Optimization
Handle optimization solver properties.
Syntax
model.sol(sname).create(fname,"Optimization")
model.sol(sname).feature(fname).set(pname,value)
model.sol(sname).feature(fname).create(aname,SolverAttribute)
Description
Operation feature. Use this feature to solve PDE-constrained optimization problems. The computed solution object contains the PDE solution evaluated for the optimal set of design variables. When the gradient-evaluation method is analytic, it also returns the adjoint solution.
The Optimization Module includes SNOPT and several other optimization solvers. See the Optimization Module Manual for details.
To add a stationary solver, substitute SolverAttribute above with StationaryAttrib. For a time-dependent solver, replace SolverAttribute with TimeAttrib.
Choosing solver is done with the following property:
Table 6-55: Property to select optimization solver.
Property
Value
Default
Description
optsolver
bobyqa | cobyla | coordsearch | lm | mma | montecarlo | neldermead | snopt | ipopt | ego
neldermead
Optimization solver
The following table includes general optimization solver properties, which a common to all optimization solvers:
Table 6-56: General Optimization Properties.
Property
Value
Default
Description
clist
String array
off
Provide values for constants as input parameters using a string array; for the corresponding constant names, use cname. See The clist and cname Properties.
cname
String array
off
Provide names of constants as input parameters using a string array; for the corresponding constant values, use clist. See The clist and cname Properties.
control
String
user
Name of the controlling study step or user, if the feature is controlled manually.
keeplog
on | off
off
Keep warnings in stored log.
message
String
 
The log message from the last solution process.
objcontrib
all | manual
all
Whether to use all objective contributions present or specify manually (not available if optsolver is lm).
opttol
real scalar
0.01
Optimality tolerance for derivative free optimization solvers.
opttolinner
real scalar
0.001
Optimality tolerance for gradient based optimization solvers.
gradientstep
String
The last study step in the list or none, if there is no supported study step.
Name of the study step to use for gradient computation.
useseed
on | off
off
Random seed. Available for montecarlo.
randseed
integer
1000
Random seed. Available for montecarlo.
nsolvemax
integer
1000
Maximum number of model evaluations.
lsqdatamethod
manual|lsq
manual
Least-squares time/parameter method. Available when there are lsq objectives in the model.
keepsol
auto | last | all
auto=last
Keep last or all solutions for derivative free optimization solvers.
keepsolgb
last | lastn | everynth
last
Keep last or all solutions for gradient based optimization solvers.
err
on | off
on
Stop if error. Available for derivative free optimization solvers.
nkeepsols
integer
2
Number of solutions to save. Available for gradient based optimization solvers, when keepsolgb=lastn.
nskipsols
integer
10
Save every Nth. Available for gradient based optimization solvers, when keepsolgb=everynth.
optobj
String array
 
User defined objective expressions.
descr
String array
 
Descriptions for used defined objective expressions.
optobjEvaluateFor
String array
 
Study to evaluate objective expressions for.
objectivetype
minimization | maximization
sum
Determines whether the objective should be minimized or maximized.
multiobjective
sum | min | max
sum
Multiple objectives. Only sum is supported for gradient based optimization solvers.
objectivesolution
auto | first | last | sum | min | max
auto
Solution. Handling of multiple solution vectors. Only auto available for SNOPT, IPOPT, and LM.
outersolution
sum | min | max
sum
Outer solution. Available for derivative free optimization solvers, when there are Parametric Sweep study steps under Optimization.
objectivescaling
init | manual | none
none
Enable/disable objective scaling.
objscaleval
real scalar
1
Objective scale.
pname
String array
 
Global parameter names to use as control variables.
initval
String array
 
Initial values for global parameters used as control variables.
scale
String array
 
Scales for global parameters used as control variables.
lbound
String array
 
Lower bounds for global parameters used as control variables.
ubound
String array
 
Upper bounds for global parameters used as control variables.
constraint
Expression
String array
 
