GlobalOptimization Options - Maple Programming Help

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GlobalOptimization Options

 This help page describes the options recognized by the commands in the GlobalOptimization package. For an overview of how the global optimization algorithm works, see the GlobalOptimization and GlobalOptimization[GlobalSolve] help pages. The global optimization solvers used by this package are controlled by various options, some of which are specific to only a single solver. The options which affected only a subset of methods are noted below.

Description of Options

avgstopstepwidth = numeric

 For example, avgstopstepwidth = k, where k must be a real numeric value greater than 0.0 and less than 0.1.
 Specifying this option is valid only for the diffevol method.
 This sets a stopping criterion for the diffevol method. When the variation of the problem variables is small then it is assumed that the quality of the objective evaluation no longer has large variation. Decreasing this value increases the overall computation cost, since there will be greater effort made to resolve additional digits during the global search stage. The default value is 0.0001.

evaluationlimit = posint

 For example, evaluationlimit = k.
 Set the maximum number of function evaluations performed by the method to k.
 For the diffevol method the maximal number of iterations performed at any generation is determined as the floor of the evaluationlimit divided by the value of the populationsize option.

initialpoint = set(equation), list(equation), list(numeric), or Vector(numeric)

 For example, initialpoint = p.
 Use p as the initial point.  When algebraic form is used, p is specified as a set or list of equalities, varname=value. When operator or Matrix form is used, the initial point is specified as a list or Vector of values.   For more information about the various forms of input, see GlobalOptimization/InputForms. The default initial point is computed using the average of the specified lower and upper bounds for each variable.

maximize = truefalse

 For example, maximize = m.
 Maximize the objective function when m is 'true' and minimize when m is 'false'.  The option 'maximize' is equivalent to 'maximize'='true'. The default is 'maximize'='false'.

goal = t

 Set the type of optimization goal t as target, sensitivity, combined, or expression. This option is only valid for the ego method.

method = diffevol or ego

 For example, method = m.
 Select the global search algorithm used by the solver.  When m is diffevol, an algorithm based on differential evolution is used. When m is ego a hybrid algorithm for efficient global optimization in which an interpolating response surface model is built after each iteration is used. The default is method=diffevol.   More information about these methods is available in the GlobalOptimization/Computation help page.

nugget = k

 Set the smoothing factor of the response surface model.

numexperiments = k

 Set the number of experiments in the first space filling Latin hypercube that is performed. The default value if 5 times the number of variables.

numsigma = k

 Set the multiple of sigma used for the next element. A low value specifies that less importance is given to the estimated standard deviation and the algorithm will behave similarly to a local optimization solver. A higher value, such as 3, specifies that more importance is given to the estimated standard deviation and the algorithm will add more points where the standard deviation is high and thus act more like a global optimizer.

objectivetarget = numeric

 For example, objectivetarget = t.
 Set the acceptable target value for the objective function to t. If the objective function achieves this value, the search terminates.

optimalitytolerance = positive and numeric

 For example, optimalitytolerance = opttol.
 Set the tolerance within which the optimization stop criterion must be reached. This option is valid only for the ego method.

optsearch = k

 Set the method to locate a new promising point. The valid values are 0 and 1. A value of 0 specifies that the promising point will be determined by a global optimization on a surface. A value of 1 specifies that the new promising point will be the result of a global optimization of the expected improvement function.

populationsize = k

 Specifying this option is valid only for the diffevol method.
 This sets the number of designs that are evaluated during each iteration (generation) of the evolutionary process. A larger population increases the probability of global convergence, at the cost of more design (function) evaluations. The default value is the maximum of 50 and 10 times the number of problem variables. Using a larger value for populationsize without increasing the value of the evaluationlimit option will decrease the allowed number of iterations.

randomseed = nonnegint

 Set the seed value for the random number generator.

timelimit = posint

 For example, timelimit = k.
 Set the maximum computation time, in seconds, to k.  This limit applies to the solver during only the global search phase, and does not include preprocessing of the optimization problem or post-processing of the solution.  The default value is 100*(n+m), where $n$ is the number of variables and $m$ is the number of constraints.  Note that, if the solver fails because the time limit has been exceeded, the last computed solution can be retrieved using the GlobalOptimization[GetLastSolution] command.

theta = k

 Set the theta value for the interpolating model. If the value is zero then optimal values will be calculated using an internal theta calculation scheme. If the value is positive then the supplied value will always be used for the interpolating response surface model and no optimization of the theta values will be performed.

thetamethod = k

 Set the theta calculation method used to estimate the optimal values for the theta parameters of the response surface model. The valid values of k are 0, 1, or 2. A value of 0 specifies that the predictive quality of the model is to be maximized. A value of 1 specifies that the likelihood of the set of points with respect to the model is to be maximized. A value of 2 specifies that the semi-norm of the correlation matrix is to be minimized.

variables = list(name) or set(name)

 Specify the problem variables when the objective function is in algebraic form. This option is useful when the objective function includes dummy variables that should not be treated as optimization variables.

Notes

 • Setting infolevel[GlobalOptimization] to $3$ or higher produces messages showing settings for the various options.
 • More information about the algorithms used by the global solver and how these options affect them can be found in the GlobalOptimization/Computation help page.
 • Because the GlobalOptimization package relies on an external solver implemented in the C language, an error may occur if any option value exceeds the corresponding C language variable limit.
 • Users familiar with the Optimization package should note that the GlobalOptimization solver uses different algorithms and that the available options in the two packages are not the same.  In particular, the assume=nonnegative option is not applicable because finite bounds are required on all variables, and the options to provide derivatives are not available because the global solver does not depend on the use of derivatives. Furthermore, options having the same name in both packages may not have the same default values.