Evolution (DE) combined with W ECDF is proposed. The results of numerical experiments show that DE with W ECDF finds a feasible solution of CCOP and outperforms DE with ECDF in the accuracy of solution.

A new multiobjective optimization problem in presence of noise is formulated and called multi-noisy-hard-objective optimization problem (MNHOP). Since considering the worst case performance is important in many real-world optimization problems, each solution of MNHOP is evaluated based on the upper bounds of noisy objective functions' values predicted statistically from multiple samples. Then an Evolutionary Multiobjective Optimization Algorithm (EMOA) based on Differential Evolution is applied to MNHOP. Three sample saving techniques, namely U-cut, C-cut, and resampling, are proposed and introduced into the EMOA for allocating its computing budget only to promising solutions. Finally, the effects of those techniques are examined through numerical experiments. (C) 2017 Wiley Periodicals, Inc.

A new approach to solve Chance Constrained Optimization Problem (CCOP) without using the Monte Carlo simulation is proposed. Specifically, the prediction interval based on Chebyshev inequality is used to estimate a stochastic function value included in CCOP from a set of samples. By using the prediction interval, CCOP is transformed into Upper-bound Constrained Optimization Problem (UCOP). The feasible solution of UCOP is proved to be feasible for CCOP. In order to solve UCOP efficiently, a modified Differential Evolution (DE) combined with three sample-saving techniques is also proposed. Through the numerical experiments, the usefulness of the proposed approach is demonstrated.

本論文では，最悪状況を考慮した最適化手法を提案する．まず，目的関数や制約条件に含まれる不確実な関数値を確率変数と見なし，チェビシェフの不等式から導出した関数値の予測区間の上限値を解の最悪状況の評価指標として最適化問題を定式化する．次に，「最悪状況を考慮した最適化問題」の解を効率的に探索するため，上限値の計算に必要となる標本数を削減できる3種類の技法（累積サンプリング，信頼性の緩和，U-カット）を示し，それらを組み込んだ差分進化に基づく最適化アルゴリズムを構築する．最後に，複数のテスト問題と工学設計問題を用いた数値実験により，提案手法の有効性を検証する．In this paper, a new worst-case optimization method is proposed. In the worst-case optimization problem, each of the uncertain functions' values included in an objective function and constraints is regarded as a random variable. Then, according to the Chebyshev inequality, the prediction interval of the random variable is evaluated from a number of samples and used to estimate the worst-case. Furthermore, for solving the worst-case optimization problem efficiently, an optimization algorithm based on differential evolution is presented with three sample-saving techniques, namely, the accumulative sampling, reliability relaxation, and U-cut. Finally, the usefulness of the proposed worst-case optimization method is demonstrated through the numerical experiment conducted on three test problems and two engineering design problems.

A new multi-objective optimization problem in presence of noise is formulated and called Multi-Noisy-Hardobjective Optimization Problem (MNHOP). Since considering the worst case performance is important in many realworld optimization problems, each solution of MNHOP is evaluated based on the upper bounds of noisy objective functions' values predicted statistically from multiple samples. Then an Evolutionary Multi-objective Optimization Algorithm (EMOA) based on Differential Evolution is applied to MNHOP. Three sample saving techniques, namely U-cut, C-cut, and re-sampling, are proposed and introduced into the EMOA for allocating its computing budget only to promising solutions. Finally, the effects of those techniques are examined through numerical experiments.

This paper presents a novel computer-aided design method of Surface Acoustic Wave (SAW) filters which are widely used in the modern RF circuits of mobile communication systems. The performance of a SAW filter is specified by a number of criteria. Besides, the performance is deteriorated due to the uncertainties of physical coefficients and design parameters. In the multi-noisy-objective optimization problem of the SAW filter, the worst-case performance of a solution is considered based on the upper bounds of respective noisy-objective functions predicted statistically by multiple sampling. For finding various solutions for the problem effectively, a new evolutionary algorithm is proposed with three sample saving techniques. Finally, the influence of noise on the SAW filter is discussed through analysis of the obtained solutions.

This paper proposes a Golden Section Search (GSS) based adaptive Local Search (LS) for enhancing the performance of two kinds of Differential Evolutions (DEs), namely Synchronous DE and Asynchronous DE. GSS is used to find the minimum between two existing solutions. Therefore, GSS-based LS can be regarded as a Crossover-based LS (XLS). The aim of GSS is not only to improve solutions obtained by DE but also break the stagnation of search. In order to balance between DE and GSS, the frequency and the intensity of GSS are adaptively controlled. Performance comparison between GSS-based LS and an existing XLS is also presented. Furthermore, in order to make the best use of multi-core CPUs, which have been widely used even in personal computers, concurrent implementation techniques of the two DEs coupled with GSS-based LS are proposed.

This paper proposes a new approach to cope with multi-objective optimization problems in presence of noise. In the first place, since considering the worst-case performance is important in many real-world optimization problems, a solution is evaluated based on the upper bounds of respective noisy objective functions predicted statistically by multiple sampling. Secondary, a rational way to decide the maximum sample size for the solution is shown. Thirdly, to allocate the computing budget of a proposed evolutionary algorithm only to promising solutions, two pruning techniques are contrived to judge hopeless solutions only by a few sampling and skip the evaluation of the upper bounds for them.

This paper proposes a novel computer-aided design method of Surface Acoustic Wave (SAW) duplexers which are used widely in the modern Radio Frequency (RF) circuits of various mobile communication systems. The desirable frequency response characteristics of a SAW duplexer are specified by a number of necessary conditions. Besides, the frequency response characteristics of the SAW duplexer depends on its geometrical structure. The major advantage of the proposed design method is that it provides the designer with a set of optimal solutions, or structures, instead of a single solution. Therefore, the designer can choose a solution which of them best lits the application under consideration. According to the proposed design method, the structural design of a SAW duplexer is described as a Multi-Hard-objective Optimization Problem (MHOP) in which each of multiple objective functions is restricted to be less than its upper bound. Then, in order to obtain a number of non-dominated feasible solutions for MHOP, a new evolutionary algorithm based on Differential Evolution (DE) is employed. Finally, through analysis of the non-dominated feasible solutions, or structures, obtained by the DE-based algorithm, suitable structures of the SAW duplexer are considered from various viewpoints.

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.

