CGO ego: Difference between revisions
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===Output printing=== | ===Output printing=== | ||
{|class="wikitable" | |||
!colspan="2"|PRINTING in MATLAB window in Iteration 0 after Experimental Design | |||
|- style="text-align:center;" | |||
|colspan="2"|'''''if ''IterPrint'' >= 1 or ''PriLev'' > 1''''' | |||
|- | |||
|colspan="2"|'''Row 0''' | |||
|- | |||
| ||Initial row with values for some important parameters from Prob.CGO for the current run | |||
|- | |||
|colspan="2"|'''Row 1''' | |||
|- | |||
|''Iter''||Number of iterations | |||
|- | |||
|''n'' ||Number of trial x, n-Iter is number of points in initial design | |||
|- | |||
|nFunc ||Number of costly f(x) computed, nFunc <= n, n-nFunc = rejected pnts | |||
|- | |||
|--->> ||Time stamp (date and exact time of this printout) | |||
|- | |||
|Cycle ||Cycle steps global to local. ''infStep'' is marked -1, 0 to ''N''-1 are global steps. Last step ''N'' in cycle is surface minimum | |||
|- | |||
|R ||If the letter ''R'' is printed, the current step is a RESCUE step, i.e. the new point is already sampled in a previous step, instead the surface minimum is used as a rescue | |||
|- | |||
|fnStar ||Target value fn_star (if set) | |||
|- | |||
|fGoal ||Goal value (if set) | |||
|- | |||
|fMin ||Best f(x) found so far. E.g. at 27/It 12 means n=27, Iter=12<br>fMinI means the best f(x) is infeasible<br>fMinF means the best f(x) is feasible (also integer feasible) | |||
|- | |||
|colspan="2"|'''Row 2''' | |||
|- | |||
|max(F) ||maximum of all f(x) in the initial set of points X | |||
|- | |||
|med(F) ||median of all f(x) in the initial set of points X | |||
|- | |||
|rng(F) ||maxF-fMin, the range of f(x) values in the initial set X | |||
|- | |||
|pDist ||The size of the simply bounded region, <nowiki>||</nowiki>''x_U''-''x_L''<nowiki>||</nowiki><sub>2</sub> | |||
|- | |||
|LipU ||Maximum Lipschitz constant for initial set X | |||
|- | |||
|LipL ||Maximum Lipschitz constant for initial set X, using transformed F | |||
|- | |||
|objType||Function transformation used during run, one of 0 to 8. | |||
|- | |||
|DACEfk ||Best DACE fitness value found | |||
|- | |||
|colspan="2"|'''Row 3''' | |||
|- | |||
| ||Information about estimation of ''p'' and ''θ'' in DACE model | |||
|- | |||
|colspan="2"|'''Row 4''' | |||
|- | |||
|xMin||Best point in initial set X | |||
|- | |||
|colspan="2"|'''Row 5''' | |||
|- | |||
|xOpt||User-given global optimum Prob.x_opt (if defined) | |||
|- style="text-align:center;" | |||
|colspan="2"|'''''if ''PriLev'' > 2 and global optimum ''xOpt'' and given in ''Prob.x_opt'' ''''' | |||
|- | |||
|colspan="2"|'''Row 6''' | |||
|- | |||
|xOpt||The known global optimum | |||
|- | |||
|colspan="2"|'''Row 7''' | |||
|- | |||
|SumXO ||Sum of distances from global optimum to all sampled points ''X'' in experimental design | |||
|- | |||
|MeanX0||Mean of distances from global optimum to all sampled points ''X'' in experimental design | |||
|- | |||
|doO ||Distance from global optimum to ''x'' with best f(x) in Experimental Design, ''xMin'' | |||
|- style="text-align:center;" | |||
|colspan="2"|'''''if ''PriLev'' > 3''''' | |||
|- | |||
|dXO ||Minimal distance from global optimum to closest point of all sampled points ''X'' in experimental design | |||
|- | |||
|snOptf||Surface value at ''xOpt'', ''sn_f(xOpt)'' | |||
|- | |||
|snOptg||Surface gradient at ''xOpt'', ''sn_g(xOpt)'' | |||
|- | |||
|snOptE||Sum of negative eigenvalues of surface Hessian at ''xOpt'', sum((eig(sn_H(xOpt)) < 0)) | |||
|} | |||
==Description== | ==Description== |
Revision as of 07:29, 21 June 2014
This page is part of the CGO Manual. See CGO Manual. |
Purpose
Solve general constrained mixed-integer global black-box optimization problems with costly objective functions.
