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Distributed GA and SA Algorithms for Structural Optimization

This paper discusses the use of Genetic Algorithm (GA) and Simulated Annealing (SA) algorithms for structural optimization, their efficiency, and the development of efficient design methods using high-performance computers.

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Distributed GA and SA Algorithms for Structural Optimization

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  1. Distributed GA and SA Algorithms for Structural Optimization Jan 11, 2002 Hyo Seon Park The Fourth World Congress of Structural and Multidisciplinary Optimization

  2. Conventional vs. Optimum Design Distinction between two approaches • Conventional design process is less formal • Performance of the system is not identified • Trend information is not calculated to make design decisions for improvement of the system Optimization is the process of maximizing or minimizing an objective function while satisfying the constraints. The Fourth World Congress of Structural and Multidisciplinary Optimization

  3. Optimization Algorithms 1st and 2nd order algorithms • Sensitivity information • Necessary or sufficient conditions 0th order algorithms • Analogy from nature • GA (Genetic Algorithm), SA (Simulated Annealing) NDM (Neural Dynamic Model) The Fourth World Congress of Structural and Multidisciplinary Optimization

  4. Introduction SA and GA have been successfully applied to structural optimization. Offers good optimum solutions Requires the excessive computational time for the solution Several approaches have been proposed to reduce the computational time for general iterative algorithms They have also pointed out the requirement for the computational time Computational time requirement is still a serious barrier to application of the algorithms in large-scale optimization problems The Fourth World Congress of Structural and Multidisciplinary Optimization

  5. Introduction Efficient Algorithm for Optimization Using High-Performance Computers Development of efficient design method • Expensive cost • Operating system • Development of software for message passing such as PVM or MPI • In advanced countries • Universal usage of High-Performance Computers • In structural engineering fields, use the HPC • Use the parallel algorithm on HPC Usage of High-Performance Computer is not real. Achieve the efficient analysis and design for large-scale structure Development of efficient structural analysis algorithm is essential for large-scale structure The Fourth World Congress of Structural and Multidisciplinary Optimization

  6. Simulated Annealing 반복적 개선법 + 확률적 수용 Metropolis 의 열평형 시뮬레이션 Random generator : and ; Acceptance ; Probability acceptance = 볼쯔만 상수 = 온도 The Fourth World Congress of Structural and Multidisciplinary Optimization

  7. Serial SA Algorithm Two-phase cooling strategy SQ(Simulated quenching) + SA Cooling schedule • SQ strategy : f = 1/N • SA strategy : f = 1/ N0.5 Terminate Conditions • SQ strategy Relative variation of Object function • SA strategy Relative variation of Object function and average variation of design variables The Fourth World Congress of Structural and Multidisciplinary Optimization

  8. Problem Formulation Minimize Subject to 1. Under Winder Load 2. Load Combination [DL+LL, (DL+LL+W)/1.5, (DL+LL-W)/1.5] The Fourth World Congress of Structural and Multidisciplinary Optimization

  9. Parallel Processing Machine • Pentium III 500MHz • Main Memory :128Mbytes • Ethernet Card : 10Mbps The Fourth World Congress of Structural and Multidisciplinary Optimization

  10. Parallelism for SQ The Fourth World Congress of Structural and Multidisciplinary Optimization

  11. Parallelism for SA The Fourth World Congress of Structural and Multidisciplinary Optimization

  12. Parallel SA Algorithm Cooling Schedule Temperature Terminate Condition This conditions are equals to serial algorithm The Fourth World Congress of Structural and Multidisciplinary Optimization

  13. Applications Regular 21-story braced frame structure Fy : 4000 kgf/cm2 Elastic Modulus : 2.04x106 kgf/cm2 Self Weight : 7.85 tonf/m3 Dead Load : 3.29 tonf/m Live Load : 1.26 tonf/m Irregular 21-story braced frame structure The Fourth World Congress of Structural and Multidisciplinary Optimization

  14. Convergence Histories Serial Algorithm : Regular Parallel Algorithm : Regular The Fourth World Congress of Structural and Multidisciplinary Optimization

  15. Convergence Histories Serial Algorithm : Irregular Parallel Algorithm : Irregular The Fourth World Congress of Structural and Multidisciplinary Optimization

  16. Performance of Algorithm 직렬알고리즘은 최대오차 2%이내로 수렴하는 비율이 약 66% 병렬 알고리즘은 약 83%로 높게 나타남 층의 연결성 제약 알고리즘의 평균 수행시간과 평균 최적 중량 (최대오차 2%) The Fourth World Congress of Structural and Multidisciplinary Optimization