A new concurrent version of a recently-developed evolutionary algorithm, namely Differential Evolution (DE), is proposed for multi-core CPUs. The proposed concurrent DE is called Island-based DE (IbDE). That is because the population of IbDE is divided into several sub-populations, or islands, in according to the distributed population model. In order to exchange information between islands, a new technique named "panmictic migration" is proposed. Furthermore, a simple but effective technique named "round trip" is employed for updating the respective islands. Through the numerical experiments and the statistical tests conducted on benchmark problems, it is shown that IbDE outperforms the canonical DE and the conventional concurrent DE based on the panmictic population model with respect to both the quality of solutions and the execution time.

In order to utilize multi-core CPUs more effectively, a new Concurrent Differential Evolution (CDE) is proposed. Then the proposed CDE (CDE/G) is compared with a conventional CDE (CDE/S). CDE/S uses only one population because it is based on the steady-state model. Therefore, CDE/S requires a time-consuming mutual exclusion or "lock" for every read-write access to the population. On the other hand, CDE/G is based on the generational model. By using a secondary population in addition to a primary one, CDE/G does not require any lock on the population and therefore is faster. Through the numerical experiment and the statistical test, it is demonstrated that CDE/G is superior to CDE/S in not only the run-time but also the quality of solutions. © 2012 Springer-Verlag.

Recently, multi-core processors, which have more than one Central Processing Unit (CPU), are introduced widely into personal computers. Authors have been proposed a concurrent program of Differential Evolution (DE). The concurrent program of DE, which is called Parallelized DE (PDE), can generate and evaluate multiple individuals in parallel on a multi-core processor. In this paper, two implementation arts of PDE are presented and compared through the numerical experiment and the statistical test. © 2011 IEEE.

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.

In this paper, a new Differential Evolution (DE) that has multiple populations, or islands, is proposed. The proposed DE is called Structured Differential Evolution (StDE). In order to generate a new individual from the current population, various characteristic strategies have been proposed for DE. However, the performances of these strategies depend on the kind of the optimization problem. The proposed StDE uses different strategies in respective islands. Therefore, it can be expected that the proposed StDE is effective for a wide range of optimization problems. Although various networks topologies among islands are reported for island-based evolutionary algorithms, the most popular ones, namely the ring network and the torus network, are employed by StDE. Furthermore, in order to enhance the performance of proposed StDE, various migration policies are examined in two kinds of networks though a variety of benchmark problems.

本論文では種々のネットワークに対する構造差分進化計算(Structued Differential Evolution, StDE)を提案する。
逐次進化計算(Sequential Differential Evolution, SqDE)は近年提案された進化計算(Evolutionary algorithm, EA)であり、SqDEは最適化問題を効率良く解く事ができる。
本論文で提案するStDEはSqDEを並列化したものである。
ベンチマーク問題に対する最適化問題において、ネットワークを用いたStDEはSqDEよりも解を高速に求めることができる。(英文)

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 (PGA) of the Pareto-optimal solutions, an obvious relationship between the objective function space and the design parameter space is disclosed.

Many of the conventional Differential Evolutions (DEs) have employed the discrete generation model that uses two populations, namely, old one and new one. Recently, a new DE based on the continuous generation model is proposed. In the continuous generation model, only one population is used. The new DE is sometimes called Sequential DE (SDE). Besides better convergence, SDE has some advantages. For instance, it becomes easy to introduce various survival selections into SDE. Therefore, four survival selections depending on the distance between two individuals are presented for SDE. Furthermore, in order to compare the effects of the distance dependent survival selections on SDE, not only the numerical experiment but also the statistical test is conducted on various benchmark problems.

進化計算の一種であるDEをMapReduceの概念に基づき並行プリグラムに拡張したCDEを考案し，マルチコア・プロセッサにおいて速度向上率を評価した．（英文）

表情アニメーションを時間オートマトンを用いてモデル化し，その安全性や活性などを時相理論に基づき検証した．

Recently, general-purpose multi-core processors have been introduced widely into personal computers. In order to utilize the additional cores to execute costly application programs such as Evolutionary Algorithms (EAs), concurrent implementations of them are demanded. Even though EAs including various Differential Evolutions (DEs) are naturally prone to parallelism, Sequential DE (SDE) is especially suited for concurrent programming. Therefore, a concurrent implementation of SDE, which is based on the map and reduce framework, is proposed. Through the numerical experiment, the speedup of SDE due to the use of multiple cores is demonstrated. Furthermore, it is shown that the concurrent programming of SDE is efficient, simple, portable and scalable.

Many of the conventional Differential Evolutions (DEs) have employed the discrete generation model that uses two populations, namely, old one and new one. Recently, a new DE based on the continuous generation model is proposed. The new DE is sometimes called Sequential DE (SDE). In the continuous generation model, only one population is used. In this paper, besides SDE, two types of extended SDEs are presented. The first one is called Transversal Differential Evolution (TDE). The second one is called Dispersive Differential Evolution (DDE). In both extended SDEs, more than one trial vectors are generated from a target vector. Then each of the trial vectors is compared with the target vector. However, the place that makes a set of the trial vectors is different in TDE and DDE. In order to evaluate the performances of the three new DEs, namely, SDE, TDE and DDE, not only the numerical experiment but also the statistical test is conducted on various benchmark problems.

Survival selections are proposed for a new Differential Evolution (DE) based on the continuous generation model. Many of the conventional DEs have employed the discrete generation model. In the discrete generation model, two populations, namely, old one and new one, are used. Also, the members of the new population are generated from those of the old one. On the other hand, in the continuous generation model, only one population is used and a newborn individual is added to the population immediately. Besides better convergence, the new DE has some advantages. For instance, various survival selections can be easily introduced into the new DE. Therefore, three survival selections depending on the distance between individuals are proposed for the new DE. In order to evaluate the effectiveness of the proposed survival selections, not only the numerical experiment but also the statistical test is conducted on various benchmark problems. © 2010 The Institute of Electrical Engineers of Japan.

In this paper, a Structured Differential Evolution (StDE) that has multiple populations, or islands, is proposed. Since various characteristic strategies have been contrived for DE, the proposed StDE uses different strategies in respective islands. This technique is called mixed strategies. Therefore, it can be expected that the proposed StDE is effective for a wide range of optimization problems. Although various networks among islands are reported for island-based evolutionary algorithms, the most common one, namely the ring network is employed by StDE. However, in order to enhance the performance of proposed StDE, various migration policies are examined in the ring network though a variety of benchmark problems. © 2010 IEEE.

