In this paper we discuss a certain constrained optimization problem which is often encountered in the geometrical optimization. Since these kinds of problems occur frequently, constrained genetic optimization becomes very important topic for research. This paper proposes a new methodology to handle constraints using the Genetic Algorithm through a multiprocessor system (FIN) which has a self-similarity network.

Genetic Algorithm (GA) is the method of approaching optimization problem by modeling and simulating the biological evolution. As the genetic algorithm is rather time consuming, the use of a parallel genetic algorithm can be advantage. This paper describes new methods for fine-grained parallel genetic algorithm using a multiprocessor system FIN. FIN has a VLSI-oriented interconnection network, and is constructed from a viewpoint of fractal geometry so that self-similarity is considered in its configuration. The performance of the proposed methods on the Traveling Salesman Problem (TSP), which is an NP-hard problem in the field of combinatorial optimization, is compared to that of the simple genetic algorithm and the traditional fine-grained parallel genetic algorithm. The results indicate that the proposed methods yield improvement to find better solutions of the TSP.

A segmentation-free learning recognition system for binary signals has been constructed by using a cellular automaton array, known as a max-product cellular automaton array. Each cellular automaton has transition functions concerning activities, similarities, and inner states. Learning is carried out by the linearly reinforcement method of the inner states. The activity is transferred from the left neighbor cells to the right neighbor cells. Terminal decisions for categories are given by outputs of categories in the case that the activity of the output cell has the maximum value. Also, another system for analogue signals has been constructed. A coefficient of separation is introduced in order to separate analogue signals. Experiments by computer simulation gave good results for both systems.

In this paper, a segmentation-free learning recognition system for two-dimensional and time-serial binary signals is proposed. This system is constructed by using an array of cells, known as the max-product automata, and can recognize time-serial signals segmentation-freely. Learning is carried out by the learning with the second moment matrix of input vectors. Decisions of this system are made by the majority of categories. Experiments by the computer simulation have given good results.