12 gbm code optimum design

8/3/2019 12 GBM Code Optimum Design

1/25

11

Center for Advanced eCenter for Advanced e--System Integration TechnologySystem Integration Technology

Introduction to Optimum Design Programand ApplicationsIntroduction to Optimum Design Programand Applications

[Contents]

Selection of Good Optimization Algorithm

DOT/VisualDOCOther Optimum Design Codes

Optimum Design Examples using Optimum

Design program


2/25


1. Selection of Good Optimization Algorithm. Selection of Good Optimization Algorithm


3/25

Center for Advanced eCenter for Advanced e--System Integration Technology,System Integration Technology,KonkukKonkuk Univ.Univ.

Attributes of a Good Optimization AlgorithmAttributes of a Good Optimization Algorithm

Aspects need to be considered Robustness, efficiency, generality, ease to use

Reliability or Robustness

Reliabil ity of an algorithm is guaranteed if it is theoretically proven to

converge

Guarantees same optim ization results starting from different initial estimates.

Has higher prior ity over efficiency

Generality

The algorithm should be able to treat equality as well as inequality constraints.

Ease of use

Ease to use by the experienced as well as inexperienced designer

Efficiency Faster rate of convergence to the minimum point

Least number of calculations w ithin one design iteration

Efficiency w ithin an iteration implies the minimum of calculations for the

search direction and the step size


4/25Center for Advanced eCenter for Advanced e--System Integration Technology,System Integration Technology,KonkukKonkuk Univ.Univ.

QuestionsBefore Selecting an Optimization Algorithm

QuestionsBefore Selecting an Optimization Algorithm

Does the algorithms have proof of convergence? Is it theoretically guaranteed to converge to an optimum point starting

from any initial design estimate?

Can the starting design be infeasible?

Can the algorithm solve a general optimization problem without any

restrictions on the constraint functions?

Can it treat equality as well as inequality constraints?

Is the algorithm ease to use?

Does it require tuning for each problem?

Does the algorithm incorporate a potential constraint strategy?

Does it provide well defined GUI?


5/25


2. DOT/VisualDOC. DOT/VisualDOC



DOT (Design Optimization Tools)DOT (Design Optimization Tools)

Description

A general purpose numerical optim ization software (Fortran-based

program) package created by Vanderplaats Research &

Development(VR&D)

DOT can be used to solve a w ide variety of nonlinear optimization

problems.

The user provides a main program for calling DOT, and an analysis

program to evaluate the necessary function. Algorithms

For constrained optimization :

Modified Method of Feasible Direction (MMFD) : option 1

Sequential Linear Programming(SLP) with adjustable move limits : option 2

Sequential Quadratic Programming (SQP) : option 3

For Unconstrained optimization :

Broydon-Fletcher-Goldfarb-Shanno (BFGS) algorithm : option 1

Fletcher-Reeves (FR) Algorithm : option 2


7/25



VisualDOC : DescriptionVisualDOC : Description

VisualDOC is a software system created by VR&D

It simplifies the addition of optimization to almost any design task.

VisualDOC is uses a graphical user interface(GUI) along with optimization

algorithms to setup and solve design problem

VisualDOCs optimization library is based on the general purpose optimization

software Design Optimization Control(DOC) and Design Optimization Tools(DOT).

Option of VisualDOC

Direct optimization by the VisualDOC optimizer

Optimization through the use of response surface techniques

(approximation technique) .

To calculate responses user can either supply a computer routine written in C/C++

or Fortran, or user can couple an existing program with VisualDOC. VisualDOC solves design problems by iteratively calling the optimizer to modify

the design variables and then calculating the resulting responses.

VisualDOC provides API and third party interface.

More options and capabilities included in VisualDOC 2.0



VisualDOC : OptimizerVisualDOC : Optimizer

For constrained optimization :

Modified Method of Feasible Direction (MMFD)

Sequential Linear Programming(SLP) w ith adjustable move l imits

Sequential Quadratic Programming(SQP)

For Unconstrained optimization :

Broydon-Fletcher-Goldfarb-Shanno (BFGS) algorithm

Fletcher-Reeves (FR) Algorithm

For problems of fewer than 10 design variables, user can use response

surfaces (approximation technique).

There are no implicit limits on problem size.

Design variables may be continuous, discrete, or any combination. Linear or nonlinear design variable linking is supported.

An arbitrary number of constraints may be specified, and multiple

optimization is supported.



VisualDOC : ComponentsVisualDOC : Components



VisualDOC : Graphical User InterfaceVisualDOC : Graphical User Interface

Using the graphical user interface (GUI), user define a catalog ofvariables and responses.