A structured implementation of Differential Evolution (DE), which can be executed in parallel by using various processor networks, is presented in this paper. Even though Evolutionary Algorithms (EAs) including DE have a parallel and distributed nature intrinsically, Sequential DE (SqDE) is especially suited for the structured implementation of DE. Therefore, the proposed Structured DE (StDE) is based on SqDE. Through the numerical experiment conducted on a variety of benchmark problems, the performances of StDE realized on some different network topologies are compared with the conventional SqDE that uses no processor network. As a result, it is shown that the number of generations spent by StDE to find optimal solutions is smaller than the number of them spent by the above SqDE in many benchmark problems. Therefore, the optimal solutions of almost of the benchmark problems are found more efficiently by using the proposed StDE realized on the processor network.

The structural design of Surface Acoustic Wave (SAW) filters is formulated as a constrained multi-objective optimization problem. Then three Evolutionary Multi-criterion Optimization (EMO) algorithms based on Differential Evolution (DE), namely, Multi-Objective DE (MODE), Non-dominated Sorting DE (NSDE), and Generalized DE 3 (GDE3), are applied to the three- and two-objective optimization problems of a balanced SAW filter. In order to compare the performances of the above EMO algorithms, several criteria including hypervolume are evaluated. As a result, it is shown that the performance of the EMO algorithm depends on the number of objective functions. Besides, in order to clarify the tradeoff relationship among the objective functions of the three-objective optimization problem, Principal Component Analysis (PCA) is employed. © 2010 The Institute of Electrical Engineers of Japan.

This paper presents several survival selection methods for a new Differentiation Evolution (DE) based on the continuous generation model. The standard DE employs the discrete generation model in which the current-generation population is replaced by the next-generation population at a time. On the other hand, only one population is used in the continuous generation model. Because a newborn excellent individual is added to the population and can be used immediately to generate offspring, it can be expected that the new DE based on the continuous generation model converges faster than the standard DE. Furthermore, it becomes easy to introduce various survival selection methods into the new DE. Therefore, five survival selection methods are contrived for the new DE. Finally, the effects of those survival selection methods are studied by using the analysis of variance (ANOVA).

世代モデル，生存選択，複製選択，集団サイズの差異が，微分進化法の性能に及ぼす影響を分散分析を用いて解析した．

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 generation's population is replaced by the next generation's 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).

The frequency response characteristics of the balanced Surface Acoustic Wave (SAW) filters are governed primarily by their geometrical structures. Therefore, in order to realize desirable frequency response characteristics, the structural design of the balanced SAW filter is formulated as a constrained multi-objective optimization problem. Then a recent Evolutionary Multi-objective Optimization (EMO) method, which is called Generalized Differential Evolution 3 (GED3), is applied to the multi-objective optimization problem. Furthermore, in order to clarify the tradeoff relationship among the objective functions of the multi-objective optimization problem, Principal Component Analysis (PCA) is used to assess the set of the non-dominated solutions obtained by GDE3.

平衡型弾性表面波フィルタの構造設計を多目的最適化問題として定式化するとともに，そのパレート最適解集合を進化計算によって求めた．（英文）

Balanced Surface Acoustic Wave (SAW) filters play a key role in the modern Radio Frequency (RF) circuits of cellular phones. The frequency response characteristics of balanced SAW filters depend on their geometrical structures. Therefore, in order to find desirable balanced SAW filters' structures, the design of them is formulated as an optimization problem. Then two types of Evolutionary Algorithms (EAs), namely Differential Evolution (DE) and Genetic Algorithm (GA), are applied to the optimization problem respectively. Experimental results indicate that DE is superior to famous GA in the quality of solution obtained with the same cost.

An optimum design technique of balanced surface acoustic wave (SAW) filters using a differential evolution (DE) is proposed. First of all, in order to evaluate the performance of balanced SAW filters based on the computer simulation, a network model of them is composed by using mixed-mode S-parameters. Then the structural design of balanced SAW filters is formulated as a function optimization problem for improving their performance in both the balance characteristics and the filter characteristics. For solving the function optimization problem, a basic DE is employed. In order to apply the basic DE to the optimization problem effectively, a distorted problem space defined by various design parameters is embedded in a regularized continuous search space. Finally, through the computational experiments conducted on a balanced SAW filter, the usefulness of the proposed optimum design technique is demonstrated. Besides, it is clarified that the non-symmetric structure of SAW filter has a possibility to improve its balance characteristics. © 2008 The Institute of Electrical Engineers of Japan.

Recently, various small devices have been developed for realizing ubiquitous computing environments. However, conventional small devices are not sufficiently support adaptation of their functions to the changes of environments and users' tastes. In this paper, a ubiquitous Q-learning engine is proposed as a small device that has a learning function. First of all, the requirements for a ubiquitous Q-learning engine are described. Then, a new learning algorithm is proposed for the ubiquitous Q-learning engine. The proposed learning algorithm is a revised version of the Q-learning, i.e., a typical reinforcement-learning algorithm, added some unique functions, namely the user's instruction function, the Q-table's exchange function with the network communication, and so on. Furthermore, we show our design and implementation of the ubiquitous Q-learning engine by using a microcontroller. Finally, the ubiquitous Q-learning engine is applied to the speed control of an air-conditioning fan fixed in clothes, and the usefulness of the ubiquitous Q-learning engine is verified through several experiments.

In order to increase the reliability of surface acoustic wave (SAW) filters, a robust optimum design technique is presented. The frequency response characteristics of SAW filters are governed primarily by their geometrical structures, that is, the configurations of the interdigital transducers (IDTs) and reflectors fabricated on piezoelectric substrates. To choose desirable structures of SAW filters through computer simulation, conventional design techniques utilize the equivalent circuit model of the IDT. However, they have rarely considered the accuracy of the underlying model, which may be degraded by the dispersion of the circuit parameters. In this paper, considering the errors of these parameters, the robust optimum design of SAW filters is formulated as a constrained optimization problem. Then, a penalty function method combined with an improved variable neighborhood search is proposed and applied to the problem. Computational experiments conducted on a practical design problem of a resonator type SAW filter demonstrate the usefulness of the proposed method. (C) 2006 Wiley Periodicals, Inc.

An optimum design technique for balanced surface acoustic wave (SAW) filters is proposed. First of all, in order to evaluate the performance of balanced SAW filters by the computer simulation, a numerical model of balanced SAW filters is derived by using mixed-mode scattering parameters. Then the structural design of balanced SAW filters is formulated as a function optimization problem that aims to improve their balance characteristics and satisfy specifications for filter characteristics. Furthermore, in order to solve the function optimization problem successfully, a simple and efficient global optimization method, i.e., the differential evolution (DE), is employed.

