The genetic algorithm (GA) is one of basic models of evolution and is one of the effective tools for constructing evalvable/adaptive complex systems. There are two distinct approaches to genetic based machine learning(GBML). These two approaches are called the Michigan approach and the Pitt approach. The Michigan approach uses a single set of production rules or classifiers. This approach needs an apportionment of credit system to adjust strength of the rules in proportion to the amount of payoffs from the task environment as well as to the contribution of the rules to the goal. The individual in the Pitt approach, on the other hand, comprises a set of rules. Each set of rules is used in the production system and the payoffs from the environment are directly given to the set of rules. The Pitt approach does not need the apportionment of credit system. However, through some experiments using the Pitt approach, it has been found that the improvement of individual rules of a chromosome is hard to achieve.This paper presents a genetic algorithm with a local improvement mechnism and the new method is applied to the machine learning. The new algorithm is efficient in improving the local portions of the chromsomes. An obstacle avoidance of mobile robot is simulated using the new method and fuzzy control rules are found.

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This paper proposes a method to organize a hierarchical structure of fuzzy model with the genetic algorithm and back-propagation method. The number of fuzzy rules increases exponentially as the number of input variables increases. Hance the fuzzy system with many input variables has extremely large number of fuzzy rules.Hierarchical structure of fuzzy reasoning is one of the methods to reduce the number of fuzzy rules and membership functions. However the hierarchical structure cannot be made without considering the relation among input and output variables. The proposed method can organize the suitale hierarchical structure for the relation among input and output variables. It is based on the genetic algorithm with an evaluation function as a strategy that adopts a system with fewer fuzzy rules and membership functions and more accurate outputs. The proposed method is applied to the approximation problems of multi-dimensional nonlinear functions in order to show the effectiveness.

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Although it is often claimed that due to their probabilistic character genetic algorithm(GA's)are able to avoid getting trapped in local minima, this statement is only valid in a very narrow sense. Especially when it comes to apply GA's for fuzzy model and controller optimization one faces several problems. The reason for this lack of performance lies in the nature of the optimization task itself. For a better understanding of the problem, we first compare the simple genetic algorithm with the simplex downhill optimization method under three different initial conditions. Consequently, we propose an anticipating GA to solve the above mentioned problem. To enhance computing time, this proposed GA is further combined with the downhill simpl exmethod in the final stage of the optimization. Thus, resulting in a hybrid algorithm.

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We propose a method to express a large amount of data using combinations of linguistic labels. With this technique, we can understand the outline of data, when a large number of data are given. In general, however, the number of combinations of linguistic labels is very large and almost impossible to search the optimum combination. In addition, the criterion to evaluate the combinations of linguistic labels tends to be complex. So, we propose the method to search the optimum combination using genetic algorithm. In the proposed method, we define new genetic operations to preserve parent individual's character. When a data set is expressed in two different combinations of linguistic labels, each of which is a parent individual, a new crossover to exchange parts of the combinations is defined. A new mutation to create a new combination or to delete the combination is also defined.These genetic operations enables us to create a new combination, and we get the optimum combination, at last.We applied the proposed method to real-estate data, and show its effectiveness.

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This paper illustrates how genetic algorithms can be applied to the rule selection problem for constructing a fuzzy-rule-based classification system by a small number of fuzzy if-then rules. First, we briefly describe our former approach where genetic algorithms were applied to the rule selection problem with two objectives : to minimize the number of selected fuzzy if-then rules and to maximize the number correctly classified patterns. Next, we introduce a fuzzy partition method that divides a pattern space into rectangular fuzzy subspaces of different sizes in order to use various combinations of antecedent fuzzy sets in fuzzy if-then rules. Then, it is demonstrated that a small number of fuzzy if-then rules conciding with our intuition are selected by incorporating the new fuzzy partition method into our former approach. It is also demonstrated that the so-called don't care attribute can be handled by treating intervals as antecedent fuzzy sets. Moreover, we show how to construct a fuzzy classification system by fuzzy if-then rules that have linguistic interpretations, i.e., by linguistic rules. Finally, we propose a hybrid algorithm that incorprates a learning procedure of the grade of certainty of each rule into the genetic algorithm. It is shown that the hybrid algorithm improves the performance of a fuzzy-rule-based classification system. In this paper, a modification of the fitness function in our former approach is also introduced by assigning a different weight to each fuzzy if-then rule in order to select general rules that are valid in large subspaces of a pattern space.

