Keiichi Niwa

Decentralized two-level 0-1 programming through genetic algorithms with double strings

We consider two-level programming problems in which there are one decision maker (the leader) at the upper level and two or more decision makers (the followers) at the lower level and decision variables of the leader and the followers are 0-1 variables. We assume that there is coordination among the followers while between the leader and the group of all the followers, there is no motivation to cooperate each other, and fuzzy goals for objective functions of the leader and followers are introduced in order to take fuzziness of their judgments into consideration. The leader maximizes the degree of satisfaction and the followers choose in concert so as to maximize a minimum among their degrees of satisfaction. A computational method, which is based on the genetic algorithms, for obtaining a solution to the above mentioned problem is developed. To demonstrate the feasibility and efficiency of the proposed algorithm, numerical experiments are carried out.

Computational Methods for Decentralized Two‐Level 0–1 Programming Problems through Distributed Genetic Algorithms

We consider two‐level programming problems in which there are one decision maker (the leader) at the upper level and two or more decision makers (the followers) at the lower level and decision variables of the leader and the followers are 0–1 variables. We assume that there is coordination among the followers while between the leader and the group of all the followers, there is no motivation to cooperate each other, and fuzzy goals for objective functions of the leader and the followers are introduced so as to take fuzziness of their judgments into consideration. The leader maximizes the degree of satisfaction (the value of the membership function) and the followers choose in concert in order to maximize a minimum among their degrees of satisfaction. We propose a modified computational method that solves problems related to the computational method based on the genetic algorithm (the existing method) for obtaining the Stackelberg solution. Specifically, the distributed genetic algorithm is introduced with...

Computational methods for two-level linear programming problems with fuzzy parameters through genetic algorithms

From the observation that possible values of parameters involved in objective functions and constraints of mathematical programming problems are often only imprecisely or ambiguously known to experts, we consider two-level linear programming problems with fuzzy parameters represented by fuzzy numbers. A computational method, which is based on genetic algorithms, for obtaining the Stackelberg solution to the two-level linear programming problem with fuzzy parameters is developed. To demonstrate the efficiency of the proposed computational method, computational experiments are carried out.

Multiobjective two-level 0–1 programming through distributed genetic algorithms

In this paper we focus on a multiobjective two-level 0–1 programming problem in which the decision maker at the upper level has an objective function and the decision maker at the lower level has multiple objective functions. We assume that there is not coordination between the decision maker at the upper level and the decision maker at the lower level. The decision maker at the upper level must take account of multiple rational responses of the decision maker at the lower level in the problem. We examine two kinds of situations based on anticipation of the decision maker at the upper level; an optimistic anticipation and a pessimistic anticipation. We show mathematical programming problems for obtaining the Stackelberg solutions based on two kinds of anticipation and propose computational methods using genetic algorithms for obtaining the Stackelberg solutions. In order to demonstrate feasibility and effectiveness of the proposed computational methods through genetic algorithms, we plan to conduct numerical experiments.

Computational Methods for Two‐Level 0–1 Programming Problems through Parallel Genetic Algorithms

This paper deals with a two‐level 0–1 programming problem in which there is not coordination between the decision maker (DM) at the upper level and the decision maker at the lower level. The authors propose a modified computational method that solves problems related to computational methods for obtaining the Stackelberg solution. Specifically, in order to shorten the computational time of a computational method implementing a genetic algorithm (GA) proposed by the authors, a parallel genetic algorithm is introduced with respect to the upper level GA, which handles decision variables for the upper level DM. Parallelization of the lower level GA is also performed along with parallelization of the upper level GA. The proposed algorithm is also improved in order to eliminate unnecessary computation during operation of the lower level GA, which handles decision variables for the lower level DM. In order to verify the effectiveness of the proposed method, we show comparisons with existing methods by performing...

Two‐level 0‐1 Programming through Genetic Algorithms with Sharing Scheme Using Cluster Analysis Methods

This paper deals with the two level 0–1 programming problems in which there are two decision makers (DMs); the decision maker at the upper level and the decision maker at the lower level. The authors modify the problematic aspects of a computation method for the Stackelberg solution which they previously presented, and thus propose an improved computation method. Specifically, a genetic algorithm (GA) is proposed with the objective of boosting the accuracy of solutions while maintaining the diversity of the population, which adopts a clustering method instead of calculating distances during sharing. Also, in order to eliminate unnecessary computation, an additional algorithm is included for avoiding obtaining the rational reaction of the lower level DM in response to upper level DM’s decisions when necessary. In order to verify the effectiveness of the proposed method, it is intended to make a comparison with existing methods by performing numerical experiments into both the accuracy of solutions and the ...