G-optimality (GOPTPEV) • TSDFGS

G-optimality minimizes the largest eigenvalue of the PEV matrix of the target, the variance in the worst direction.

Type	Optimal design
Direction	Smaller is better
Uses a test set	yes
Score a given set	`gopt_score()`
Search with it	`optTrain(method = "GOpt")`

Definition

With $B$ as for PEVmax: $\mathrm{G} = \lambda_{\max}(X_0 B X_0')$ , computed from the $p \times p$ matrix $L^{-1}X_0'X_0L^{-T}$ with $LL' = X'X + \lambda I$ .

Use in TSDFGS

library(TSDFGS)
data(geno)
gopt_score(geno[1:50, ], geno[51:100, ])

## [1] 20127415

fit <- optTrain(geno, cand = 1:404, n.train = 50, method = "GOpt",
                 min.iter = 300, console = FALSE, seed = 1)
fit$OPTtrain

##  [1] 391 347 173 336 127 315 146  62 342 393 330 290 134 153 158 369 297 217 392
## [20] 389 390 128 373 244 350 364 222 162  69 304  20 283 343 300 151 376  81  15
## [39] 229  44 135 298 149 160  36 388  45 250 281  80

# targeted: the test set is known
fit2 <- optTrain(geno, cand = 1:300, n.train = 50, test = 301:404,
                  method = "GOpt", min.iter = 300, console = FALSE, seed = 1)
fit2$OPTtrain

##  [1] 256 126 143 137 140  93  97  84 298 129 196 278  31  89 259 152 127  44 168
## [20]  76 108 212  71 117 198 216 162 232  67  39 245  74  10 220  72  24 300  52
## [39] 151 150  65 225 260  32 141 116 230 249  43  77

The search is a random-start exchange (hill-climbing) search; see How the scores are computed. Use min.iter larger than 300 on real data and check fit$converged.

Original work

Akdemir, D., Sanchez, J. I., & Jannink, J.-L. (2015). Optimization of genomic selection training populations with a genetic algorithm. Genetics Selection Evolution, 47, 38. https://doi.org/10.1186/s12711-015-0116-6

Isidro y Sánchez, J., & Akdemir, D. (2021). Training set optimization for sparse phenotyping in genomic selection: a conceptual overview. Frontiers in Plant Science, 12, 715910. https://doi.org/10.3389/fpls.2021.715910

Repository or website of the original authors: R package STPGA by Akdemir and colleagues: CRAN.R-project.org/package=STPGA (GPL-3).

License review

Formulas and algorithms are ideas and methods, which copyright does not protect. Where an original package is under a GPL license, we read it to check our results and credit it; TSDFGS is GPL-3, which is compatible with GPL-3 and GPL (>= 3) code. This is our reading of the public record, not legal advice; see the license review.

Original software: STPGA, GPL-3 (GOPTPEV); compared, not copied.
Verdict: included.

Reviewed 2026-11-04. All criteria and the ones left out.