Global Response Search Method (GRSM)

A response surface based approach. During each iteration, the response surface based optimization generates a few designs. Additional designs are generated globally to ensure a good balance on local search capability and global search capability. Response surface is adaptively updated with the newly generated designs to have a better fit of the model.

Usability Characteristics

Global Response Search Method can disposes of both single objective problems and multi-objective problems.
Default method for multi-objective optimization problems. Global Response Search Method is also the suggested method when you are solving a single objective optimization problem with a large number of input variables and/or when a global optima is required.
It is recommend to use Global Response Search Method directly on a solver and not on a Fit. If you have a Fit, consider using an Inclusion matrix with your data.
Consists of a global search capability.
Supports discrete optimization.
All the designs generated in one iteration can be solved in parallel.
If the model analysis is time consuming, then Global Response Search Method is a good choice. If the model analysis is quite cheap and a thorough search of the design space is needed (for example, 100000 model evaluations are needed), then Genetic Algorithm or Multi - Objective Genetic Algorithm are recommended.
In the case of a failed run, it is possible to ignore a failed analysis or terminate an optimization. When omitting failed runs, the optimizer randomly generates designs in under-sampled region in order to explore the whole design space effectively.
Terminates when the maximum number of evaluations (Number of Evaluations) is reached.
Supports input variable constraints.
The size of the first iteration is controlled by the Initial Sampling Points setting. The number of evaluations in subsequent iterations is controlled by the Points per Iteration setting. All designs generated within one iteration can be executed in parallel.

Figure 1. Global Response Search Method Process Phases

Settings

In the Specifications step, change method settings from the Settings and More tabs.

Note: For most applications the default settings work optimally, and you may only need to change the Number of Evaluations and On Failed Evaluation.

Table 1. Settings Tab
Parameter	Default	Range	Description
Number of Evaluations	Single objective: 50 Multiple objectives: 200	>0	Number of evaluations allowed.
On Failed Evaluation	Terminate optimization	Terminate optimization Ignore failed evaluations	Terminate optimization Optimizer terminates with an error message when an analysis run fails. Ignore failed evaluations Optimizer ignores the failed analysis run, randomly generates a design, and re-tries the analysis.

Table 2. More Tab
Parameter	Default	Range	Description
Initial Sampling Points	min(20,n+2)	Integer >=0	The number of initial sample points. Default is min(20,n+2) initial sample points; n is the number of input variables; > 0 use the user defined value.
Random Seed	1	Integer 0 to 10000	Controlling repeatability of runs depending on the way the sequence of random numbers is generated. 0 Random (non-repeatable) >0 Triggers a new sequence of pseudo-random numbers, repeatable if the same number is specified.
Points per Iteration	2	1 to Initial Sampling Points	Number of designs to be evaluated for optimum design search and response surface update. After the initial Initial Sampling Points designs, Points per Iteration designs are generated from response surface based optimization and/or incremental sampling. In the iteration that follows, these designs are used to adaptively update the response surface to have a better fit of the model. Note: These designs can be evaluated in parallel.
Max Failed Evaluations	20,000	>=0	When On Failed Evaluations is set to Ignore failed evaluations (1), the optimizer will tolerate failures until this threshold for Max Failed Evaluations. This option is intended to allow the optimizer to stop after an excessive amount of failures.
Stop after no Improvement	1000	> 0.0	Terminates the optimization if the number of iterations without improvement exceeds this value.
Improvement Threshold	0.03	> 0.0	A threshold option to track improvement of objective value over the span of user-defined number of iterations through “Stop after no Improvement”. Once the threshold is reached, GRSM terminates.
Use Inclusion Matrix	With Initial	With Initial Without Initial	With Initial Runs the initial point. The inclusion set and initial point are used to build the initial response surface. Without Initial Does not run the initial point. The inclusion set is used to build the initial response surface.