[Article] Global Optimization Using a Sequential Algorithm with Orthogonal Arrays and a Genetic Algorithm in a Discrete Space

Bum-Sang Cho
Ph.D. student,
Department of Mechanical Design and Production Engineering,
Hanyang University,17 Haengdang-dong, Sungdong-gu, Seoul 133-791, South Korea

Jeong-Wook Yi
Senior engineer,
Defense Products Division, Doosan Infracore Co., Ltd.
Institute of Advanced Engineering, Goan-ri, Packam-myun, Yongin, Gyeonggi-do 449-860, South Korea

Gyung-Jin Park
Corresponding author, Professor,
Division of Mechanical and Information Management, College of Engineering Science, Hanyang University, 1271 Sa-1-dong, Sangnok-gu, Ansan, Gyeonggi-do 426-791, South Korea

Key Words :
Discrete design, Sequential algorithm using orthogonal arrays, Genetic algorithm, Orthogonal arrays, Global solution

Abstract
In structural design, the design variables are frequently selected from certain discrete values. Various optimization algorithms have been developed for discrete design. It is well known that many function evaluations are needed in such an optimization. Recently, the sequential algorithm with orthogonal arrays (SOA), which is a search algorithm for a local minimum in a discrete space, has been developed. It considerably reduces the number of function evaluations. However, it only finds a local minimum and the final solution depends on the initial values of the design variables. A new algorithm is proposed to adopt the genetic algorithm (GA) in the SOA. The GA can find a globally excellent solution. The solution from the GA is used as the initial design of the SOA. The sequential usage of the GA and the SOA is carried out in an iterative manner until the convergence criteria are satisfied. The performance of the algorithm is evaluated by various examples.