Global constraint expressions.
constraintL
bound
String array
 
Lower bounds for global constraint expressions.
constraintU
bound
String array
 
Upper bounds for global constraint expressions.
constrmethod
penalty | augLagrange
augLagrange for BOBYQA, penalty for others.
Constraint handling method, not available for COBYLA.
coefrho
auto | manual
auto
Strategy for penalty parameter rho. Available when constrmethod=penalty.
rho
real scalar
10
Penalty parameter rho. Available when constrmethod=penalty and coefrho=manual.
tau
real scalar
0.5
Tolerance for the penalty parameter. Available when constrmethod=augLagrange.
gamma
real scalar
10
Multiplication factor for the penalty parameter. Available when constrmethod=augLagrange.
mu
real scalar
Max double value
Upper bound on Lagrange multipliers. Available when constrmethod=augLagrange.
nlagevals
integer
10
Maximum number of augmented iterations. Available when constrmethod=augLagrange.
deltachoice
dynamic | dynamic2 | static
dynamic
Strategy for the subsolver tolerance.
aCoef
real scalar
2
Tolerance parameter for the subsolver. Available when deltachoice=dynamic2.
delta
real scalar
0.001
Tolerance parameter for the subsolver. Available when deltachoice=static.
enfdesconstr
on | off
on
Enforce design constraints strictly. Available when optsolver is equal to neldermead, cobyla, montecarlo, or coordsearch.
plot
on | off
off
Enable/disable plot while solving.
plotgroup
String
default
Tag of the plotgroup to plot while solving.
probesel
all | none | manual
all
The probes to compute while solving.
probes
String array
 
Probes to use, if probesel=manual.
useobjtable
on | off
on
Keep objective values in table.
objtable
String
new
Output table to use, when useobjtable=on.
showindobj
on | off
off
Show individual objective values in table.
plotobj
on | off
off
Plot objective while solving.
window
String
new
Window to use, if plotobj=bj=on.
useconstrtable
on | off
on
Keep values of constraints in table. Only available with the derivative free optimization solvers.
constrtable
String
new
Table to use, when useconstrtable=on.
pdistrib
on | off
off
Distribute parametric sweep. Available when optsolver is equal to coordsearch, neldermead, or montecarlo.
nparallelsolve
integer
1
Maximum number of model evaluations in each parametric sweep, available when pdistrib=on.
convinfo
on | off | detailed
on
Optimization log.
keepaccumtable
on | off
off
Keep accumulated probe table. Available for derivative free optimization solvers.
When the optimization solver is set to SNOPT (snopt), the following properties are accepted:
Table 6-57: Valid Properties for optsolver snopt.
Property
Value
Default
Description
cendiff
real scalar
6e-6
Central difference interval (only available when gradientsnopt is numeric)
difint
real scalar
1.5e-8
Difference interval (only available when gradientsnopt is numeric).
feastol
real scalar
1e-6
Linear constraint tolerance.
funcprec
real scalar
3.8e-11
Function precision.
gradientsnopt
analytic | numeric | forward|adjoint| forward_numeric
analytic
Gradient/Jacobian evaluation method for SNOPT.
hessupd
integer
10
Hessian updates.
linesearch
derivative | nonderivative
derivative
Use a derivative (gradient) or nonderivative (gradient free) linesearch strategy.
linestol
real scalar
0.9
Linesearch tolerance (a value between 0 and 1). A lower value gives a more accurate search.
majfeastol
real scalar
1e-6
Nonlinear constraint tolerance.
manualhessupd
on | off
off
Whether to use the property hessupd.
manualstepcond
on | off
off
Whether to use manual step condition.
optobj
String
 
Objective function that is minimized when objcontrib=manual.
qpsolver
cholesky | cg | qn
cholesky
QP subproblem algorithm.
snoptmaxiter
integer
1
Maximum number of major iterations
snoptmaxiteractive
on | off
off
Enable maximum major iterations.
snoptprintdir
String
 