A robust optimum design technique for the structural design of resonator-type surface acoustic wave (SAW) filters is presented. For deciding desirable structures of SAW filters based on the computer simulation, the equivalent circuit model of interdigital transducer (IDT), which includes several uncertain constant parameters, is usually used. In order to cope well with the designing imperfections caused by the inevitable dispersion of these parameters, the quality engineering technique, or the Taguchi method, combined with a genetic local search (GLS) is employed. Besides the traditional Taguchi's two-step design maximizing the robustness of products before the realization of their specified functions, the concurrent design of robustness and functions is also described.

In this paper, we propose a ubiquitous Q-learning engine realized by a small-sized microcomputer. In order to reduce the convergence time of Q-learning, we introduce a user's instruction learning mechanism into the engine. As a practical application of the engine, we have developed a fan control device that is fixed on user's clothes and makes a confortable environment for user.

For deciding suitable structures of surface acoustic wave (SAW) filters based on the computer simulation, the equivalent circuit model of interdigital transducer (IDT), which includes several uncertain constant parameters, is usually used. In order to cope with the imperfections of the optimum design caused by the inevitable dispersion of these constant parameters, a technique based on the Taguchi's quality engineering coupled with a memetic algorithm (MA) is presented. Besides the traditional Taguchi's two-step design approach maximizing the robustness of SAW filters before realizing their specified functions, the proposed MA enables us to improve their robustness and functions simultaneously.

A robust multi-objective optimization technique for the structural design of double mode surface acoustic wave (DMS) filters is proposed. The frequency response characteristics of DMS filters are governed primarily by their geometrical structures: the configurations of interdigital transducers (IDTs) and grating reflectors fabricated on piezoelectric substrates. For deciding suitable structures of DMS filters based on the computer simulation, the equivalent circuit models of IDT and grating reflector, which include several uncertain constant parameters, are usually used. In order to cope well with the designing imperfections caused by the inevitable dispersion of these constant parameters, the robust engineering, or the Taguchi method, is employed to evaluate the robustness of DMS filters. Then, because there is a trade-off relationship between the robustness of DNIS filters and their ideal functions, the robust optimum design of DMS filters is formulated as a multi-objective optimization problem. Furthermore, an efficient multi objective evolutionary algorithm, or revised NSGA-II, is used to obtain a set of Pareto-optimal solutions of the problem.

In order to increase the reliability of Surface Acoustic Wave (SAW) filters, a robust optimum design technique is presented. The frequency response characteristics of SAW filters are governed primarily by their geometrical structures, i.e., the configurations of Interdigital Transducers (IDTs) and reflectors fabricated on piezoelectric substrates. For deciding desirable structures of SAW filters through the computer simulation, conventional design techniques utilize the equivalent circuit model of IDT. However, they have rarely considered the accuracy of the underlying model that may be spoiled by the dispersion of circuit parameters. In this paper, considering the errors of these parameters, the robust optimum design of SAW filters is formulated as a constrained optimization problem. Then, a penalty function method combined with an improved variable neighborhood search is proposed and applied to the problem. Computational experiments conducted on a practical design of a resonator type SAW filter demonstrate the usefulness of the proposed method.

Piecewise linear Lyapunov functions are used to design control gain matrices so that closed systems are robust stable and attractive regions are expanded as large as possible in given polytopic regions. The design problems for these specifications are formulated as bilinear programming problems whose constraints are divided into two groups, namely, linear inequalities and bilinear inequalities. In order to solve the constrained optimization problems, this paper presents a genetic algorithm that differs from traditional ones based on penalty techniques. The genetic algorithm starts from a feasible solution and retains its offspring, or population, within feasible region. Besides the method creating such a starting point, several techniques are proposed to develop the diversity of population.

From the viewpoint of the Affordance Theory advocated by J. J. Gibson, an ecological approach for realizing artificial skills is presented in contrast to the conventional paradigm of behavior-based robots known as "sense, think and act".A perception-driven robot demonstrates the usefulness of the ecological approach through the assembly task of mating several parts on a plane. Instead of action-rules based on sensory information, the proposed robot employs a kind of oscillator, Action Pattern Generator (APG), for taking active action before perception. The limitations of the simple robot, the actions of which are dominated by APG, are also discussed. Then, in order to compensate APG for lack of the rationality in choosing actions, two types of memories, namely Working Memory (WM) and Episodic Memory (EM), are introduced into the robot's brain. Consequently, the perception-driven robot has the abilities to distinguish the shapes of various parts, mount them in right places, and stop its motion automatically.

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 grating reflectors fabricated on piezoelectric substrates. In the process of designing optimal structures for SAW filters, computer-aided design techniques utilize theoretical model of IDT for estimating their performances. In this paper, considering dispersion of uncertain parameters included in IDT's model, the robust design of SAW filters is formulated as a constrained optimization problem. Then, a new penalty function method combined with a variable neighborhood search (VNS) is applied to the optimization problem. Computational experiments conducted on a practical design of SAW filter demonstrate the usefulness of the proposed robust design approach.

An optimal design approach for Surface Acoustic Wave (SAW) filters is presented. The frequency response characteristics of SAW filters are governed primarily by their geometrical structures, i.e., the configurations of respective interdigital transducers (IDTs) arranged on piezoelectric substrates. First of all, for realizing a desirable bandpass filter, the structural design of a three-IDT type SAW filter, which consists of three IDTs 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 variable neighborhood search based on the k-degree-neighborhood is proposed for solving the optimization problem. Changing the number of examined variables in the process of local search, it avoids being trapped in the first local optimal solution found. Computational experiments conducted on the practical design problem of the three-IDT type SAW filter demonstrate the usefulness of the proposed variable neighborhood search. © 2003, The Institute of Electrical Engineers of Japan. All rights reserved.

The inverse kinematics of redundant arms is formulated as a constrained optimization problem, where the configuration of the arm is optimized for decoupling its endpoint compliance matrix as much as possible. Then a global optimization method using the interval analysis is presented for solving the problem. Experimental results demonstrate the characteristic of the proposed method and also exhibit the best configuration of a redundant arm engaged in the Peg-in-Hole task.

In order to find the plural number of optimal solutions for the module placement problem, which is of particular significance in the design of VLSI, a new Genetic Algorithm (GA) based on Imanishi's evolutionary theory is proposed. First of all, a phenotypic distance between two solutions, or individuals, is defined as the shortest Hamming distance between sets of isomorphic genotypes. If the phenotypic distance between two individuals is shorter than a threshold value, they are regarded as the same species. Then, a new generation alternation model that is analogous to the habitat segregation is presented. Since each individual in the population represents an isolating species, the diversity of the population is maintained spontaneously. Even though the selection of individuals based on their fitness is not employed, excellent individuals are created effectively by using the harmonic crossover operation combined with a local optimization method.

