runTPLS {multiDoE} | R Documentation |
Multi-Stratum Two-Phase Local Search (MS-TPLS) Algorithm
Description
This function implements the Multi-Stratum Two-Phase Local
Search (MS-TPLS) algorithm described in Borrotti, Sambo, Mylona and Gilmour
(2016). This algorithm is useful to obtain exact optimal multi-stratum
designs through a multi-criteria approach. When using runTPLS the user must
establish the search problem (structure of the experiment, number of trials,
optimization criteria, etc.) and the total number of iterations of MS-TPLS.
The resulting experimental designs can minimize up to six criteria simultaneously
from the following: "I", "Id", "D", "Ds", "A" and "As". runTPLS
is able
to provide the set of solutions building the approximate Pareto front for
the specified optimization problem.
Usage
runTPLS(facts, units, criteria, model, iters, ...)
Arguments
facts |
A list of vectors representing the distribution of factors across strata. Each item in the list represents a stratum and the first item is the highest stratum of the multi-stratum structure of the experiment. Within the vectors, experimental factors are indicated by progressive integer from 1 (the first factor of the highest stratum) to the total number of experimental factors (the last factor of the lowest stratum). Blocking factors are differently denoted by empty vectors. |
units |
A list whose |
criteria |
A list specifying the criteria to be optimized. It can contain any combination of:
More detailed information on the available criteria is given in
|
model |
A string which indicates the type of model, among “main", “interaction" and “quadratic". |
iters |
An integer indicating the number of iterations of the MS-TPLS algorithm. |
... |
optional arguments (see below). |
Details
Additional arguments can be specified as follows:
-
'Restarts', restarts
: A string and an integer, used in pair.r
defines the number of times the MS-Opt procedure is altogether called within each iteration of the MS-TPLS algorithm. The default value isr=100
. -
'Levels', levels
: A string and a vector, used in pair.levels
is a vector containing the number of available levels for each experimental factor in the argumentfacts
(blocking factors are excluded). If all experimental factors share the number of levels one integer is sufficient. -
'Etas', etas
: A string and a list, used in pair. Inetas
the user must specify the ratios of error variance between subsequent strata, starting from the highest strata. It follows thatlength(etas)
must be equal tolength(facts)-1
. -
'RestInit', restInit
: A string and an integer, used in pair. Through these parameters, it is possible to determine how many of ther
iterations of MS-Opt should be used for each criterion in the first step of the MS-TPLS algorithm (lines 3-6 of the pseudo-code of MS-TPLS, see Borrotti, Sambo, Mylona and Gilmour (2017)). The default value isrestInit=50
. Letn
be the number of criteria under consideration. One can calculate accordingly asr - (n * restInit)
the number of times MS-Opt is called in the second step (lines 7-11 of the pseudo-code of MS-TPLS) of each iteration of MS-TPLS. -
'RngSeed', rngSeed
: A number indicating the seed for reproducibility. Default is to leave the random number generator alone.
Value
runTPLS
returns a list, whose elements are:
-
ar
: A list of length equal toiters
. Thei
-th element is a list whose elements are:-
nsols
: Number of designs produced during thei
-th iteration. -
dim
: The criteria space dimension. -
scores
: A matrix ofnsols
rows anddim
columns. Every row contains the value of the criteria for each solution of thei
-th iteration. -
solutions
: A list of length equal tonsols
containing the design matrices produced during thei
-th iteration. The values of the criteria corresponding at the first element ofsolutions
are placed in the first row of thescores
matrix and so on.
-
-
stats
: A list of length equal toiters
. Every element is a vector of sizer - (n * restInit) + 1
, wheren
is the number of the considered criteria. The first element represents the number of function evaluations during the first step of the MS-TPLS algorithm; thei
-th element (excluding the first one) is the sum of the number of evaluations for thei
-th scalarization and the maximum value in thestats
. -
megaAR
: A list whose elements are:-
nsols
: The number of the Pareto front solutions. -
dim
: The criteria space dimension. -
scores
: A matrix ofnsols
rows anddim
columns. Every row contains the criteria values for each Pareto front design. -
solutions
: A list of length equal tonsols
containing the design matrices for the Pareto front designs. The values of the criteria corresponding at the first element ofsolutions
are placed in the first row of thescores
matrix and so on.
-
References
M. Borrotti and F. Sambo and K. Mylona and S. Gilmour. A multi-objective coordinate-exchange two-phase local search algorithm for multi-stratum experiments. Statistics & Computing, 2017.