The graphical user interface lets user enter and modify all optimization

components of a design problem.

User can supply initial values and limits for the variables.

User can also supply limits on some responses, which are called

constraints, and specify one or more responses as design objectives.

The design objectives can be minimized, maximized, or driven to target

values by a simple click of the mouse.

Different windows organize users design data, providing a clear,

concise description of users design problems.


12/25


GUI Example(Windows) in VisualDOCGUI Example(Windows) in VisualDOC


13/25


How VisualDOC Interface Works?How VisualDOC Interface Works?

The primary function of the VisualDOCinterface is to set up the optimization problem.

The data is passed between these modules

using a global data structure

Optimizer adjusts the values of theindependent design variables.

The modified design variable values are sent

back to the analysis routine.

The analysis code returns the direct response

values to the optimizer.

Values of objective and constraint functions

are calculated.

The objective and constraint values are

passed back to the optimizer, which then

adjusts the design variables once again.

This process continues in the same fashion

until optimum has been found.

VisualDOCGraphical User Interface

VisualDOC

Optimizer

AnalysisRoutine


14/25


3. Other Optimum Design Codes. Other Optimum Design Codes

GBM d liGBM d li t


15/25


GBM code listsGBM code lists

Several GBM codes for general design optimization purpose CFSQP - nonl inear and minmax optimizat ion.

CONOPT - nonlinear programming.DOT - Design Optimization Tools.

FSQP - nonl inear and minmax optimizat ion.GINO - nonl inear programming.GRG2 - nonl inear programming.LANCELOT - large-scale problems.LSGRG2 - nonlinear programming.

MINOS - l inear programming and nonlinear optimization.NLPQL - nonl inear programming.NLPQLB - nonlinear programming with constraints.NLPSPR - nonl inear programming.

NPSOL - nonl inear programming.OPSYC - OPt imisation de SYstmes Creux.OPTIMA Library - optimization and sensitivity analysis.OPTPACK- constrained and unconstrained optimization.SQP - nonl inear programming.

MINOS 5 1MINOS 5 1


16/25


MINOS 5.1MINOS 5.1

MINOS is a Fortran-based computer system designed to solve large-

scale optimization problems.

Algorithms

Linear problem : the primal Simplex method

Nonlinear objective : a linearly constrained nonlinear program.

a reduced gradient algorithm in conjunction with a quasi-Newton algorithm

(BFGS)

Nonlinear Constraints :

a projected augmented Lagrangian algorithm

MINOS is designed to find solutions that are locally optimum.

No GUI and APIs are available (Consol Application)


17/25


GENESIS-Structural Optimization SoftwareENESIS-Structural Optimization Software

Genesis GENESIS is a fully integrated structural analysis and design optimization

software. Analysis is based on the finite element analysis (FEA) for static,

normal modes, direct and modal analysis, heat transfer calculations, and

buckling analysis.

Design optimization is based on the advanced approximation concepts

approach to find an optimum design efficiently and reliably. Actual

optimization is performed by the well established DOT and BIGDOT

(excess of 2 mill ion design variables) optim izers, also from VR&D.

GENESIS performs both sizing (member dimension) and shape

(geometry) optimization. Typical problem sizes involve well over 100

design variables and many thousands of constraints. Almost any

calculated response (or nonlinear function of variables and responses)

can be chosen as the objective or may be constrained. These include mass,volume, eigenvalues, stresses, and deflections.

Pre- and post-processing is done by the PDA/ PATRAN and SDRC/ IDEAS

programs.


18/25


Excel Solverxcel Solver

Excel Solver The Solver option in EXCEL 2000 (and earlier versions) may be

used to solve linear and nonlinear optimization problems.

Integer restrictions may be placed on the decision variables.

Solver may be used to solve problems w ith up to 200 decision

variables (design variables), 100 explicit constraints and 400

simple constraints (lower and upper bounds and/ or integer

restrictions on the decision variables).

Algorithms

Newtons method

Conjugate gradient method


19/25


4. Optimum Design Examples usingOptimum Design program4. Optimum Design Examples usingOptimum Design program

Space Launch Vehicle DesignSpace Launch Vehicle Design


20/25


Space Launch Vehicle DesignSpace Launch Vehicle Design

Design problem

Minimize CD : Drag Coefficient

Subject to Ch a : Surface heat t ransfer rateNose Pairing Volume bFineness ratio = c, where a, b, c are constant

Number of design variables : Xi, i= 1, 4

Linearization of objective function and design constraints

Sensitivity Analysis

Update the design

44

43

3

32

3

21

1

1 XX

CXX

CXX

CXX

CCCDDDD

nomialDD

++

++

1

432143211

1

1 ),,,(),,,(

X

XXXXCXXXXXC

X

CDDD

=

XXXnomialnew

44

43

3

32

3

21

1

1 XX

CX

X

CX

X

CX

X

CCC

hhhh

nomialhh

++

++

Updated Design variables


21/25

DOT Main program (main for)DOT Main program (main for)


22/25


DOT Main program (main.for)DOT Main program (main.for)

DIMENSION X(100),XL(100),XU(100),G(100),

*WK(800),IWK(200),RPRM(20),IPRM(20)

C DEFINE NRWK, NRIWK.