An intelligent robot which distinguishes several different environments and completes the task demanded in each environment is described. Through the interaction with the surrounding environment, the robot recognizes not only current environment but also its own position successfully, whereas the robot has no map representing the world in which it is going to act. For the great work, the robot finds and uses the appropriate affordance lurking in the surrounding environment. The brain of the robot is defined by a Finite State Machine (FSM) and is evolved by using a Genetic Algorithm (GA) . In order to create the target FSM effectively, new genetic operations based on the Lamarckism are also proposed. Computational experiments show that the proposed genetic operations are superior to the conventional ones in both the quality of FSM and the velocity of evolution. Furthermore, observing the behavior of the intelligent robot, affordance is specified in each environment concretely.

This paper presents a new task-generation method for robot-arm control computation on a multi-processor system with an arbitrary number of processors. In order to execute the effective parallel processing which achieves high speed-up ratio, the definition of optimal task-set is an essential problem. The proposed task-generation method, which is based on algebraic computation techniques, consists of three phases: 1) Derive a robot-control law by using symbolic languages, such as Mathematica or REDUCE, as a set of expressions; 2) Transform the expressions into a simplest possible form which does not contain any redundant operations. In this phase, the factorization algorithm which was recently proposed by the authors is used; 3) Divide each equation into subexpressions repeatedly to induce the parallelism of computation. Consequently, each of the optimized expressions is regarded as one task. By using the proposed task-generation method, an automatic parallelizing compiler is also developed. Experiment on the inverse dynamics computation of a six-joint robot-arm demonstrates the effectiveness and the usefulness of the proposed task-generation method.

In this paper, a method to compute an almost correct region of PID parameters which guarantees robust stability and several robust performances for systems with real uncertain parameters is proposed. The proposed method can be compute the region in a short computing time by adopting the following idea and technique : The first one is the computational strategy to avoid the unnecessary small splitting of the parameter space of the PID controller. The second one is adopting the idea of computational geometry approach to reduce the time for executing the algorithm. The third one is to use the Non-convex Polygon Interval Arithmetic (NPIA) to compute the "good" estimate of value sets of transfer functions.

This paper presents a genetic algorithm (GA) for scheduling problem of a robot control computation. That is very difficult problem which belongs to the class of NP-hard problems. The authors have already proposed several algorithms, which are based on heuristic and branch-and-bound approaches, for the scheduling problem. The conventional algorithms, however, have the limits of their ability in quality of solutions and computational time. The scheduling problem is a typical partitioning problem : partitioning objects into a fixed number of groups to optimize an objective function. Consequently, this paper proposes a new crossover method named weighted-edge crossover which preserves both the structure and the characteristic of the feasible solution of partitioning problem. Furthermore, in order to improve the performance of GA, this paper defines a distance between feasible solutions and uses it in the adaptive control of crossover rate. To demonstrate the effectiveness of the proposed GA, comparative study of the GA with the conventional algorithms is carried out on several computational experiments.

A parallel processing scheme is described for robot control computation on MIMD shared memory multi-processor model. Since dynamic control law of robot arm usually contains a large amount of operations compared with the number of available processors, it is important to consider not only the effect of parallel processing but also the efficiency of serial processing in each of the processors. In order to obtain such a desirable solution for the complex scheduling problem, optimization and quasi-optimization algorithms are proposed. The excellent optimization algorithm is based on a branch-and-bound method. On the other hand, the practical quasi-optimization algorithm is based on a partial enumeration method which effectively combines the optimization algorithm and the approximation algorithm (GCF/LPT) ; that was recently developed by authors. The proposed scheduling algorithms are applicable to parallel processing of any kinds of control laws represented by sum of products. The test results on the dynamic control computation of robot arms demonstrate the usefulness of the algorithms.

Dynamic control is one of the methods which enable quick and accurate motion of robot arms. However, this method has been rarely applied to industrial robots. One reason is that dynamic control has been difficult to be performed real time by using presently available processors since it requires huge amount of computation. Described in this paper is an optimizing compiler which can automatically generate an efficient program for dynamic control computation of robot arms. Source program, which can be developed with an algebraic computation system like REDUCE, is given as symbolic equations. The optimizing compiler transforms the equations into a set of statements which has a possible simple form of computation. The method is based on the factorization algorithms proposed by authors. After that, the optimized statements are encoded by C Language and arranged for an object program. The optimizing compiler is designed according to an object oriented approach. The effectiveness of the optimizing compiler is also shown through experiments.

In this paper, a method to compute almost exact gain margin of uncertain control systems using Polygon Interval Arithmetic (PIA) is proposed. The main problem here is to determine 0-exclusion property of the value set of the characteristic polynomial. By using PIA, we can compute the convex hull of the value set very fast. When we need a better estimate of the value set, we need to split a region of uncertain parameters : however, the method to decide which region should be split was not given, and it may require very large computing time to get a good estimate. In this paper, we confine ourselves to the case when an expression of characteristic polynomial which corresponds to a totally decomposable tree structure decomposition is given, and we propose a method to decide which region should be split. By adopting this method, we Can compute a good estimate in a short time.

A parallel processing scheme is described for dynamic control computation of a robot-arm on any number of parallel processors. The control law for dynamic control of the robot-arm is generally represented by the sum of products. Such a control law usually consists of a huge number of operations. However, some of these operations are redundant and may be reduced by factorization. This paper proposes a practical scheduling algorithm which assigns the operations of the control law to parallel processors considering how many of them could be reduced by factorization.<BR>Based on the proposed algorithm, a scheduling system is also developed by using an object oriented approach (<I>g</I>++). Then, a wonderful effect of the proposed algorithm is demonstrated through examples.

In this paper, we consider the implementation of real-time digital controller under multi-DSP's environment. Proposed is a new configuration of multi-DSP system and parallel processing scheme which possibly shorten the sampling period under minimum throughput time for the digital controller. We formulate the schenduling problem of the multi-DSP system to realize the given control law as a difference equation, and derive a reasonable solution of the problem. We also illustrate a concrete hardware configuration of the multi-DSP system. Then we show that the multi-DSP system successfully avoid data collision by using bus buffers and the suitable scheduling for DSPs. In the discussion of memory allocation and management, we propose the way to conserve the data struture without moving any data in the memory. Finally, we evaluate the proposed multi-DSP system compared wiht the other multi-DSP system in an application. The proposed methods can be applied to general DSPs, and examples are given for particular DSP, TMS 320 C 25.