The optimization problem is of the following form
where ; ;
the linear constraints are defined by , ;
and the nonlinear constraints are defined by .
The variables are restricted to be integers,
where is an index subset of possibly empty.
It is assumed that the function is continuous with respect to all
variables, even if there is a demand that some variables only take integer values.
Otherwise it would not make sense to do the surrogate modeling of used by all CGO solvers.
f (x) is assumed to be a costly function while c(x) is assumed to be cheaply computed. Any costly constraints can be treated by adding penalty terms to the objective function in the following way:
where weighting parameters wj have been added. The user then returns p(x) instead of f (x) to the CGO solver.
Calling Syntax
Result=ego(Prob,varargin) Result = tomRun('ego', Prob);
Usage
See CGO solver usage
Description of Inputs
Problem structure
The following fields are used in the problem description structure Prob:
Field | Description |
---|---|
Name | See Common input for all CGO solvers |
FUNCS.f | |
FUNCS.c | |
x_L | |
x_U | |
b_L | |
b_U | |
A | |
c_L | |
c_U | |
WarmStart | |
user | |
MaxCPU | |
PriLevOpt | |
optParam | |
CGO | See the table below but also this table for input common to all CGO solvers |
GO | See common input for all CGO solvers |
MIP | See common input for all CGO solvers |
varargin | Additional parameters to ego are sent to the costly f(x) |
- Special EGO algorithm parameters in Prob.CGO - | |
---|---|
EGOAlg | Main algorithm in the EGO solver
=1 Run expected improvement steps (modN = 0,1,2,...). If no f (x) improvement, use DACE surface minimum (modN = -1) in 1 step =2 Run expected improvement steps (modN=0) until ExpI / |yMin| < TolExpI for 3 successive steps (modN = 1,2,3) without f (x) improvement (fRed <= 0). =3 Compute trial points from both Expexted Improvement and DACE surface minimum in every step =4 Compute DACE surface minimum in every step Default EGOAlg = 1, but if any x is integer valued, EGOAlg = 3 is default |
pEst | Norm parameters, fixed or estimated, also see p0, pLow, pUpp (default pEst = 0).
0 = Fixed constant p-value for all components (default, p0=1.99). 1 = Estimate one p-value valid for all components. 2 = Estimate d|| ||p parameters, one for each component. |
p0 | Fixed p-value (pEst==0, default = 1.99) or initial p-value (pEst == 1, default 1.9) or d-vector of initial p-values (pEst > 1, default 1.9*ones(d,1)) |
pLow | If pEst == 0, not used
if pEst == 1, lower bound on p-value (default 1.98) if pEst == 2, lower bounds on p (default 1.99*ones(d,1)) |
pUpp | If pEst == 0, not used
if pEst == 1, upper bound on p-value (default 1.99999) if pEst == 2, upper bounds on p (default 1.99999*ones(d,1)) |
snPLim | Avoid the time consuming global optimization in DACEFit for iterations > snPLim. Instead just do a local search from the previous DACE parameter model This part is the most time consuming in ego Default 15 if pEst = 0, Default 20 if pEst = 1, Default 25 if pEst > 1 |
TolExpI | Convergence tolerance for expected improvement (default 10-7). |
SAMPLEF | Sample criterion function:
0 = Expected improvment (default) 1 = Kushner's criterion (related option: KEPS) 2 = Lower confidence bounding (related option: LCBB) 3 = Generalized expected improvement (related option: GEIG) 4 = Maximum variance 5 = Watson and Barnes 2 |
KEPS | The ε parameter in the Kushner's criterion If set to a positive value, the epsilon is taken as KEPS. If set to a negative value, then epsilon is taken as |KEPS|*f_min Default: -0.01 |
GEIG | The exponent g in the generalized expected improvement function Default: 2 |
LCBB | Lower Confidence Bounding parameter b Default 2 |
AddSurfMin | Add up to AddSurfMin global or local minima on DACE surface as search points, based on estimated Lipschitz constants, number of components on bounds, and distance to sampled set X. AddExpIMin=0 implies no additional minimum added. |
AddExpIMin | Add up to AddExpIMin global or local minima on ExpI surface as search points, based on estimated Lipschitz constants, number of components on bounds, and distance to sampled set X. AddExpIMin=0 implies no additional minimum added. Only possible if globalSolver = 'multiMin' or 'glcCluster'. Default AddExpIMin = 1 |
Description of Outputs
Result structure
The output structure Result contains results from the optimization.
