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![Porto, June 20 2017
OPENSEES SOLVER WITH A DIFFERENTIAL EVOLUTIONARY ALGORITHM FOR
STRUCTURAL OPTIMIZATION OF HOLLOW SECTIONS STEEL STRUCTURES 18
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OpenSees solver with a differential evolutionary algorithm for structural optimization of hollow sections steel structures
- 1. Giuseppe Carlo Marano,Cristoforo Demartino, Rita Greco, Bruno Briseghella, Alessandra Fiore Porto, June 20 2017 OPENSEES SOLVER WITH A DIFFERENTIAL EVOLUTIONARY ALGORITHM FOR STRUCTURAL OPTIMIZATION OF HOLLOW SECTIONS STEEL STRUCTURES 1
- 2. Outline Use Opensees forstructural optimization Develop a Matlab – OpenSees connection using GA Deal with constraints in a «smart» way Application to simple steel structure Porto, June 20 2017 OPENSEES SOLVER WITH A DIFFERENTIAL EVOLUTIONARY ALGORITHM FOR STRUCTURAL OPTIMIZATION OF HOLLOW SECTIONS STEEL STRUCTURES 2
- 3. Structural Optimization Porto, June20 2017 OPENSEES SOLVER WITH A DIFFERENTIAL EVOLUTIONARY ALGORITHM FOR STRUCTURAL OPTIMIZATION OF HOLLOW SECTIONS STEEL STRUCTURES
- 4. ( ){ } () ( ) min 0 1, , 0 1, , , q q r r l u f g q n h r n ≤ = = = ∈ x x x x x x Paradigm • Classical • Non-classical Evolutive algorhitms for structural optimization Porto, June 20 2017 OPENSEES SOLVER WITH A DIFFERENTIAL EVOLUTIONARY ALGORITHM FOR STRUCTURAL OPTIMIZATION OF HOLLOW SECTIONS STEEL STRUCTURES
- 5. Artificial Neural Networks (ANN) Evolutive/Genetic Algorithms(GA) Soft computing Porto, June 20 2017 OPENSEES SOLVER WITH A DIFFERENTIAL EVOLUTIONARY ALGORITHM FOR STRUCTURAL OPTIMIZATION OF HOLLOW SECTIONS STEEL STRUCTURES
- 6. •One seeks thesolution of a problem in the form of strings of numbers (traditionally binary, although the best representations are usually those that reflect something about the problem being solved), by applying operators such as recombination and mutation; Genetic algorithm •Here the solutions are in the form of computer programs, and their fitness is determined by their ability to solve a computational problem.Genetic programming •Similar to genetic programming, but the structure of the program is fixed and its numerical parameters are allowed to evolve; Evolutionary programming •Works with vectors of real numbers as representations of solutions, and typically uses self- adaptive mutation rates;Evolution strategy •Based on vector differences and is therefore primarily suited for numerical optimization problems.Differential evolution •Based on the ideas of animal flocking behaviour. Also primarily suited for numerical optimization problems.Particle swarm optimization •Based on the ideas of ant foraging by pheromone communication to form paths. Primarily suited for combinatorial optimization problems.Ant colony optimization •Based on the ideas of weed colony behavior in searching and finding a suitable place for growth and reproduction. Invasive weed optimization algorithm •Based on the ideas of musicians' behavior in searching for better harmonies. This algorithm is suitable for combinatorial optimization as well as parameter optimization.Harmony search •Based on information theory. Used for maximization of manufacturing yield, mean fitness or average information. See for instance Entropy in thermodynamics and information theory.Gaussian adaptation
- 7. Porto, June 202017 OPENSEES SOLVER WITH A DIFFERENTIAL EVOLUTIONARY ALGORITHM FOR STRUCTURAL OPTIMIZATION OF HOLLOW SECTIONS STEEL STRUCTURES 7 1 1 2 2 , , , ,l u l u l u l u j j n n x x x x x x x x = ⊗ ⊗ ⊗ ⊆ Ω ( ) ( ){ }1 max 0, 0 q rn n k k i p i p g + = Φ ≥∑x x ( ){ }min f x Structural optimization using soft computing
- 8. X1,x2,….Xn Verification ( ) (){ }1 max 0, 0 q rn n k k i p i p g + = Φ ≥∑x x Porto, June 20 2017 OPENSEES SOLVER WITH A DIFFERENTIAL EVOLUTIONARY ALGORITHM FOR STRUCTURAL OPTIMIZATION OF HOLLOW SECTIONS STEEL STRUCTURES
- 9. Constraint Violation x1 feasible x2 infeasible ( )0k iΦ =x ( ) 0k iΦ >x
- 10. Penalty functions-based methods Methodsbased on special operators and representations Methods based on repair algorithms Methods based on the separation between OF and constraints Hybrid methods
- 11.