進化計算の一種である差分進化（DE）につて解説した．

進化計算を利用した平衡型SAWフィルタの設計法につて解説した．（英文）

フェースディスプレイとは，人間とコンピュータのインタラクションを円滑にすることを目的として，様々なアプリケーションに 「顔」 を与えるものであり，アプリケーションの状態に応じた表情アニメーションをリアルタイムで実行する．本稿では，教育支援システム 「ロボット TA」 を対象として，時間オートマトンを用いたフェースディスプレイの上位設計法を紹介する．さらに，ゲームニクス理論に基づき，テレビゲームの技法を取り入れることで，フェースディスプレイの機能を拡張する．For achieving the smooth interaction between humans and computers, the face display gives a face to an arbitrary application. Exactly speaking, the face display performs the animation of human's faces synchronizing with various states of the application. This paper presents a face display designed for a computer-aided education system called robot TA. First of all, a high-level design method of the face display that uses timed automata is described. Then, in accordance with Gamunics theory, the function of the above face display is extended by importing some techniques from popular video games.

プロセッサネットワーク上での混合戦略を用いた差分進化計算を提案し、いくつかのテスト関数に対して数値実験を行った．

本論文では種々のネットワークに対する構造差分進化計算(Structued Differential Evolution, StDE)を提案する。 逐次進化計算(Sequential Differential Evolution, SqDE)は近年提案された進化計算(Evolutionary algorithm, EA)であり、SqDEは最適化問題を効率良く解く事ができる。 本論文で提案するStDEはSqDEを並列化したものである。 ベンチマーク問題に対する最適化問題において、ネットワークを用いたStDEはSqDEよりも解を高速に求めることができる。(英文)

進化計算アルゴリズムの一種であるDifferential Evolutionを並行プログラムとしてマルチコア・プロセッサにより実装する技法を考案した。

本論文では種々のネットワークに対する構造差分進化計算(Structued Differential Evolution, StDE)を提案する。 逐次進化計算(Sequential Differential Evolution, SqDE)は近年提案された進化計算(Evolutionary algorithm, EA)であり、SqDEは最適化問題を効率良く解く事ができる。 本論文で提案するStDEはSqDEを並列化したものである。 ベンチマーク問題に対する最適化問題において、ネットワークを用いたStDEはSqDEよりも解を高速に求めることができる。(英文)

Conventional Differentiation Evolution (DE) has been based on the discrete generation model in which the current generation's population is replaced by the next generation's population at a time. In this paper, a new DE based on the continuous generation model is presented. Then, by using the techniques of the analysis of variance, the effects of the two generation models on the performance of DE are compared statistically. As results, the advantage of the new DE based on the proposed continuous generation model is clarified.

This paper proposes a robust optimum design technique for Surface Acoustic Wave (SAW) filters. The frequency characteristics of SAW filters are governed primarily by their geometrical structures, namely, both of the configurations and the arrangements of Interdigital Transducers (IDTs) fabricated on piezoelectric substrates. For deciding optimal structures of SAWfilters, traditional design techniques estimate their frequency characteristics based on the equivalent circuit mode of IDT. However, they have rarely considered the reliability of the equivalent circuit mode of IDT even though it may be spoiled by the scattering of parameters' values. In the robust optimum design of SAW filters, the proposed design technique employs a penalty function method combined with a variable neighborhood search and counts errors due to inaccuracy of the equivalent circuit mode of IDT. Computational experiments conducted on an optimum design of a practical three-IDT type SAW filter demonstrate the usefulness of the proposed design technique.

This paper proposes a robust optimum design technique for Surface Acoustic Wave (SAW) filters. The frequency characteristics of SAW filters are governed primarily by their geometrical structures, namely, both of the configurations and the arrangements of Interdigital Transducers (IDTs) fabricated on piezoelectric substrates. For deciding optimal structures of SAW filters, traditional design techniques estimate their frequency characteristics based on the equivalent circuit mode of IDT. However, they have rarely considered the reliability of the equivalent circuit mode of IDT even though it may be spoiled by the scattering of parameters' values. In the robust optimum design of SAW filters, the proposed design technique employs a penalty function method combined with a variable neighborhood search and counts errors due to inaccuracy of the equivalent circuit mode of IDT. Computational experiments conducted on an optimum design of a practical three-IDT type SAW filter demonstrate the usefulness of the proposed design technique.

In this paper, a method to implement Non-convex Polygon Interval Arithmetic (NPIA) is presented. NPIA is an arithmetic defined on the set of all (non-convex) polygons in the complex plane. The operations (that is, addition, multiplication and inversion) gives a polygon contained an ε neighborhood of the value set of the corresponding operation. The main issue of this approach is to compute the outer boundary of the union of many polygons. An implementation method based on the computer geometry the geometric intersection algorithm is presented. NPIA can give an estimate region which is included an ε neighborhood of the value set of a given function f(s, q) which includes uncertain parameters q.

The main results obtained through the research are summarized as follows: 1. On-line reference input shaping using reference governor and regulator theory. We proposed to use the optimal regulation control for a given servo systems. By using this with reference governor, we can improve the control performance very much. 2. An efficient method to use reference governor. For each constant reference input r, the maximal admissible set O (r) is determined. To execute reference input shaping using reference governor, for each t, we need to determine the state x(t) of the systems is contained in which O(r). We proposed an efficient algorithm to do it. 3. Maximal admissible set computation for continuous time systems. We proposed a computation method of subset of the maximal admissible set for continuous nonlinear systems with uncertainty. This is a generalization of the previous result for linear continuous time system without uncertainty. 4. Design of nonlinear digital servo systems. It is not easy to characterize the uncertainty class for discrete time systems which are obtained by some discretization of continuous systems. 5. On-line reference input shaping using sliding mode control. By applying on-line reference input management method, we proposed a sliding mode control scheme for systems with constraints. 6. Model predictive type control. We proposed a model predictive type control scheme which is quite similar to the model predictive control scheme. The advantage of our model predictive type control is it gives quasi globally optimal solution of the original optimization problem.

