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31 Important Information
Setting patterns is especially important for large-scale problems as
memory needs to be managed more properly (a dense problem is
normally assumed otherwise). Solver timings and recursive calls
primarily applies to smaller problems but could also be important
issues for larger test cases.
31.1 Passing addition variables
If the user wishes to pass additional variables to the user
functions written the parameters need to be included in the
Prob structure. The code snippets below illustrates how to do
it.
In the main function where TOMLAB is called do:
Prob = *Assign(...);
Prob.user.a = a;
Prob.user.b = b;
Result = tomRun('solver', Prob, 1);
If for example the objective function needs the additional variables
a and b do the following in the file:
function f = myobjective(x, Prob)
a = Prob.user.a;
b = Prob.user.b;
f = sum(x)*a + sum(x.^3)*b;
31.2 Using Patterns
For most problems it is critical to set the proper problem patterns
(
ConsPattern,
HessPattern and
d2LPattern) for
memory allocation purposes and to speed up numerical
differentiation. If analytical derivatives are given only the memory
benefit will be seen.
See for example the minlpQG problem and use the following code:
minlpQG
Prob.ConsDiff = 1;
Result = tomRun('npsol', Prob, 1);
Prob.ConsDiff = 11;
Result = tomRun('npsol', Prob, 1);
As can be seen only 43 constraint evaluations are done for the
second run with NPSOL. The reason being that the solver (numerical
differentiation routines) can see which variables to perturb at the
same time from the
ConsPattern.
31.3 Solver Timings
Comparing different solvers with solution times under 5-10 seconds
may yield incorrect results. When running a problem and a solver for
the first time general overhead and loading of dll's consume the
majority of the time. The following code illustrates the problem:
clear all
Prob = probInit('lp_prob', 1);
R = tomRun('minos', Prob, 1);
R = tomRun('minos', Prob, 1);
The first run may report a solution time around 0.3 seconds, while
the second run shows that the real time spent on optimization is
less than 0.01 seconds. When evaluating different solver solutions,
all tests need to be run at least twice (more recommended).
There are ways to avoid the extra overhead associated with the
driver routines
tomRun. For example one can call the solver
directly.
clear all
Prob = probInit('lp_prob', 1);
Prob = ProbCheck(Prob, 'minos');
R = minosTL(Prob);
PrintResult(R);
This is especially important when recursively calling the solver.
31.4 Recursive Calls
When doing recursive calls to a solver and modifying some of the
inputs (not the size of the problem) one should call the solver as
shown above. This minimizes the overhead during the solver call.
Warm start is commonly used when doing recursive calls. Several of
the TOMLAB solvers support warm start.
clear all
Prob = probInit('lp_prob', 1);
R = tomRun('minos', Prob, 1);
Prob = WarmDefSOL('minos', Prob, R);
R = tomRun('minos', Prob, 1);
Similar code will work for MINOS (also LP-, QP-MINOS), SNOPT, SQOPT,
NPSOL, NLSSOL, LPOPT, QPOPT, LSSOL.
When running the TOMLAB /MINLP solvers the following code is needed.
Observe that only BQPD and filterSQP can be warm started, while
miqpBB and minlpBB accept a starting point.
clear all
Prob = probInit('con_prob', 10);
R = tomRun('filterSQP', Prob, 1);
Prob = WarmDefDUNDEE('filterSQP', Prob, R);
R = tomRun('filterSQP', Prob, 1);
It is also possible to warm start TOMLAB /CPLEX for LP problems
(only simplex solvers). When doing this one has to supply a basis.
See 'help cplex' for more information.
The global solvers in the TOMLAB Base Module and TOMLAB /CGO are
easily warm started. One simply sets
Prob.WarmStart = 1
before calling the solver the second round.
31.5 Verifying Problems
There are several routines and functionality in TOMLAB for verifying
problem setup.
checkDerivs can be used to check the absolute
error of user supplied derivatives.
checkFuncs make general
user function checking and problem validation. One can also check
the derivatives with for example SNOPT, MINOS and NPSOL. The code
below illustrates how to generate a print file for further analysis.
clear all
Prob = probInit('con_prob', 10);
Prob.SOL.optPar(1) = 111111; % Major print level
Prob.SOL.optPar(2) = 10; % Minor print level
Prob.SOL.optPar(13) = 3; % Verify level
Prob.SOL.PrintFile = 'snoptP.txt'; % SNOPT print file name
Prob.SOL.SummFile = 'snoptS.txt'; % SNOPT summary file name
R = tomRun('snopt', Prob, 1);
The print file
snoptP.txt will provide details on the user
supplied derivatives. Observe that this checking should never be
done for production code. Once the derivatives have been verified it
is recommended to set Prob.SOL.optPar(13) = -1 to avoid one extra
function call.
31.6 Optimization Toolbox
There is an optimization toolbox interface included in
/tomlab/optim. These routines can be used for quick testing
of the TOMLAB capabilities when problems are setup for use with
optimization toolbox. In general, the routines should be avoided as
unnecessary overhead is introduced from the format conversion. If
one has embedded calls they should be used as is.
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