Tutorial 2, Part 1: Optimization of a damped oscillator

2 Tutorial 2, Part 1: Optimization Damped oscillator Mass m, damping c, stiffness k and initial kinetic energy Equation of motion: Undamped eigen-frequency: Lehr's damping ratio D Damped eigen-frequency

3 Tutorial 2, Part 1: Optimization Damped oscillator Time-dependent displacement function Optimization goal: Minimize maximum amplitude after 5s free vibration Optimization constraint: Optimization parameter bounds & constant parameters:

4 Tutorial 2, Part 1: Optimization Task description Parameterization of the problem Definition and evaluation of DOE scheme Definition and evaluation of MOP Single objective, constraint optimization Gradient based optimization Global response surface method Adaptive response surface method Evolutionary algorithm Multi objective optimization Pareto optimization with evolutionary algorithm

5 Tutorial 2, Part 1: Optimization Project manager 1.Open the project manager 2.Define project name 3.Create a new project directory 4.Copy optiSLang examples/Oscillator into project director

6 Tutorial 2, Part 1: Optimization Parameterization of the problem 1.Start a new parametrize workflow 2.Define workflow name 3.Create a new problem specification 4.Enter problem file name

7 Tutorial 2, Part 1: Optimization Parameterization of the problem 1.Click “open file” icon in parametrize editor 2.Browse for the SLang input file oscillator.s 3.Choose file type as INPUT

8 Tutorial 2, Part 1: Optimization Parameterization of the problem 1.Mark value of m in the input file 2.Define m as input parameter 3.Define parameter name

9 Tutorial 2, Part 1: Optimization Parameterization of the problem 1.Open parameter in parameter tree 2.Enter lower and upper bounds (0.1 … 5.0) 1. 2.

10 Tutorial 2, Part 1: Optimization Parameterization of the inputs 1.Repeat procedure for k

11 Tutorial 2, Part 1: Optimization 1.Click “open file” icon in parametrize editor 2.Browse for the SLang output file oscillator_solution.txt 3.Choose file type as OUTPUT Parameterization of the output signal

12 Tutorial 2, Part 1: Optimization Parameterization of the problem 1.Mark output value in editor 2.Define omega as output parameter 3.Repeat for x_max and x_max_env

13 Tutorial 2, Part 1: Optimization Parameterization of the problem 1.Create new objective function 2.Define objective as x_max 2. 1.

14 Tutorial 2, Part 1: Optimization Parameterization of the problem 1.Create new constraint equation 2.Define inequality constraint 0≤8-omega 2. 1.

15 Tutorial 2, Part 1: Optimization Parameterization of the problem 1.Check overview for inputs 2.Check overview for outputs 1. 2.

16 Tutorial 2, Part 1: Optimization Parameterization of the problem 1.Check overview for objectives 2.Check overview for constraints 1. 2.

17 Tutorial 2, Part 1: Optimization Design Of Experiments (DOE) Start a new DOE workflow 2.Define workflow name and workflow identifier 3.Enter problem file name 4.Enter solver call (slang –b oscillator.s) 5.Start DOE evaluation with 100 LHS samples

18 Tutorial 2, Part 1: Optimization Meta-Model of Optimal Prognosis (MOP) Start a new MOP workflow 2.Define workflow name and workflow identifier 3.Choose DOE result file 4.Choose optional problem file 4.

19 Tutorial 2, Part 1: Optimization Meta-Model of Optimal Prognosis (MOP) CoP settings (sample splitting or cross validation) 2.Investigated approximation models 3. CoP - accepted reduction in prediction quality to simplify model 4.Filter settings 5.Selection of inputs and outputs 5.

20 Tutorial 2, Part 1: Optimization Meta-Model of Optimal Prognosis (MOP) Check approximation quality to identify solver problems and for a possible use of MOP for the optimization task

21 Tutorial 2, Part 1: Optimization Gradient-based optimization Start a new Gradient-based workflow 2.Define workflow name and workflow identifier 3.Enter problem file name 4.Choose optimization method 5.Enter solver call (slang –b oscillator.s) 6.Start gradient workflow 2. 4.