  17. Relative Speedup The Fourth World Congress of Structural and Multidisciplinary Optimization

  18. Conclusions-SA Slave 컴퓨터의 수가 2, 4, 8대 인 경우, 본 알고리즘의 Relative Speedup은 2.7, 4.3, 5.4로 높게 나타났다. 고층 철골조 구조물을 위한 효율적 병렬 최적 설계 알고리즘 SQ단계 : 알고리즘의 구성상 높은 효율성을 발휘 SA 단계 : 국부최소점 탈출효과를 충분히 얻을 수 있었다. SQ단계에서 너무 이른 수렴으로 인해 알고리즘의 수행시간이 증가될 수 있다. SQ단계와 SA 단계의 적절한 냉각스케쥴에 대한 연구 필요 The Fourth World Congress of Structural and Multidisciplinary Optimization

  19. 직렬 유전 알고리즘 • 유전 알고리즘의 장점 • 개념이 단순하고 전역적 탐색능력이 우수 • 이식성과 유연성이 높음 • 기존 최적화 알고리즘과 차이점 • 설계변수를 coding하여 직접사용 • 복수개의 해집단 운용 • 목적함수 값만을 사용 • 내재적인 병렬성

  20. 유전 연산자 • Coding • 교 차 • 돌연변이 YONSEI UNIV. Highrise Building Structural Lab.

  21. 유전 알고리즘 개요 YONSEI UNIV. Highrise Building Structural Lab.

  22. 정 식 화 • Minimize • Subjected to 1. 횡변위 제약 2. 응력 제약 대한건축학회 강구조계산규준 (1983) • Penalty Function YONSEI UNIV. Highrise Building Structural Lab.

  23. Parameter Setting • 유전 파라메터 • 종료조건 전체 해집단 가운데 50%이상이 설계 가용영역이고 최고의 적응도를 가지는 개체가 설계 가용 영역중 50%이상 차지하는 경우가 2회 이상 반복될 때 수렴하는 것으로 가정 YONSEI UNIV. Highrise Building Structural Lab.

  24. Parameter Setting 교차율별 수렴곡선 돌연변이율별 수렴곡선 YONSEI UNIV. Highrise Building Structural Lab.

  25. 예제 적용 (직렬) 25부재 3차원 트러스 구조물 8 variable YONSEI UNIV. Highrise Building Structural Lab.

  26. Variable Mutation Rate I : 반복수 Pm final: 최종 돌연변이율 Pm initial : 초기 돌연변이율 Maxgen : 감소 구간 초기 돌연변이율에 따른 Variable Mutation Rate 감소구간에 따른 Variable Mutation Rate YONSEI UNIV. Highrise Building Structural Lab.

  27. 최적해 비교 YONSEI UNIV. Highrise Building Structural Lab.

  28. 종료시 반복수 비교 초기 돌연변이율에 따른 반복수 감소구간에 따른 반복수 YONSEI UNIV. Highrise Building Structural Lab.

  29. 예제 적용(병렬) 35 variable KS 규준에 의거 풍력 산정 3경간 21층 평면 가새골조 YONSEI UNIV. Highrise Building Structural Lab.

  30. Slave 개수별 수렴곡선 직렬 알고리즘 병렬 알고리즘 YONSEI UNIV. Highrise Building Structural Lab.

  31. Speedup 평가 전체 최적화 시간 중 구조해석에 소요된 시간 99.996 % Slave 개수별 최적화 수행시간 YONSEI UNIV. Highrise Building Structural Lab.

  32. 최적화 과정중 단면선택 초기 단면 선택 30회 반복후 단면선택 YONSEI UNIV. Highrise Building Structural Lab.

  33. 최적화 과정중 단면선택 30회 반복후 단면선택 90회 반복후 단면선택 YONSEI UNIV. Highrise Building Structural Lab.

  34. SA와 비교 • DL +LL 동시에 작용할 때 SA와 비교 GA : 104.31 t SA : 103.07 t GA의 수렴곡선 GA와 SA의 선택된 단면적 비교 YONSEI UNIV. Highrise Building Structural Lab.

  35. 결 론 • 토너먼트 선택의 실용성 구조 최적화의 선택전략으로 적합 • 가변형 돌연변이율의 적용 최적점 부근의 불필요한 탐색을 제거하여 수렴유도 • 적응도 평가의 병렬화 최적화 수행시간이 선형적으로 감소 • 슬래이브 수와 무관하게 선형적으로 감소 • PC 에서 구조 최적화를 위한 유전 알고리즘 의 실용성 확보 YONSEI UNIV. Highrise Building Structural Lab.

  36. The range of application of optimization is limited only by the imagination or Ingenuity of Engineers.

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