Common input for all CGO solvers
Input parameters
Prob structure
The following fields are used in the problem description structure Prob | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Field | Description | ||||||||||||
Name | Name of the problem. Used for security when doing warm starts. | ||||||||||||
FUNCS.f | The routine to compute the function, given as a string, e.g. CGOF. | ||||||||||||
FUNCS.c | The routine to compute the nonlinear constraint, e.g. CGOC. | ||||||||||||
x_L | Lower bounds for each element in x. Must be finite. | ||||||||||||
x_U | Upper bounds for each element in x. Must be finite. | ||||||||||||
b_L | Lower bounds for the linear constraints. | ||||||||||||
b_U | Upper bounds for the linear constraints. | ||||||||||||
A | Linear constraint matrix. | ||||||||||||
c_L | Lower bounds for the nonlinear constraints. | ||||||||||||
c_U | Upper bounds for the nonlinear constraints. | ||||||||||||
WarmStart | If true, >0, the solver reads the output from the last run from the mat-file cgoSave.mat, and continues from the last run.
If Prob.CGO.WarmStartInfo has been defined through a call to WarmDefGLOBAL, this field is used instead of the cgoSave.mat file. In the last case, exactly the same points are used. In the first case, a new test is made which points to use. | ||||||||||||
MaxCPU | Maximal CPU Time (in seconds) to be used. | ||||||||||||
user | User field used to send information to low-level functions. | ||||||||||||
PriLevOpt | Print Level.
| ||||||||||||
PriLevSub | Print Level in subproblem solvers, see help in snSolve and gnSolve. | ||||||||||||
f_Low | Lower bound on the optimal function value. If defined, used to restrict the target values into interval ['f_Low,min(surface)]. | ||||||||||||
optParam | Structure with optimization parameters. See Input parameters#the optParam structure. |
the optParam structure
fields used in Prob.optParam: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Field | Description | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
MaxFunc | Maximal number of costly function evaluations, default 300 for rbfSolve and arbfMIP, and default 200 for ego. MaxFunc must be <= 5000. If WarmStart = 1 and MaxFunc <= nFunc (Number of f(x) used) then set MaxFunc := MaxFunc + nFunc. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
IterPrint | Print one information line each iteration, and the new x tried. Default IterPrint = 1. fMinI means the best f(x) is infeasible. fMinF means the best f(x) is feasible (also integer feasible). | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
fGoal | Goal for function value, not used if inf or empty. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
eps_f | Relative accuracy for function value, fTol == eps_f. Stop if |f - f Goal| <= |fGoal| * fTol, if fGoal ≠ 0. Stop if |f - fGoal| <= fTol, if fGoal = 0. See the output field maxTri. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
bTol | Linear constraint tolerance. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
cTol | Nonlinear constraint tolerance. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
MaxIter | Maximal number of iterations used in the local optimization on the re- sponse surface in each step. Default 1000, except for pure IP problems, then max(GO.MaxFunc, MaxIter);. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
CGO | Structure (Prob.CGO) with parameters concerning global optimization options. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Percent | Type of strategy to get the initial sampled values:
Negative values of Percent result in constrained versions of the experimental design methods 7-16. It means that all points sampled are feasible with respect to all given constraints. For ExD 5,6-12,14-16 user defined points are used. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
nSample | Number of sample points to be used in initial experimental design. nSample is used differently dependent on the value of Percent:
where LATIN = [21 21 33 41 51 65 65] and k = |nSample|. Otherwise nSample as input does not matter. Description of the experimental designs: ExD 1, All Corners. Initial points is the corner points of the box given by Prob.x_L and Prob.x_U. Generates 2d points, which results in too many points when the dimension is high. ExD 2, Lower and Upper Corner point + adjacent points. Initial points are 2 * d + 2 corners: the lower left corner xL and its d adjacent corners xL + (xU(i) - xL (i)) * ei, i = 1, ..., d and the upper right corner xU and its d adjacent corners xU - (xU (i) - xL (i)) * ei, i = 1, ..., d ExD 3. Initial points are the upper right corner xU and its d adjacent corners xU - (xU (i) - xL (i)) * ei , i = 1, ..., d ExD 4. Initial points are the lower left corner xL and its d adjacent corners xL + (xU (i) - xL (i)) * ei , i = 1, ..., d ExD 5. User given initial points, given as a matrix in CGO.X. Each column is one sampled point. If d >= length(Prob.x L), then size(X,1) = d, size(X,2) = d + 1. CGO.F should be defined as empty, or contain a vector of corresponding f (x) values. Any CGO.F value set as NaN will be computed by solver routine. ExD 6. Use determinstic global optimization methods to find the initial design. Current methods available (all DIRECT