Tadahiko Murata

A multi-objective genetic local search algorithm and its application to flowshop scheduling

We propose a hybrid algorithm for finding a set of nondominated solutions of a multi objective optimization problem. In the proposed algorithm, a local search procedure is applied to each solution (i.e., each individual) generated by genetic operations. Our algorithm uses a weighted sum of multiple objectives as a fitness function. The fitness function is utilized when a pair of parent solutions are selected for generating a new solution by crossover and mutation operations. A local search procedure is applied to the new solution to maximize its fitness value. One characteristic feature of our algorithm is to randomly specify weight values whenever a pair of parent solutions are selected. That is, each selection (i.e., the selection of two parent solutions) is performed by a different weight vector. Another characteristic feature of our algorithm is not to examine all neighborhood solutions of a current solution in the local search procedure. Only a small number of neighborhood solutions are examined to prevent the local search procedure from spending almost all available computation time in our algorithm. High performance of our algorithm is demonstrated by applying it to multi objective flowshop scheduling problems.

Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling

This paper shows how the performance of evolutionary multiobjective optimization (EMO) algorithms can be improved by hybridization with local search. The main positive effect of the hybridization is the improvement in the convergence speed to the Pareto front. On the other hand, the main negative effect is the increase in the computation time per generation. Thus, the number of generations is decreased when the available computation time is limited. As a result, the global search ability of EMO algorithms is not fully utilized. These positive and negative effects are examined by computational experiments on multiobjective permutation flowshop scheduling problems. Results of our computational experiments clearly show the importance of striking a balance between genetic search and local search. In this paper, we first modify our former multiobjective genetic local search (MOGLS) algorithm by choosing only good individuals as initial solutions for local search and assigning an appropriate local search direction to each initial solution. Next, we demonstrate the importance of striking a balance between genetic search and local search through computational experiments. Then we compare the modified MOGLS with recently developed EMO algorithms: the strength Pareto evolutionary algorithm and revised nondominated sorting genetic algorithm. Finally, we demonstrate that a local search can be easily combined with those EMO algorithms for designing multiobjective memetic algorithms.

Performance evaluation of fuzzy classifier systems for multidimensional pattern classification problems

We examine the performance of a fuzzy genetics-based machine learning method for multidimensional pattern classification problems with continuous attributes. In our method, each fuzzy if-then rule is handled as an individual, and a fitness value is assigned to each rule. Thus, our method can be viewed as a classifier system. In this paper, we first describe fuzzy if-then rules and fuzzy reasoning for pattern classification problems. Then we explain a genetics-based machine learning method that automatically generates fuzzy if-then rules for pattern classification problems from numerical data. Because our method uses linguistic values with fixed membership functions as antecedent fuzzy sets, a linguistic interpretation of each fuzzy if-then rule is easily obtained. The fixed membership functions also lead to a simple implementation of our method as a computer program. The simplicity of implementation and the linguistic interpretation of the generated fuzzy if-then rules are the main characteristic features of our method. The performance of our method is evaluated by computer simulations on some well-known test problems. While our method involves no tuning mechanism of membership functions, it works very well in comparison with other classification methods such as nonfuzzy machine learning techniques and neural networks.

Multi-objective genetic algorithm and its applications to flowshop scheduling

Abstract In this paper, we propose a multi-objective genetic algorithm and apply it to flowshop scheduling. The characteristic features of our algorithm are its selection procedure and elite preserve strategy. The selection procedure in our multi-objective genetic algorithm selects individuals for a crossover operation based on a weighted sum of multiple objective functions with variable weights. The elite preserve strategy in our algorithm uses multiple elite solutions instead of a single elite solution. That is, a certain number of individuals are selected from a tentative set of Pareto optimal solutions and inherited to the next generation as elite individuals. In order to show that our approach can handle multi-objective optimization problems with concave Pareto fronts, we apply the proposed genetic algorithm to a two-objective function optimization problem with a concave Pareto front. Last, the performance of our multi-objective genetic algorithm is examined by applying it to the flowshop scheduling problem with two objectives: to minimize the makespan and to minimize the total tardiness. We also apply our algorithm to the flowshop scheduling problem with three objectives: to minimize the makespan, to minimize the total tardiness, and to minimize the total flowtime.