NRWK=800

NRIWK=200

C ZERO RPRM AND IPRM.DO 10 I=1,20

RPRM(I)=0.0

10 IPRM(I)=0

c

RPRM(1)=-0.0005

RPRM(2)=0.00005

C DEFINE METHOD,NDV,NCON.METHOD=2

NDV=4

NCON=2

C DEFINE BOUNDS AND INITIALDESIGN .DO 20 I=1,NDV

X(I) = 0.0

XL(I)=-0.2

20 XU(I)= 0.2

100 CALL DOT (INFO,METHOD,IPRINT,NDV,NCON,X,XL,XU,

*OBJ,MINMAX,G,RPRM,IPRM,WK,NRWK,IWK,NRIWK)

C FINISHED?

IF(INFO.EQ.0) STOP

C EVALUATE OBJECTIVE AND CONSTRAINT.

CALL EVAL(OBJ,X,G)

C GO CONTINUE WITH OPTIMIZATION.

GO TO 100

END

c-----OBJECTIVE & CONSTRAINTS------------------------------------------

SUBROUTINE EVAL (OBJ,X,G)

implicit real*8 (a-h, o-z)

IMENSION X(*),G(*), d(5), h(5),aold(4)

OBJ = d1 + d2* X(1) + d3* X(2) + d4* X(3) + d5* X(4)

G(1)=h1 + h2* X(1) + h3*X(2) + h4* X(3) + h5*X(4)-

0.012453

G(2)= (-1.)* vol + 0.198919

RETURN

END

Optimization method : SLP

No. of design variables : 4

No. of constraints : 2

OBJ:Objectivefunction

G(1),G(2): Constraintfunction

X(i):DesignvariableSide Constraints

2-Bar Truss Design : Structural Optimization2-Bar Truss Design : Structural Optimization


23/25


2 Bar Truss Design : Structural Optimization2 Bar Truss Design : Structural Optimization

Description The symm etric 2-bar truss design shown in below has been studied by several

researchers

Ball ing and Clark(1992), Schmit, (1981), Sobieszczanski-Sobieski et al(1982)

The objective of this optimum problem is to min imize the weight of truss systemsubject to behavioral constraints

Related parameters

- B = 30 in

- t = 0.1 in

- = 0.3 lbs/ in3- y = 60,000 psi- E = 30E6 ps i



24/25



Formulation for Optimization Minimize W(X)=2Dt(B2+H2)1/ 2

Minimize the weight of truss system

Subject to

g1(X) = e - 0 the first constraint prevents failure due to Euler buckling

g2(X) = y - 0 the second constraint prevents failure due to yield stress

Where,0.5D5.0 (in) X(1) : mean tube diameter5.0H50.0 (in) X(2) : height of the truss

The resulting optimum value from (Schmit, 1981) for W(x) is 19.8lbs.

- W * = 19 .8 lbs (at D* = 2.47 in , H* = 30.15 in )



25/25



Comparisons with Algorithm and initial Valueinitial values X(1) =0. , X(2)= 0.

DOTProgram

Constrained Unconstrained

Algorithm MMFD SLP SQP BFGS F-R -X1 (D) 2.481 2.476 2.476 4.558 4.558 2.47

X2 (H) 29.870 29.992 30.00 15.031 15.031 30.15

Opt. val. (W) 19.800 19.800 19.800 28.828 28.828 19.8

Num. of Iter. 9 20 11 3 3 -

Num. of fun. eval. 77 69 45 24 24 -

true

initial values X(1) =1. , X(2)= 5.

-2626406626Num. of fun. eval.

-3310205Num. of Iter.

19.823.60123.60119.80019.80022.690Opt. val. (W)

30.1517.82017.82030.04129.99017.588X2 (H)

2.473.5883.5882.4742.4803.462X1 (D)

-F-RBFGSSQPSLPMMFDAlgorithm

UnconstrainedConstrainedtrue

DOTProgram

12 gbm code optimum design

Documents