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Parameterizations and Fixed-Point Operators on Control Categories

Kakutani Y., Hasegawa M.

Fundamenta Informaticae

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2005

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Vol. 65, nr 1,2

153--172

EN

The lm-calculus features both variables and names together with their binding mechanisms. This means that constructions on open terms are necessarily parameterized in two different ways for both variables and names. Semantically, such a construction must be modeled by a biparameterized family of operators. In this paper, we study these biparameterized operators on Selinger's categorical models of the lm-calculus called control categories. The overall development is analogous to that of Lambek's functional completeness of cartesian closed categories via polynomial categories. As a particular and important application of such consideration, we study the parameterizations of uniform fixed-point operators on control categories. We show a bijective correspondence between biparameterized fixed-point operators and nonparameterized ones under the uniformity conditions.

2

Optimization using chaotic neural network and its application to lighting design

Nanba R., Hasegawa M., Nishita T., Aihara K.

Control and Cybernetics

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2002

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Vol. 31, no 2

249-269

EN

We have developed a chaotic neurodynamical searching method for solving the lighting design problems. The goal of this method is to design interior lighting that satisfies required illuminance distribution. We can obtain accurate illuminance distribution by using the radiosity method to calculate interreflection of lights. We formulate the lighting design problem that considers the interreflection of lights as a combinatorial optimization problem, and construct a chaotic neural network which searches the optimum solution of the lighting design problem. The calculated illuminance distribution is visualized using computer graphics. We compare this optimization method with the conventional neural network with gradient dynamics, simulated annealing, and the genetic algorithm, and clarify the effectiveness of the proposed method based on the chaotic neural network.

3

Exponential and chaotic neurodynamical tabu searches for quadratic assignment problems

Hasegawa M., Ikeguchi T., Aihara K.

Control and Cybernetics

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2000

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Vol. 29, no 3

773-788

EN

We propose a chaotic neurodynamical searching method for the Quadratic Assignment Problems (QAPs). First, we construct a neural network whose behavior is the same as that of the conventional tabu search. Using the dynamics of the tabu search neural network, we realize the exponential tabu search, whose tabu effect decreases exponentially with time, and we show the effectiveness of this type of exponential tabu search. Next, we extend this novel tabu search to a chaotic version. This chaotic method includes both effects of the chaotic dynamical search and the exponential tabu search, and exhibits better performance than the conventional and exponential tabu searches. Last, we propose an automatic parameter tuning method and show that the proposed method exhibits high performance even on large QAPs.