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MULTIOBJECTIVE OPTIMIZATION OF STRUCTURE USING MODIFIED - CONSTRAINT APPROACH

MULTIOBJECTIVE OPTIMIZATION OF STRUCTURE USING MODIFIED - CONSTRAINT APPROACH. Ju-Tae Kim 1 , Sun-Kyu Park 2 and In-Won Lee 3. 1) Graduate Student, Department of Civil Eng., KAIST, KOREA 2) Professor, Department of Civil Eng., Sung Kyun Kwan Univ., KOREA

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MULTIOBJECTIVE OPTIMIZATION OF STRUCTURE USING MODIFIED - CONSTRAINT APPROACH

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  1. MULTIOBJECTIVE OPTIMIZATION OF STRUCTURE USING MODIFIED - CONSTRAINT APPROACH Ju-Tae Kim1, Sun-Kyu Park2 and In-Won Lee3 1) Graduate Student, Department of Civil Eng., KAIST, KOREA 2) Professor, Department of Civil Eng., Sung Kyun Kwan Univ., KOREA 3) Professor, Department of Civil Eng., KAIST, KOREA

  2. CONTENTS • INTRODUCTION • MODIFIED CONSTRAINT APPROACH • NUMERICAL EXAMPLE • CONCLUSIONS VIBRATION CONTROL LAB. KAIST

  3. INTRODUCTION COMPETING OBJECTIVES VIBRATION CONTROL LAB. KAIST

  4. OBJECTIVE SPACE • COST • SAFETY • DEFLECTION • FREQUENCY MULTI-OPTIMAL STRUCTURE DECISION MAKING Multiobjective Optimization VIBRATION CONTROL LAB. KAIST

  5. f2 Feasible Design Region Pareto Solutions f2, min f1, min f1 Pareto Solution Set VIBRATION CONTROL LAB. KAIST

  6. Decision Making ConstraintApproach Game Theory Weighting Method Deterministic Fuzzy Rule Base Probabilistic VIBRATION CONTROL LAB. KAIST

  7. - Constraint Approach Multiobjective Optimization Problem (1.a) (1.b) (1.c) VIBRATION CONTROL LAB. KAIST

  8. - Constraint Approach (2.a) (2.b) (2.c) (2.d) Transformed into Single Objective Problem VIBRATION CONTROL LAB. KAIST

  9. MODIFIED APPROACH (3.a) (3.b) (3.c) (3.d) (3.e) (3.f) VIBRATION CONTROL LAB. KAIST

  10. Differences of Two Approaches Initial Value Pareto Set Pareto Set -constraint approach Modified approach VIBRATION CONTROL LAB. KAIST

  11. (3.e) (3.f) Limitation and Assumption is inside the Feasible Design Region Due to the Convexity of the Problem Considered VIBRATION CONTROL LAB. KAIST

  12. Initial values of optimization are generated independently Each Pareto Solution can be found in Parallel Advantages VIBRATION CONTROL LAB. KAIST

  13. NUMERICAL EXAMPLE Steel Box Girder Bridge 80 19.5 2.75 7.0 2.75 7.0 B 0.25 tw D tuf tbf VIBRATION CONTROL LAB. KAIST

  14. Material Properties of Steel VIBRATION CONTROL LAB. KAIST

  15. Formulation of the Problem (4.a) (4.b) (4.c) (4.d) (4.e) (4.f) VIBRATION CONTROL LAB. KAIST

  16. Constraints (4.g) (4.h) (4.i) (4.j) (4.k) (4.l) (4.m) (4.n) VIBRATION CONTROL LAB. KAIST

  17. Area Minimization =1699.8 cm2 Design Value( ) B : 2.00 m D : 2.23m tbf : 2.46cm tuf : 2.21cm tw : 1.72cm VIBRATION CONTROL LAB. KAIST

  18. Deflection Minimization = 1.82cm Design Value( ) B : 2.66 m D : 3.0m tbf : 3.0cm tuf : 3.0cm tw : 3.0cm VIBRATION CONTROL LAB. KAIST

  19. Pareto Optimization VIBRATION CONTROL LAB. KAIST

  20. Pareto Solution Set VIBRATION CONTROL LAB. KAIST

  21. CONCLUSIONS • Independent initial values for Pareto optimization can be generated • Pareto solution set can be found in Parallel VIBRATION CONTROL LAB. KAIST

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