Semi-automatic transition from simulation to one-shot optimization with equality constraints Lisa Kusch , Tim Albring, Andrea Walther, Nicolas Gauger Chair for Scientific Computing, TU Kaiserslautern, www.scicomp.uni-kl.de Institute of Mathematics, Universit¨ at Paderborn September 15, 2016 AD 2016
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Semi-automatic transition from simulation to one-shotoptimization with equality constraints
Lisa Kusch, Tim Albring, Andrea Walther, Nicolas Gauger
Chair for Scientific Computing, TU Kaiserslautern, www.scicomp.uni-kl.deInstitute of Mathematics, Universitat Paderborn
September 15, 2016
AD 2016
Outline
1 The One-Shot Approach with Additional Constraints
2 AD-Based Discrete Adjoint in SU2
3 Multi-Objective Optimization
4 Application and ResultsApplication to Airfoil DesignMulti-Objective Optimization with Single ConstraintMulti-Objective Optimization with Multiple ConstraintsSecond-Order Adjoints
5 Summary and Outlook
Kusch,Albring,Walther,Gauger From simulation to one-shot optimization with constraints 2/ 18
Problem Definition
PDE-constrained optimization problem
minu,y
f (y , u)
s.t. c(y , u) = 0,
h(y , u) = 0
→fixed point iteration||Gy || ≤ ρ < 1
minu,y
f (y , u)
s.t. G (y , u) = y ,
h(y , u) = 0
objective function f ∈ R, state y ∈ Y ⊂ Rn, design u ∈ U ⊂ Rm
state equation c : Y × U → Y , constraints h : Y × U → V ⊂ Rp
(notation: G = (G (y , u)− y , h(y , u))T )
⇒ one-shot approach using the AD-based discrete adjoint[Hamdi, Griewank(2010)],[Walther, Gauger, Kusch, Richert(2016)]
L(y , y , u) = f (y , u) + (G (y , u)− y)T y + hTµ = N(y , y , µ, u)− yT y
Kusch,Albring,Walther,Gauger From simulation to one-shot optimization with constraints 3/ 18