For log files for SNOPT, specify the directory of the log file. Use the snoptprintfile to specify the log file.
snoptprintfile
String
snoptout.txt
For log files for SNOPT, specify the name of the log file. Use the snoptprintdir to specify the directory. If no name is specified, the log-file name is snoptout.txt.
snopttotitlim
integer
Integer.
MAX_VALUE
Total number of iterations in SNOPT.
snoptverifylevel
integer
-1
Verify the objective and constraint gradients using finite differences. This property takes values from -1 to 3. See the User’s Guide for SNOPT for more information.
stepcond
String
empty
Manual step condition.
The property gradientsnopt is used to control if the gradient should be computed analytically (by solving the adjoint problem) or numerically. If the number of design variables is large, numerical computation of the gradient can be very time consuming. Analytic gradient is only supported when the underlying PDE problem is stationary.
If manualstepcond is set to on, the expression in the property stepcond is evaluated when new values for the design variables have been computed. If the expression becomes negative, the new values are discarded and the optimization solver reduces the step length in the current line search.
When the optimization solver is set to IPOPT (ipopt), the following properties are accepted:
Table 6-58: Valid Properties for optsolver IPOPT.
Property
Value
Default
Description
evaluate_orig_obj_at_resto_trial
on | off
off
Determines if the original objective function should be evaluated at restoration phase trial points.
expect_infeasible_problem
on | off
off
Enable heuristics to quickly detect an infeasible problem.
gradientipopt
analytic | forward | adjoint | forward_numeric
analytic
Gradient/Jacobian evaluation method for IPOPT.
ipopt_acceptable_iter
integer
15
Number of acceptable iterates before triggering termination.
ipopt_acceptable_constr_viol_tol
real scalar
1
Constraint violation acceptance absolute tolerance factor
ipopt_acceptable_compl_inf_tol
real scalar
1
Complementarity conditions acceptance absolute tolerance factor
ipopt_acceptable_tol_fact
real scalar
10
Acceptable convergence tolerance (relative).
ipopt_dual_inf_tol
real scalar
1
Absolute tolerance on the dual infeasibility factor.
ipopt_expect_infeasible_problem_ctol
real scalar
1e-2
Threshold for disabling expect_infeasible_problem option.
ipopt_expect_infeasible_problem_ytol
real scalar
1e8
Multiplier threshold for activating expect_infeasible_problem option.
ipopt_file_print_level
integer
5
Verbosity level for output file.
ipopt_linear_solver
mumps | pardiso
mumps
Linear solver used for step computations.
ipopt_mumps_mem_percent
real scalar
1000
Percentage increase in the estimated working space for MUMPS.
ipopt_mumps_pivtol
real scalar
1e-6
Pivot tolerance. Available for MUMPS.
ipopt_mumps_pivtolmax
real scalar
0.1
Maximum pivot tolerance. Available for MUMPS.
ipoptprintdir
String
 
For log files for IPOPT, specify the directory of the log file. Use the ipoptprintfile to specify the log file.
ipoptprintfile
String
ipoptout.txt
For log files for IPOPT, specify the name of the log file. Use the ipoptprintdir to specify the directory. If no name is specified, the log-file name is snoptout.txt.
optobj
String
 