Single-objective and two-objective genetic algorithms for selecting linguistic rules for pattern classification problems

Abstract This paper proposes various methods for constructing a compact fuzzy classification system consisting of a small number of linguistic classification rules. First we formulate a rule selection problem of linguistic classification rules with two objectives: to maximize the number of correctly classified training patterns and to minimize the number of selected rules. Next we propose three methods for finding a set of non-dominated solutions of the rule selection problem. These three methods are based on a single-objective genetic algorithm. We also propose a method based on a multi-objective genetic algorithm for finding a set of non-dominated solutions. We examine the performance of the proposed methods by applying them to the well-known iris data. Finally we propose a hybrid algorithm by combining a learning method of linguistic classification rules with the multi-objective genetic algorithm. High performance of the hybrid algorithm is demonstrated by computer simulations on the iris data.

Genetic algorithms for flowshop scheduling problems

Abstract In this paper, we apply a genetic algorithm to flowshop scheduling problems and examine two hybridizations of the genetic algorithm with other search algorithms. First we examine various genetic operators to design a genetic algorithm for the flowshop scheduling problem with an objective of minimizing the makespan. By computer simulations, we show that the two-point crossover and the shift change mutation are effective for this problem. Next we compare the genetic algorithm with other search algorithms such as local search, taboo search and simulated annealing. Computer simulations show that the genetic algorithm is a bit inferior to the others. In order to improve the performance of the genetic algorithm, we examine the hybridization of the genetic algorithms. We show two hybrid genetic algorithms: genetic local search and genetic simulated annealing. Their high performance is demonstrated by computer simulations.

Three objective genetics-based machine learning for linguisitc rule extraction

Abstract This paper shows how a small number of linguistically interpretable fuzzy rules can be extracted from numerical data for high-dimensional pattern classification problems. One difficulty in the handling of high-dimensional problems by fuzzy rule-based systems is the exponential increase in the number of fuzzy rules with the number of input variables. Another difficulty is the deterioration in the comprehensibility of fuzzy rules when they involve many antecedent conditions. Our task is to design comprehensible fuzzy rule-based systems with high classification ability. This task is formulated as a combinatorial optimization problem with three objectives: to maximize the number of correctly classified training patterns, to minimize the number of fuzzy rules, and to minimize the total number of antecedent conditions. We show two genetic-algorithm-based approaches. One is rule selection where a small number of linguistically interpretable fuzzy rules are selected from a large number of prespecified candidate rules. The other is fuzzy genetics-based machine learning where rule sets are evolved by genetic operations. These two approaches search for non-dominated rule sets with respect to the three objectives.

Multi-objective genetic local search algorithm

Proposes a hybrid algorithm for finding a set of non-dominated solutions of a multi-objective optimization problem. In the proposed algorithm, a local search procedure is applied to each solution (i.e. to each individual) generated by genetic operations. The aim of the proposed algorithm is not to determine a single final solution but to try to find all the non-dominated solutions of a multi-objective optimization problem. The choice of the final solution is left to the decision makers preference. The high searching ability of the proposed algorithm is demonstrated by computer simulations on flowshop scheduling problems.

Performance evaluation of genetic algorithms for flowshop scheduling problems

The aim of this paper is to evaluate the performance of genetic algorithms for the flowshop scheduling problem with an objective of minimizing the makespan. First we examine various genetic operators for the scheduling problem. Next we compare genetic algorithms with other search algorithms such as local search, taboo search and simulated annealing. By computer simulations, it is shown that genetic algorithms are a bit inferior to the others. Finally, we show two hybrid genetic algorithms: genetic local search and genetic simulated annealing. Their high performance is demonstrated by computer simulations.<<ETX>>

Genetic algorithms and neighborhood search algorithms for fuzzy flowshop scheduling problems

Abstract This paper examines two fuzzy flowshop scheduling problems with fuzzy due dates. The membership function of a fuzzy due date assigned to each job represents the grade of satisfaction of a decision maker for the completion time of that job. One fuzzy flowshop scheduling problem is to maximize the minimum grade of satisfaction over given jobs, and the other is to maximize the total grade of satisfaction. First, we investigate the relations between the fuzzy scheduling problems and conventional scheduling problems. We next apply a genetic algorithm and neighborhood search algorithms (multi-start descent, taboo search and simulated annealing) to the fuzzy flowshop scheduling problems in order to examine the ability of these algorithms to find near optimal solutions. By computer simulations, it is shown that the maximization problem of the total satisfaction grade is even more tractable by these algorithms than that of the minimum satisfaction grade. Then, we show how the performance of these algorithms can be improved for the latter problem by utilizing problem domain knowledge. Finally, high performance of a hybrid genetic algorithm with neighborhood search is demonstrated.