22 Tutorial 2, Part 1: Optimization Gradient-based optimization 1. 1.Keep default settings and start optimization task  Differentiation interval is too small for noisy objective  Optimizer runs into local optimum 2.Change differentiation interval to 5%  Slow convergence but global optimum is found

23 Tutorial 2, Part 1: Optimization Gradient-based optimization 1.Objective history 2.Best design input parameters 3.Best design response data 4.Objective and constraints data 5.Parameter history

24 Tutorial 2, Part 1: Optimization Gradient-based optimization using MOP 3b. 1.Start a new Gradient-based workflow 2.Define workflow name, workflow identifier and problem file name 3.Use MOP as solver and choose MOP data file 4.Enter solver call (slang –b oscillator.s) to verify best design 5.Start gradient workflow 3a. 4.

25 Tutorial 2, Part 1: Optimization Gradient-based optimization using MOP 1. 1.Keep default settings and start optimization task

26 Tutorial 2, Part 1: Optimization Gradient-based optimization using MOP 1.Objective history 2.Best design input parameters (MOP and calculated) 3.Best design response data (MOP and calculated) 4.Objective and constraints data (MOP and calculated)

27 Tutorial 2, Part 1: Optimization Adaptive response surface (local) Start a new ARSM workflow 2.Define workflow name and workflow identifier 3.Enter problem file name 4.Enter solver call (slang –b oscillator.s) 5.Start ARSM workflow 2.

28 Tutorial 2, Part 1: Optimization Adaptive response surface (local) NLPQL as optimization method 2.Approximation settings: keep polynomial regression 3.Advanced settings: no recycle of previous support points 2.

29 Tutorial 2, Part 1: Optimization Adaptive response surface (local) 1.Objective history for each iteration step 2.Best design input parameters (ARSM and original) 3.Best design response data (ARSM and original) 4.Objective and constraints data (ARSM and original) 5.Parameter history for each iteration step

30 Tutorial 2, Part 1: Optimization Adaptive response surface (global) 1. 1.GA & NLPQL as optimization method 2.Approximation settings: choose Moving Least Squares 2.

31 Tutorial 2, Part 1: Optimization Adaptive response surface (global) 1. 1.Increase stopping criteria to 0.1% 2.Advanced settings: choose recycle previous support points 2.

32 Tutorial 2, Part 1: Optimization Adaptive response surface (global)

33 Tutorial 2, Part 1: Optimization Evolutionary algorithm (EA) 1.Start a new NOA workflow 2.Define workflow name and workflow identifier 3.Enter problem file name 4.Choose optimization algorithm (EA with global search is default) 5.Enter solver call (slang –b oscillator.s) and start workflow

34 Tutorial 2, Part 1: Optimization Evolutionary algorithm (EA) 1. 1.Choose start population size 2.Keep defaults for Selection, Crossover and Mutation

35 Tutorial 2, Part 1: Optimization Evolutionary algorithm (EA) 1.Objective history for each design 2.Best design input parameters 3.Best design response data 4.Penalized objective and constraints data 5.Parameter history for each design, new generations are marked

36 Tutorial 2, Part 1: Optimization Parameterization of second objective 1.Start a new parametrize workflow 2.Define workflow name 3.Create a copy and modify it 4.Open Tutorial_Oscillator.pro and enter new problem file name

37 Tutorial 2, Part 1: Optimization Parameterization of second objective 1.Create a new objective 2.Enter name, activate and enter function obj2 = omega 3.Delete omega constraint 4.Close editor and check objectives

38 Tutorial 2, Part 1: Optimization Pareto optimization with EA Start a new Pareto workflow 2.Define workflow name and workflow identifier 3.Enter problem file name 4.Choose EA as optimization algorithm 5.Enter solver call (slang –b oscillator.s) and start workflow 2. 4.

39 Tutorial 2, Part 1: Optimization Pareto optimization with EA 1.Choose start population size 2.Keep defaults for Selection, Crossover and Mutation 1.

40 Tutorial 2, Part 1: Optimization Pareto optimization with EA 1.Plot of objective values of designs including Pareto front 2.Best design input parameters 3.Best design response data 4.Objectives data 5.Parameter history for each design, new generations are marked