The main results obtained through the research are summarized as follows. 1.Generalization of the class of piecewise linear Lyapunov functions. We proposed a new class of piecewise linear Lyapunov functions (PWLLFs) and derived stability results. A candidate of PWLLF has parameters corresponding to piecewise linear function defined in the region divided by hyperplanes. The set of stability conditions are formulated as Linear Programming Problem (LP) in terms of parameters inserted by piecewise linear functions. If the computed optimal value is negative, we construct a PWLLF using the solution. When the optimal value of the LP is nonnegative, we modify the PWLLF candidate by adding appropriate hyperplanes to introduce more freedom in the LP formulation and arrive at the desired result. We derived a new condition for generating hyperplanes such that the optimal value of the new LPs is less than that of the old LP. This condition is an improvement of the previous result. By adopting this method, we can generate a PLLF for some systems, for which we could not generate a PLLF. 2.Enlargement of estimates of stability regions. In this research project, we are interested in semi-global stability rather than the global stability. In this respect, it is very important issues to compute larger estimates of stability regions or to design controller so that the closed system has large stability region. We proposed a method to achieve this. 3.Design of nonlinear servo systems. We proposed a design method of nonlinear servo systems by using PLLFs. This method reduces conservativeness included in previous results. To improve the transient response characteristic, we proposed a scheme, which adopts idea based on the reference governor and the linear quadratic regulator theory. 4.Fast solving methods for bilinear optimization problems. When we design controller using PLLFs, we need to solve bilinear optimization problems, which are not convex problems. To solve bilinear optimization problems, we applied the Zoutendijk's method, a genetic algorithm based on Imanishi's evolution theory and the probabilistic approach for some examples. Each method has both the advantage and the disadvantage. Further research on this issue is needed.

In this research, we developed new methods of knowledge discovery under incomplete knowledge. The proposed systems compute abductive and inductive hypotheses based on consequence-finding procedures. Research results can be summarized as the following three items. 1. Efficient computation for consequence finding We adopted SOL resolution by Inoue as a consequence-finding procedure and made it more efficient. In particular, we developed SOL-S(Г) tableaux for efficient speculative computation in multi-agent systems and default reasoning. Moreover, we re-implemented SOL tableaux in Java, and developed a faster consequence-finding procedure SOLAR (SOL for Advanced Reasoning). 2. Basic theories for consequence finding and knowledge discovery We proved that SOL resolution is complete for answer extraction in first-order clausal theories. This is a solution of an open problem for answer completeness in a connection tableaux format. We also considered a hypothesis-finding procedure based on consequence finding (called CF-induction), and found a complete method for generalization in CF-induction. Moreover, we established a unified theory for induction, which combines explanatory induction and descriptive induction. This inductive formalization is based on circumscription, and uses SOL resolution and CF-induction for computing hypotheses. 3. Evaluation and applications of hvpothesis-finding procedures We applied SOL resolution to bioinformatics, and considers the use of extended abduction, which enables us to remove hypotheses as well as addition of them.

In recent years, manufactures are required to product many kinds and small numbers of manufactured goods effectively and economically. The purpose of this research is to present a new design methodology of products that considers functional diversity and structural similarity among them. First of all, the procedure of designing products is formulated as an appropriate optimization problem. Then, for finding various optimal solutions of the optimization problem, a meta-heuristic method, such as genetic algorithm and variable neighborhood search, is employed. In order to demonstrate the usefulness of our proposed design technique, we have studied the following practical problems. 1. Module Placement Problem In order to find the plural number of optimal solutions for the module placement problem, which is of particular significance in the design of VLSI, a new Genetic Algorithm (GA) based on the Imanishi's evolutionary theory is proposed. A new metric function is also employed to evaluate the diversity of solutions, or individuals, included in the population. 2. Assembly Robot Control For sampling various solutions from the entire Pareto front of the multiobjective resource division problem, functional and structural distances between two solutions are introduced. Then, the Imanishian GA is applied to the problem. 3. Optimal Design of Electronic Device The structural design of a three-IDT type Surface Acoustic Wave filter is formulated as a combinatorial optimization problem. Then, a new local search method based on the k-degree-neighborhood is proposed and applied to the problem.

In this research project, a new concept so-called "interactive algorithm" is advocated, where some superior function is emerged through the interaction among several systems including a human being. Concretely, five types of systems are considered, namely, computer, human, robot, optimization algorithm, and environment. First of all, an intelligent robot that distinguishes several different environments and completes a given task is studied. Through the interaction with surrounding environment, the robot recognizes not only current environment but also its own position successfully, whereas the robot has no map representing the world in which it is going to act. Next, in order to realize the emergent approach for design of artificial systems, a man-machine cooperative design tool, Interactive Genetic Algorithm Viewer (IGAV), is developed and applied to the optimal design of mobile manipulators. Finally, a meta-heuristic strategy that combines the global search power of GA with the local search power of conventional local optimization algorithm effectively is proposed.

帰納的論理プログラミング(ILP)は,関係記述の帰納的学習のための理論と実用的な学習アルゴリズムを研究する分野であるが,従来の研究では,学習されるプログラムの形式として,主に確定ホーンプログラムのような単調なクラスのものが考えられていた.本研究では,ILPにおいて常識規則やデフォルト規則を学習するために,非単調推論なクラスを学習できる帰納推論の枠組を考案し,不完全な情報下での学習方式の理論の確立とその実装システムの開発を行った.2年間の研究実績は以下の通りである。 1.背景知識と正負例を入力として与えたときに,拡張論理プログラムの形式で学習されたプログラムを出力するシステムLELPに関して,その正当性の証明を含む理論的整備を行った. 2.正例をすべてカバーする一般規則を生成するシステムを,ボトムアップおよびトップダウンの2種のアルゴリズムを用いて開発した.さらにこの部分を高速化するために,Java言語を用いたり,遺伝的アルゴリズムの適用も図った.また,規則を生成する際の探索空間を絞るために,帰納推論に適したバイアスを自動的に定めるための方式を開発した. 3.アブダクション(発想)の機能を有するアブダクティブ論理プログラムを出力とするようなLELPの変形についても基礎的な考察を行った.この中で,新仮説発見の手法を考案し,非単調推論において優先度に関するメタ知識を自動的に発見する方法に応用した.