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In this paper, we propose a genetic-algorithm-based approach to the selection of linguistic rules for classification problems. A small number of significant linguistic rules are selected from a large number of rules which are generated in a pattern space. Our rule selection problem is to find a compact rule set that has high classification power. Therefore our problem has two objectives : to maximize the number of correctly classified patterns and to minimize the number of selected rules. For this two-objective problem, we propose a two-objective genetic algorithm (GA) to find a set of Pareto optimal solutions. Pareto optimal solutions are showed to the decision maker, then the decision maker can choose one of the Pareto optimal solutions. In this paper, first a selection procecdure and an eliltist strategy for finding a set of Pareto optimal solutions are proposed. Next we combined a learning method of linguistic rules with the two-objective GA. The learning method is applied to rule sets generated in the execution of the two-objective GA. Finally our two-objective GA is illustrated by computer simulations on the well-known iris data.

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In the paper, the concept of fuzzy die-time is defined in the vehicle routing and scheduling context. Usually customers' preferences for service can be classified into two kind of types : the tolerable interval of service time and the desirable time for service. Conventional approaches just consider the tolerable interval of service time and do not care for customers' desired time. The proposed fuzzy approach can handle both kind of customers' preferences simultaneously.Fuzzy due-time for each customers is given as a triangular fuzzy number and the membership function is corresponding to the grade of satisfaction of service time. Fuzzy vehicle routing problem is formulated with the concept of fuzzy due-time. The objectives considered here are to minimize the fleet size of vehicles, maximize the average grade of satisfaction over customers, minimize total travel distance, and total waiting time for vehicles.Genetic algorithm is investigated for solving the fuzzy vehicle routing problem. An insertion heuristic based crossover is designed towards to generate improved offspring. A push-bump-throw heuristic procedure is proposed to handle the fuzzy feature of the problem.Preliminary computational experiments on several randomly generated test problems have been executed and the results demonstrate that genetic algorithms and fuzziness approach can be a promising way for vehicle routing and scheduling problems.

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We propose a method for solving the optimal system reliability problems considering several failure models with fuzzy goal and fuzzy constrains by introducing genetic algorithms(GA). By considering several failure modes, system designer can systematically and accurately analyze the reliability of the practical system which might be complicatedly composed of units in series and/or in parallel. Also, the proposed method can consider the fuzziness based on the system designer's subjective judgement and the fluctuation of system environment by introducing fuzzy goals and fuzzy constrains. In addition, the trade-off relationship which is generally considered conflict between system reliability required by system designer and the system constrains such as total weight, volume, cost and so on can take into account in the system designing process. Therefore, the proposed method enables the system designer to design more flexible and satisfactory system. Further, by introducing GA, the proposed method makes it easy to handle the problem with nonlinear function without any transformation and computationally advantage on memory restriction. Further, by introducing the simple GA, the proposed method can gain the precise approximate solution with relatively simple algorithms.

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Job-shop Scheducling Problem(JSP) is one of extremely is one of extremely hard problems because it requires very large combinatorial search space and there are some precedence constraints between machines. The Genetic Algorithm(GA) is known as one of the most powerful tools for solving this kind of problems, especially it is more useful for large scale real-world problem.Generally, the data of real-world problems are imprecise, vague or uncertain. In this situation, we should estimate the input data with considering their uncertainty, and the uncertainty may be represented by a fuzzy number, and so reduce errors of imprecision.In this paper, we formulate fuzzy JSP and propose a new method for solving it after integrating GA in which processing time is represented by fuzzy number. We demonstrate its performance by the standard benchmark of job-shop scheduling problems with two different methods of ranking fuzzy subsets.

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In this paper, we focus on a scheduling problem of a machining center which produces a variety of parts with a monthly plan of process. Some parameters which reflect the decision maker's judgements for due-datas are introduced in the formulation of the objective function. Unfortunately, direct application of genetic algorithms to the formulated scheduling problems does not give acceptable results because a lot of infeasible solutions appear in genetic operations. Thus we propose a genetic algorithm which is suitable for the formulated scheduling problems and demonstrate the efficiency of the proposed algorithm through a number of numerical simulations.

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