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. value output 0 Silent 1 Summary 2 Printing each iteration 3 Info about local / global solution 4 Progress in x.
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 the table below describing the fields used in the optParam structure.
CGO	Structure with parameters specific to costly global optimization. See the table below describing the fields used in the CGO structure.
MIP	Structure with parameters specific mixed integer optimization. See the table below describing the fields used in the MIP structure.

optParam structure

The most important field is MaxFunc, normally use default values for other fields.

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

The CGO solvers need an initial set of at least n+1 points, where n = dim(x).
Either an initial Experimental Design is needed or the user may input its own choice of points, or a combination of both.
A warm start with points from previous run(s) using any CGO solver is also possible.

The input parameters for the Experimental Design are given as fields in Prob.CGO.
See help expDesign for details on how to set the following fields in Prob.CGO defining the Experimental Design:
Percent, nSample, X, F, Cc, RandState, AddMP, nTrial, CLHMethod
Note that the setting of RandState might influence parts of the CGO solvers as well.

fields used in Prob.CGO:
Field	Description
Percent	See expDesign for detailed information on how to set the experimental design parameters.
nSample
X
F
CX
RandState
AddMP
nTrial
CLHMethod
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 $-\infty$-step first in cycle. 3: fStar = $-\infty$-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.