本研究においては,さまざまな最適化問題に対して,効果的な進化型計算の構築法を提案するとともに,その有効性について計算機実験による多角的な評価を行った。また,個体間の構造的な距離を導入することにより,進化型計算の挙動を定量的に評価するための解析手法を提案した。提案した手法によれば,進化の過程における個体集団の多様性や交叉における形質遺伝性を,問題固有の解空間の観点から直観的に理解することが容易となり,進化型計算の挙動解析のみならず,理論的な発展にも寄与できるものと期待される。本年度は,昨年度からの自立行動ロボットに関する研究に加えて,NP困難な組合せ最適化問題の実質的なベンチマーク・テストである巡回セールスマン問題に対して,効果的な遺伝的アルゴリズムの構築を提案するとともに,個体間の距離に基づく挙動の解析を行った。 (1) ロボットプログラムの自動生成:包摂アーキテクチャなど実際の自立行動ロボットのプログラムが,有限状態機械として記述されていることに着目して,進化型計算による有限状態機械の自動生成を試みた。特に,進化型計算の効率化においては,ラマルク進化論の概念を遺伝演算子に導入することにより,個体集団の進化速度を向上させるとともに,最終的に得られる個体の性能を高めることに成功した。昨年度は,有限状態機械に対するラマルク的な突然変異を提案したが,本年度は,新たに有限状態機械のラマルク的な交叉法を考案して,進化型計算による有限状態機械の自動生成手法を完成させた。 (2) 巡回セールスマン問題における遺伝的アルゴリズムの挙動解析:完全グラフ上のハミルトン閉路を個体と見なし,個体間に構造的な距離を定義することにより,巡回セールスマン問題対する遺伝的アルゴリズムの挙動を定量的に評価するための解析手法を提案した。さらに,順序問題に対する従来の交叉法において,個体間の距離を利用する調和交叉法を提案した。調和交叉法によれば,新たに得られる子の個体が解空間において常に両親の中間に位置するため,従来の交叉に比べて局所的探索能力が向上するとともに,交叉における形質遺伝性が個体間の距離に基づき定量的に保証されることを証明した。

We studied practical methodology to design an effective genetic algoritym for the scheduling problem of robot control computation. Then, we proposed the following techniques applicable to the implementation of genetic algorithms for many combinatorial optimization problems. (1) Encoding of isomorphic genotype : A phenotype is usually represented by several genotypes. We have proposed a new technique to represent each phenotype uniquely by using a set of isomorphic genotypes. We could maintain the diversity of population with the encoding technique. (2) Phenotypic Distance : We have defined the phenotypic distance between two phenotypes by the least Hamming distance between isomorphic genotypes. By using the phenotypic distance in genetic operations, we could evaluate and control the diversity of population. (3) Weight-Edge Crossover : We have proposed a new crossover which combines the conventional edge crossover with a heuristic insight to preserve the excellent characteristic of parents. Experimental results showed that the proposed crossover was superior to the conventional ones.

Results obtained by this project are summerlized as follows : 1) Definition and Implementation of Polygon Interval Arithmetic. We proposed two kinds of the polygon interval arithmetic and implemented both of them. One is the arithmetic defined on the sets of convex polygons (we call this CPIA), and the other is that defined on (not necessarily convex) polygons (we refer this NPIA). Operations are the addition, the multiplication, and the inversion of polygons. In the implementation of them, we used recent results on computational geometry. 2) Computation of Gain Margin We proposed four method using PIA,which are improvement of the method proposed by Gaston, and one method using NPIA.The latter method is superior to the former when a totally decomposable expression of transfer functions. 3) Robust Root Loci Method. In the practical points of view, we proposed a robust root loci method which is able to assign the regions of the representative roots, dipoles, and other roots. 4) Design of Robust PID Controllers. We developed a CAD system for the design of PID controller which satisfies several robust performances. 5) Development of CAD System for Robust 2 Degree of Freedom Systems. We developed CAD system for robust 2 degree of freedom systems which has functions described in 3) and 4), and classical frequency response method.

本研究においては、実際の並列処理システムにおいて適用可能な、最適な負荷分散手法を提案すると共に、ロボット・アームの計算機制御に応用して、その有効性を確認した。 (1)スケジューリング問題の定式化:並列計算機モデルとしては、実用性と汎用性に優れたMIMD分散メモリ方式を採用した。また、並列化するプロセッサとしては、シグナル・プロセッサ(DSP)を使用した。この並列処理システム(マルチDSPシステム)において、データ処理のタイミングに関わる、幾つかの時間的な制約条件を明かにすると共に、スケジューリング問題を組合せ最適化問題として定式化した。 (2)最適化アルゴリズムの提案:対象とするスケジューリング問題に対して、分枝限定法に基づき最適解を厳密に求めることができる最適化アルゴリズムと、実用的な準最適化アルゴリズムをそれぞれ提案した。 (3)最適化コンパイラの開発:並列処理全体としての効率を高めるためには、並列化された各プロセッサ事に行われる逐次処理の計算効率を高める必要がある。そこで、数式処理的な手法を用いて、計算プログラムを、含まれる演算回数が最少であるという意味で最適化することができる最適化コンパイラを開発した。 (4)ロボット・アームの制御への応用:提案した並列処理手法とスケジューリング・アルゴリズムを、ロボット・アームの計算機制御による実時間処理に応用して、その有効性と実用性を確認した。 (5)今後の研究の展開:並列処理は、ロボット・アームの制御則の計算のように、膨大な演算を含む計算の実時間処理において、特に嘱望されている。ところが、スケジューリング問題の規模が大きくなると、最適化アルゴリズムが使用できないために、効率的な並列処理が行えないというジレンマに陥る。 そこで、今後の研究の展開としては、スケジューリング問題に対する確率的アルゴリズム(遺伝的アルゴリズム)の構築方法を検討すると共に、今回提案した各アルゴリズムとの比較を行いたい。

1. Algorithm for lmproving polytope lyapunov Function : We examined several method to improve polytope Lyapunov functions, and we conclude that the most useful method is that adding vectors which are extreme points of vector field generated by the generalized sector conditions to the present polytope. Moreover, by using real Jordan canonical form, we proposed a method to generate useful an initial polytope. 2. Dynamic Convex Hull Algorithm : We proposed a new dynamic convex hull algorithm which requires less memories and computing time than the Beneath-Beyond method. 3. Discontinuous Systems : We derived a stability result for discontinuous systems which may have sliding modes. The result is almost same with that for continuous systems. Moreover, by using a polytope Lyapunov function, we proposed a design method for variable structure control systems. This method can eliminate chattering. 4. Applications : We applied the polytope Lyapunov function to the stability analysis of composite systems. We also applied it to the stability analysis of fussy control systems, and showed that, by applying generalized sector conditions, we can guarantee the stability with less conservative conditions than the traditional Lyapunov functions such as quadratic Lyapunov functions and so on.