大域的最適化問題のための同種および異種粒子群最適化法の研究

The premature convergence problem and the exploration-exploitation trade-off problem are the two major problems encountered by many swarm intelligence algorithms in both global optimization and large scale global optimization. This thesis proposes that the two main problems could be handled by several variants of Particle Swarm Optimization (PSO) developed below. Five variants of homogeneous PSO have been developed for multimodal and large scale global optimization problems, and two variants of dynamic heterogeneous PSO for complex real-world problems.First of all, an individual competition strategy is proposed for the new variant of PSO, namely Fitness Predator Optimization (FPO), for multimodal problems. The development of individual competition plays an important role for the diversity conservation in the population, which is crucial for preventing premature convergence in multimodal optimization.To enhance the global exploration capability of the FPO algorithm for high multimodality problems, a modified paralleled virtual team approach is developed for FPO, namely DFPO. The main function of this dynamic virtual team is to build a paralleled information-exchange system, strengthening the swarm\u27s global searching effectiveness. Furthermore, the strategy of team size selection is defined in DFPO named as DFPO-r, which based on the fact that a dynamic virtual team with a higher degree of population diversity is able to help DFPO-ralleviate the premature convergence and strengthen the global exploration simultaneously. Experimental results demonstrate that both DFPO-r and DFPO have desirable performances for multimodal functions. In addition, DFPO-r has a more robust performance in most cases compared with DFPO.Using hybrid algorithms to deal with specific real-world problems is one of the most interesting trends in the last years. In this thesis, we extend the FPO algorithm for fuzzy clustering optimization problem. Thus, a combination of FPO with FCM (FPO-FCM) algorithm is proposed to avoid the premature convergence and improve the performance of FCM.To handle the large scale global optimization problem, a variant of modified BBPSO algorithm incorporation of Differential Evolution (DE) approach, namely BBPSO-DE, is developed to improve the swarm\u27s global search capability as the dimensionality of the search space increases. To the best of our knowledge, the Static Heterogeneous PSO (SHPSO) has been studied by some researchers, while the Dynamic Heterogeneous PSO (DHPSO) is seldom systematically investigated based on real problems. In this thesis, two variants of dynamic Heterogeneous PSO, namely DHPSO-d and DHPSO-p are proposed for complex real-world problems. In DHPSO-d, several differential update rules are proposed for different particles by the trigger event. When the global best position p_g is considered stagnant and the event is confirmed, then p_g is reset and all particles update their positions only by their personal experience. In DHPSO-p, two proposed types of topology models provide the particles different mechanism choosing their informers when the swarm being trapped in the local optimal solution. The empirical study of both variants shows that the dynamic self-adaptive heterogeneous structure is able to effectively address the exploration-exploitation trade-off problem and provide excellent optimal solutions for the complex real-world problem.To conclude,the proposed biological metaphor approaches provide each of the PSO algorithms variants with different search characteristics, which makes them more suitable for different types of real-world problems.博士(理学)法政大学 (Hosei University

A Ranking Fuzzy Cluster Algorithm for Multidimensional Data

Abstract—　Data classification is an important problem in various scientific fields. Data analysis algorithm such as the fuzzy c-means algorithm and k-means algorithm are wildly used on multidimensional data but still suffers from several drawbacks. To get higher classification accuracy, the Ranking Fuzzy Cluster (RFC) algorithm which uses the method Dimension Ranking (DR) and a new center moving formula is proposed in this paper. The method DR is used to calculate the weight of each instance among all the data set in each dimension. The new center moving formula which uses the non-gradient descent iterative to avoid the local minimum problems of FCM. In the experiment, five benchmark data sets are used to test the classification accuracy of RFC. The fuzzy c-means algorithm and k-means algorithm are also used in the experiment comparison. Experimental result shows that the RFC has higher classification accuracy than fuzzy c-means and k-means with multidimensional data. Keywords—Fuzzy Cluster; Multidimensional Data; Dimension Ranking; Cluster Center Moving