methods), dependent on the value of Percent: 99 = glcDirect, 98 = glbDirect, 97 = glcSolve, 96 = glbSolve, 95 = glcFast, 94 = glbFast. ExD 7-11. Optimal Latin Hypercube Designs (LHD) with respect to different norms. The following norms and designs are available, dependent on the value of Percent: 1 = Maximin 1-Norm, 2 = Maximin 2-Norm, 3 = Maximin Inf-Norm, 4 = Audze-Eglais Norm, 5 = Minimax 2-Norm. All designs taken from: http://www.spacefillingdesigns.nl/ Constrained versions will try bigger and bigger designs up to M = max(10 * d, nTrial) different designs, stopping when it has found nSample feasible points. ExD 12. Latin hypercube space-filling design. For nSample < 0, k = |nSample| should in principle be the problem dimension. The number of points sampled is: k : 2 3 4 5 6 > 6 Points : 21 33 41 51 65 65 The call made is: X = daceInit(abs(nSample),Prob.x_L,Prob.x_U); Set nSample = [] to get (d+1)*(d+2)/2 sampled points: d : 1 2 3 4 5 6 7 8 9 10 Points : 3 6 10 15 21 28 36 45 55 66 This is a more efficient number of points to use. If CGO.X is nonempty, these points are verified as in ExD 5, and treated as already sampled points. Then nSample additional points are sampled, restricted to be close to the given points. Constrained version of Latin hypercube only keep points that fulfill the linear and nonlinear constraints. The algorithm will try up to M = max(10 * d, nTrial) points, stopping when it has found nSample feasible points (d + 1 points if nSample < 0). ExD 13. Orthogonal Sampling, LH with subspace density demands. ExD 14-16. Random strategies, the |Percent| value gives the percentage size of an ellipsoid, circle or rectangle around the so far sampled points that new points are not allowed in. Range 1%-50%. Recommended values 10% - 20%. If CGO.X is nonempty, these points are verified as in ExD 5, and treated as already sampled points. Then nSample additional points are sampled, restricted to be close to the given points. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
X,F,CX | The fields X,F,CX are used to define user given points. ExD = 5 (Percent = 0) needs this information. If ExD == 6-12,14-16 these points are included into the design. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
X | A matrix of initial x values. One column for every x value. If ExD == 5, size(X,2) >= dim(x)+1 needed. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
F | A vector of initial f (x) values. If any element is set to NaN it will be computed. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
CX | Optionally a matrix of nonlinear constraint c(x) values. If nonempty, then size(CX,2) == size(X,2). If any element is set as NaN, the vector c(x) = CX(:,i) will be recomputed. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
RandState | If >= 0, rand('state', RandState) is set to initialize the pseudo-random generator. If < 0, rand('state', 100 * clock) is set to give a new set of random values each run. If isnan(RandState), the random state is not initialized. RandState will influence if a stochastic initial experimental design is applied, see input Percent and nSample. RandState will also influence if using the multiMin solver, but the random state seed is not reset in multiMin. The state of the random generator is saved in the warm start output rngState, and the random generator is reinitialized with this state if warm start is used. Default RandState = 0. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
AddMP | If = 1, add the midpoint as extra point in the corner strategies. Default 1 for any corner strategy, i.e. Percent is 900, 997, 998 or 999. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
nTrial | For experimental design CLH, the method generates M = max(10 * d, nTrial) trial points, and evaluate them until nSample feasible points are found. In the random designs, nTrial is the maximum number of trial points randomly generated for each new point to sample. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
CLHMethod | Different search strategies for finding feasible LH points. First of all, the least infeasible point is added. Then the linear feasible points are considered. If more points are needed still, the nonlinear infeasible points are added.
1 - Take the sampled infeasible points in order. 2 - Take a random sample of the infeasible points. 3 - Use points with lowest constraint error (cErr). | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
SCALE | 0 - Original search space (default if any integer values).
1 - Transform search space to unit cube (default if no integers). | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
REPLACE | 0 - No replacement, default for constrained problems.
1 - Large function values are replaced by the median. > 1 - Large values Z are replaced by new values. The replacement is defined as Z := FMAX + log10(Z - FMAX + 1), where FMAX = 10REPLACE , if min(F ) < 0 and FMAX = 10(ceil(log10(min(F )))+REPLACE), if min(F ) = 0. A new replacement is computed in every iteration, because min(F ) may change. Default REPLACE = 5, if no linear or nonlinear constraints. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
LOCAL | 0 - No local searches after global search. If RBF surface is inaccurate, might be an advantage.
