An Evolutionary Algorithm on Finding Nearly A-Optimal One-way Layout in the Presence of a Quadratic Trend

• Main Authors: Yi-Sheng Lai, 賴意昇
• Other Authors: none
• Format: Others
• Language: zh-TW
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/70625886083289995088

碩士 === 逢甲大學 === 統計與精算所 === 93 === In one-way experimental design, the response variable may be influenced by a quadratic trend. In order to estimate the treatment differences as accurately as possible, we should minimize the average of variance of treatment comparison, which is the idea of A-optimal design, through applying proper allocation of treatments to the experiment units. In this thesis,the evolutionary algorithm is considered to find nearly A-optimal one-way layout in the presence of a quadratic trend. Evolutionary algorithms have been successfully applied to optimal problems in literature. Choosing the right parameters of evolutionary algorithms, however, is a time-consuming task. Therefore, we adopt parameters which are suggested by literature. We test the evolutionary algorithm by 15 one-way layout plans. The A-efficiency of designs found by the evolutionary algorithm is exceeded 99%. It means that the evolutionary algorithm performed very well on finding nearly A-optimal one-way designs.