Objective function that is minimized when objcontrib=manual.
start_with_resto
on | off
off
Tells algorithm to switch to restoration phase in first iteration.
The property gradientipopt is used to control if the gradient should be computed analytically (by solving the adjoint problem) or numerically. If the number of design variables is large, numerical computation of the gradient can be very time consuming. Analytic gradient is only supported when the underlying PDE-problem is stationary.
When the optimization solver is set to Levenberg–Marquardt (lm), the following properties are accepted:
Table 6-59: Valid Properties for optsolver lm.
Property
Value
Default
Description
cendiff
real scalar
6e-6
Central difference interval (only available when gradientlm is numeric and gradorder is second)
difint
real scalar
1.5e-8
Difference interval (only available when gradientlm is numeric and gradorder is first).
gammaf
real scalar
1
Defect reduction tolerance factor.
gammafactive
on | off
off
Terminate also for defect reduction.
gammax
real scalar
1
Control variable tolerance factor.
gradientlm
analytic | numeric | forward | adjoint | forward_numeric
analytic
Gradient/Jacobian evaluation method.
gradorder
first | second
first
Approximation order of the gradient.
lmfact
real scalar
1e-3
Initial Levenberg-Marquardt factor.
lmmaxiter
integer
1
Maximum number of outer iterations.
lmmaxiteractive
on | off
off
Enable maximum outer iterations.
outfsens
on | off | onpws
on
Store functional sensitivity. onpws is equivalent to on, except the sensitivity is also stored in the solution while solving. This is relevant when using the results while solving functionality.
When the optimization solver is set to MMA, the following properties are accepted:
Table 6-60: Valid Properties for optsolver MMA.
Property
Value
Default
Description
gcmma
on | off
on
Use the globally convergent MMA algorithm.
gradientmma
analytic | forward | numeric | adjoint | forward_numeric
analytic
Gradient/Jacobian evaluation method.
mmamaxiter
positive integer
1
Maximum outer iterations.
mmamaxiteractive
on | off
off
Enable maximum outer iterations.
mmainnmax
positive integer
10
Maximum inner iterations per outer iteration (only for gcmma=off ).
mmagepsfactor
real scalar
0.1
Internal tolerance factor.
mmacfactor
real scalar
1000
Constraint penalty factor.
mmaghinit
real scalar
0.5
Initial asymptote factor (ghinit).
mmaghdecr
real scalar
0.7
Decreasing asymptote factor (ghdecr).
mmaghincr
real scalar
1.2
Increasing asymptote factor (ghincr).
mmaasymin
real scalar
0.01
Minimum asymptote level (asymin).
mmaasymax
real scalar
10
Maximum asymptote level (asymax).
mmaalbefa
real scalar
0.1
Bounds asymptote factor (albefa).
mmaxxmove
real scalar
0.5
Bounds control factor (xxmove).
mmaraai
real scalar
0.00001
Approximation increment (raai).
mmaraamin
real scalar
0.000001
Lower approximation bound (raamin).
mmalsq
on | off
on
Automatically transform least-squares objectives to constraints for efficiency.
mmaminmax
on | off
on
Automatically transform minimax and maximin problems to constraints for efficiency.
movelimit
real scalar
0.1
Limit the maximum absolute change of any scaled control variable between outer iterations.
movelimitactive
on | off
off
Enable movelimit.
When the optimization solver is set to EGO, these additional properties are available:
Table 6-61: Valid Properties for Optsolver EGO
Property
Value
Default
Description
acquisitionmaxmethod
direct | montecarlo
direct
Optimization method for acquisition function.
covfunction
se | matern32 | matern52 | nn
matern32
Type of covariance function to use in the Gaussian process function. Use se for Squared exponential, matern32 for Matérn 3/2, matern52 for Matérn 5/2 and nn for Single-layer neural network.
globalgpconstrfunction
new | Gaussian Process function
new
Constraint Gaussian process function to use.
globalgpfunction
new | Gaussian Process function
new
Gaussian process function to use.
gpusage
restart | continue
restart
Usage: restart or continue to improve.
maxgpevalsacquisition
positive integer
10000
Maximum surrogate evaluations for optimization, if acquisitionmaxmethod is set to direct.
maxgpitersacquisition
positive integer
500
Maximum number of optimization iterations, if acquisitionmaxmethod is set to direct.
meanfunction
const | linear | quadratic
const
Defines the overall trend of the trained function(s).
ninitsample
positive integer
10
Initial sample per control variable, if gpusage is set to restart.
nmontecarlo
positive integer
10000
Surrogate evaluations for optimization, if acquisitionmaxmethod is set to montecarlo.
restol
double
1e-16
Resolution tolerance for the Gaussian process function.
For a description of the optimization properties, see Advanced Solver Properties in the Optimization Module User’s Guide.
Table 6-62: Removed femoptim Properties.
Property
Reason
Callblevel
Handled by attribute features
Solprop
Handled by stationary or time
Solcomp
Handled by variables
Report
Handled by variables
Out
Solution should be exported