The following fields are set:
Field | Description | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
x_k | See Common output for all CGO solvers for details. | ||||||||||||||||||
f_k | |||||||||||||||||||
Iter | |||||||||||||||||||
FuncEv | |||||||||||||||||||
ExitText | |||||||||||||||||||
ExitFlag | Always 0 | ||||||||||||||||||
Inform | Information parameter.
| ||||||||||||||||||
CGO | Subfield WarmStartInfo saves warm start information, the same information as in cgoSave.mat, see Common output for all CGO solvers#WSInfo. |
Output printing
PRINTING in MATLAB window in Iteration 0 after Experimental Design | |
---|---|
if IterPrint >= 1 or PriLev > 1 | |
Row 0 | |
Initial row with values for some important parameters from Prob.CGO for the current run | |
Row 1 | |
Iter | Number of iterations |
n | Number of trial x, n-Iter is number of points in initial design |
nFunc | Number of costly f(x) computed, nFunc <= n, n-nFunc = rejected pnts |
Cycle | Cycle steps global to local. infStep is marked -1, 0 to N-1 are global steps. Last step N in cycle is surface minimum |
R | If the letter R is printed, the current step is a RESCUE step, i.e. the new point is already sampled in a previous step, instead the surface minimum is used as a rescue |
fnStar | Target value fn_star (if set) |
fGoal | Goal value (if set) |
fMin | Best f(x) found so far. E.g. at 27/It 12 means n=27, Iter=12 fMinI means the best f(x) is infeasible fMinF means the best f(x) is feasible (also integer feasible) |
Row 2 | |
max(F) | maximum of all f(x) in the initial set of points X |
med(F) | median of all f(x) in the initial set of points X |
rng(F) | maxF-fMin, the range of f(x) values in the initial set X |
pDist | The size of the simply bounded region, ||x_U-x_L||2 |
LipU | Maximum Lipschitz constant for initial set X |
LipL | Maximum Lipschitz constant for initial set X, using transformed F |
objType | Function transformation used during run, one of 0 to 8. |
DACEfk | Best DACE fitness value found |
Row 3 | |
Information about estimation of p and θ in DACE model | |
Row 4 | |
xMin | Best point in initial set X |
Row 5 | |
xOpt | User-given global optimum Prob.x_opt (if defined) |
if PriLev > 2 and global optimum xOpt and given in Prob.x_opt | |
Row 6 | |
xOpt | The known global optimum |
Row 7 | |
SumXO | Sum of distances from global optimum to all sampled points X in experimental design |
MeanX0 | Mean of distances from global optimum to all sampled points X in experimental design |
doO | Distance from global optimum to x with best f(x) in Experimental Design, xMin |
if PriLev > 3 | |
dXO | Minimal distance from global optimum to closest point of all sampled points X in experimental design |
snOptf | Surface value at xOpt, sn_f(xOpt) |
snOptg | Surface gradient at xOpt, sn_g(xOpt) |
snOptE | Sum of negative eigenvalues of surface Hessian at xOpt, sum((eig(sn_H(xOpt)) < 0)) |
Description
ego implements the algorithm EGO by D. R. Jones, Matthias Schonlau and William J. Welch presented in the paper "Efficient Global Optimization of Expensive Black-Box Functions".
Please note that Jones et al. has a slightly different problem formulation. The TOMLAB version of ego treats linear and nonlinear constraints separately.
ego samples points to which a response surface is fitted. The algorithm then balances between sampling new points and minimization on the surface.
ego and rbfSolve use the same format for saving warm start data. This means that it is possible to try one solver for a certain number of iterations/function evaluations and then do a warm start with the other. Example:
>> Prob = probInit('glc_prob',1); % Set up problem structure >> Result_ego = tomRun('ego',Prob); % Solve for a while with ego >> Prob.WarmStart = 1; % Indicate a warm start >> Result_rbf = tomRun('rbfSolve',Prob); % Warm start with rbfSolve
M-files Used
iniSolve.m, endSolve.m, conAssign.m, glcAssign.m
See Also
rbfSolve
Warnings
Observe that when cancelling with CTRL+C during a run, some memory allocated by ego will not be deallocated.
To deallocate, do:
>> clear egolib