@article{oai:kanazawa-u.repo.nii.ac.jp:00007854,
 author = {北山, 哲士 and 荒川, 雅生 and 山崎, 光悦 and Kitayama, Satoshi and Arakawa, Masao and Yamazaki, Koetsu},
 issue = {742},
 journal = {Nihon Kikai Gakkai Ronbunshu, C Hen / Transactions of the Japan Society of Mechanical Engineers, Part C},
 month = {Jun},
 note = {In this paper, a simple method for the multi-objective optimization problems by the Particle Swarm Optimization (PSO) is proposed. The objectives of the Multi Objective Evolutionary Algorithms (MOEA) are summarized as follows : (1) To find the pareto optimal solutions, (2) To find the pareto optimal solutions as diverse as possible. To achieve these objectives by the PSO for the single objective problems, we propose how to define the g-best in this swarm without introducing some new parameters. That is, one particle among the non-inferior solutions is selected as the g-best to achieve the diversity among the non inferior solutions. The relative distance in the objective space is utilized to select the gbest among the non-inferior solutions. Additionally, some particles among the non inferior solutions are also selected as the gbest of the inferior solutions to find the pareto optimal solutions. The absolute distance in the objective space is utilized to select the g-best of the inferior solutions. We also show the geometric interpretation about the movement of particles. The validity of proposed approach is examined through typical numerical examples.},
 pages = {1575--1583},
 title = {Multi-objective Particle Swarm Optimization considering the diversity of the inferior solutions},
 volume = {74},
 year = {2008}
}