Evolutionary Strategies for Multidisciplinary ... - Dynardo GmbH
Evolutionary Strategies for Multidisciplinary ... - Dynardo GmbH Evolutionary Strategies for Multidisciplinary ... - Dynardo GmbH
Operators: Mutation – one σ Self-adaptive ES with one step size: One σ controls mutation for all x i Mutation: N(0, σ) Individual before mutation v a = (( x1,..., xn ), σ ) v a′ = (( x′ ,..., x′ ), σ ′ ) i x i 1 σ ′ = σ ⋅exp( τ ⋅ N x′ = n 0 + σ ′ ⋅ N i ( 0, 1) ( 0, 1)) Individual after mutation 1.: Mutation of step sizes 2.: Mutation of objective variables Here the new σ‘ is used! 16
Operators: Mutation – one σ Thereby τ 0 is the so-called learning rate Affects the speed of the σ-Adaptation τ 0 bigger: faster but more imprecise τ 0 smaller: slower but more precise How to choose τ 0 ? According to recommendation of Schwefel*: τ 0 = *H.-P. Schwefel: Evolution and Optimum Seeking, Wiley, NY, 1995. 1 n 17
- Page 1 and 2: Evolutionary Strategies for Multidi
- Page 3 and 4: Background I Biology = Engineering
- Page 5 and 6: Optimization f : objective function
- Page 7 and 8: Dynamic Optimization Dynamic Functi
- Page 9 and 10: The Fundamental Challenge Global co
- Page 11 and 12: Evolution Strategies 11
- Page 13 and 14: Evolution Strategy - Basics Mostly
- Page 15: Evolution Strategy: Algorithms Muta
- Page 19 and 20: Evolution Strategy Algorithms Selec
- Page 21 and 22: Operators: Selection Possible occur
- Page 23 and 24: Self-adaptation Self adaptation No
- Page 25 and 26: Self-adaptation Self adaptation: :
- Page 27 and 28: Mixed-Integer Mixed Integer Evoluti
- Page 29 and 30: Mixed-Integer Mixed Integer ES: Mut
- Page 31 and 32: Multidisciplinary Optimization (MDO
- Page 33 and 34: MDO Crash / Statics / Dynamics Mini
- Page 35 and 36: MDO Production Runs (II) Mass NuTec
- Page 37 and 38: MDO ASF ® Front Optimization Pre-o
- Page 39 and 40: MDO Run Comparison Initial design,
- Page 41: Corporate Headquarters: Charlotte,
Operators: Mutation – one σ<br />
Self-adaptive ES with one step size:<br />
One σ controls mutation <strong>for</strong> all x i<br />
Mutation: N(0, σ)<br />
Individual be<strong>for</strong>e mutation<br />
v<br />
a = (( x1,...,<br />
xn<br />
), σ )<br />
v<br />
a′<br />
= (( x′<br />
,..., x′<br />
), σ ′ )<br />
i<br />
x<br />
i<br />
1<br />
σ ′ = σ ⋅exp(<br />
τ ⋅ N<br />
x′<br />
=<br />
n<br />
0<br />
+ σ ′ ⋅ N<br />
i<br />
( 0,<br />
1)<br />
( 0,<br />
1))<br />
Individual after mutation<br />
1.: Mutation of step sizes<br />
2.: Mutation of objective variables<br />
Here the new σ‘ is used!<br />
16
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