- 12. Both two feasible Feasibleand infeasible Both two infeasible
- 13. denotes that (k-1)xi Pbis dominated bykxi. , , k k k i i jk b i j k k k j j k if if = x x x x x x x ( ) ( ) ( ) ( )( ) ( )( ) ( ) ( )( ) ( )( ) ( ) ( )( ) ( ) ( ) ( ) 1 1 1 1 1 0 0 0 0 k kk Pb k Pb i i i i kk Pb kk Pb i i i i kk Pb i i f f − − − − − < ∧ Φ = ∧ Φ = ∨ ⇔ Φ = ∧ Φ > ∨ Φ < Φ x x x x x x x x x x
- 14.
- 15. 0k k Pb µΦ=≥Φ ( ) ( ) ( ){ }1 k Pb k Pb k Pb k Pb i N=Φ Φ ΦΦ x x x ( ) ( ) ( ) ( )( ) ( )( ) ( ) ( )( ) ( )( ) ( ) ( )( ) ( )( ) ( ) ( )( ) ( ) ( ) ( )( ) 1 1 1 1 1 1 k kk Pb k k k Pb k k i i i i k kk Pb k k k Pb k k i i i i k kk k k Pb k k k Pb i i i i f f µ µ µ µ µ µ − − Φ Φ − − Φ Φ − − Φ Φ < ∧ Φ ≤ Ψ ∧ Φ ≤ Ψ ∨ ⇔ Φ ≤ Ψ ∧ Φ > Ψ ∨ Φ > Ψ ∧ Φ > Ψ ∧ Φ < Φ x x x x x x x x x x x x ( ) [ ] ( )01 0,1 0, , ;k k k L L η η + Ψ= − ∈ = ∈
- 16.
- 17. 17 Application to staticanalysis of steel structure
- 18. Porto, June 202017 OPENSEES SOLVER WITH A DIFFERENTIAL EVOLUTIONARY ALGORITHM FOR STRUCTURAL OPTIMIZATION OF HOLLOW SECTIONS STEEL STRUCTURES 18 3 33 A s s ε − ≤ ] ] 3 33,38 A s s ε − ∈ ] ] 3 38,42 A s s ε − ∈ 3 42 A s s ε − > Section Class •1 •2 •3 •4 235 yf ε =
- 19. Porto, June 202017 OPENSEES SOLVER WITH A DIFFERENTIAL EVOLUTIONARY ALGORITHM FOR STRUCTURAL OPTIMIZATION OF HOLLOW SECTIONS STEEL STRUCTURES 19 Buckling resistance of steel bars , 1.0Ed b Rd N N ≤ 1 , y b Rd M Af N χ γ = 1 , eff y b Rd M A f N χ γ = 1-2-3 4
- 20. Structural optimization More thanminimizing weight! Technological/constructive constraints New class of “shapes”
- 21. Porto, June 202017 OPENSEES SOLVER WITH A DIFFERENTIAL EVOLUTIONARY ALGORITHM FOR STRUCTURAL OPTIMIZATION OF HOLLOW SECTIONS STEEL STRUCTURES 21 Optimal topology (?)
- 22. Conclusions Interface OpenSees withEA • External Optimization algorithm • External constraint evaluation • Constrained handling Futures • Parallel computing • General Constrained handling • More complex problems Porto, June 20 2017 OPENSEES SOLVER WITH A DIFFERENTIAL EVOLUTIONARY ALGORITHM FOR STRUCTURAL OPTIMIZATION OF HOLLOW SECTIONS STEEL STRUCTURES 22 Conclusions