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A Non-Uniform Convergence Tolerance Scheme for Enhancing the Branch-and-Bound Method

비균일 수렴허용오차 방법을 이용한 분지한계법 개선에 관한 연구

  • Jung, Sang-Jin (Graduate School of Mechanical Engineering, Hanyang Univ.) ;
  • Chen, Xi (Eaton Corporation) ;
  • Choi, Gyung-Hyun (Dept. of Industrial Engineering, Hanyang Univ.) ;
  • Choi, Dong-Hoon (The Center of Innovative Design Optimization Technology (iDOT), Hanyang Univ.)
  • 정상진 (한양대학교 대학원 기계공학과) ;
  • ;
  • 최경현 (한양대학교 산업공학과) ;
  • 최동훈 (한양대학교 최적설계신기술연구센터)
  • Received : 2011.01.27
  • Accepted : 2012.01.17
  • Published : 2012.04.01

Abstract

In order to improve the efficiency of the branch-and-bound method for mixed-discrete nonlinear programming, a nonuniform convergence tolerance scheme is proposed for the continuous subproblem optimizations. The suggested scheme assigns the convergence tolerances for each continuous subproblem optimization according to the maximum constraint violation obtained from the first iteration of each subproblem optimization in order to reduce the total number of function evaluations needed to reach the discrete optimal solution. The proposed tolerance scheme is integrated with five branching order options. The comparative performance test results using the ten combinations of the five branching orders and two convergence tolerance schemes show that the suggested non-uniform convergence tolerance scheme is obviously superior to the uniform one. The results also show that the branching order option using the minimum clearance difference method performed best among the five branching order options. Therefore, we recommend using the "minimum clearance difference method" for branching and the "non-uniform convergence tolerance scheme" for solving discrete optimization problems.

Keywords

Discrete Optimization;Mixed-Discrete Nonlinear Programming;Branch-and-Bound Method;Convergence Tolerance;Branching Order

Acknowledgement

Grant : 터보펌프 볼 베어링의 시제품 개발

Supported by : 한국연구재단

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