1 - Local search from best points after global search. If equal best function values, up to 20 local searches are done. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
SMOOTH | 1 - The problem is smooth enough for local search using numerical gradient estimation methods (default).
0 - The problem is nonsmooth or noisy, and local search methods using numer- ical gradient estimation are likely to produce garbage search directions. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
globalSolver | Global optimization solver used for subproblem optimization. Default glcCluster (SMOOTH=1) or glcDirect (SMOOTH=0). If the global- Solver is glcCluster, the fields Prob.GO.maxFunc1, Prob.GO.maxFunc2, Prob.GO.maxFunc3, Prob.GO.localSolver, Prob.GO.DIRECT and other fields set in Prob.GO are used. See the help for these parameters in glcCluster. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
localSolver | Local optimization solver used for subproblem optimization. If not defined, the TOMLAB default constrained NLP solver is used.
- Special RBF algorithm parameters in Prob.CGO - | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
rbfType | Type of radial basis function: 1 - thin plate spline; 2 - Cubic Spline (default); 3 - Multiquadric; 4 - Inverse multiquadric; 5 - Gaussian; 6 - Linear. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
idea | Type of search strategy on the response surface.
idea = 1 - cycle of N+1 points in target value fnStar. if fStarRule =3, then N=1 default, otherwise N=4 default. By default idea =1, fStarRule =1, i.e. N =4. To change N, see below. idea = 2 - cycle of 4 points (N+1, N=3 always) in alpha. alpha is a bound on an algorithmic constraint that implicitly sets a target value fStar. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
N | Cycle length in idea 1 (default N=1 for fStarRule 3, otherwise default N=4) or idea 2 (always N=3). | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
infStep | If =1, add search step with target value -8 first in cycle. Default 0. Always
=1 for the case idea =1, fStarRule =3. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
fStarRule | Global-Local search strategy in idea 1, where N is the cycle length. Define minsn as the global minimum on the RBF surface. The following strategies for setting the target value fStar is defined: 1: fStar = minsn - ((N - (n - nInit))/N )2 * Δn (Default), 2: fStar = minsn - (N - (n - nInit))/N * Δn .
Strategy 1 and 2 depends on Δ n estimate (see DeltaRule). If infStep =1, add -step first in cycle. 3: fStar = -step, minsn-k *0.1*|minsn|k = N, ..., 0. These strategies had the following names in Gutmanns thesis: III, II, I. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
DeltaRule | 1 = Skip large f(x) when computing f(x) interval ?. 0 = Use all points. Default 1. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
AddSurfMin | Add up to AddSurfMin interior local minima on RBF surface as search points, based on estimated Lipschitz constants. AddSurfMin=0 implies no additional minimum added (Default). This option is only possible if globalSolver = multiMin. Test for additional minimum is done in the local step (modN == N) If these additional local minima are used, in the printout modN = -2, -3, -4, ... are the iteration steps with these search points. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
TargetMin | Which minimum, if several minima found, to select in the target value problem:
=0 Use global minimum. =1 Use best interior local minima, if none use global minimum. =2 Use best interior local minima, if none use RBF interior minimum. =3 Use best minimum with lowest number of coefficients on bounds. Default is TargetMin = 3. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
eps_sn | Relative tolerance used to test if the minimum of the RBF surface, minsn , is sufficiently lower than the best point (fM in ) found (default is 10-7 ). | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
MaxCycle | Max number of cycles without progress before stopping, default 10. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
GO | Structure Prob.GO (Default values are set for all fields).
The following fields are used: | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
MaxFunc | Maximal number of function evaluations in each global search. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
MaxIter | Maximal number of iterations in each global search. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
DIRECT | DIRECT solver used in glcCluster, either glcSolve or glcDirect(default). | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
maxFunc1 | glcCluster parameter, maximum number of function evaluations in the first call. Only used if globalSolver is glcCluster, see help globalSolver. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
maxFunc2 | glcCluster parameter, maximum number of function evaluations in the second call. Only used if globalSolver is glcCluster, see help globalSolver. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
maxFunc3 | glcCluster parameter, maximum sum of function evaluations in repeated first calls to DIRECT routine when trying to get feasible. Only used if globalSolver is glcCluster, see help globalSolver. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
localSolver | The local solver used by glcCluster. If not defined, then Prob.CGO.localSolver is used | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
MIP | Structure in Prob, Prob.MIP.
Defines integer optimization parameters. Fields used: | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
IntVars | If empty, all variables are assumed non-integer.
If islogical(IntVars) (=all elements are 0/1), then 1 = integer variable, 0 = continuous variable. If any element > 1, IntVars is the indices for integer variables. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
varargin | Other parameters directly sent to low level routines. |