# `ga_select` — GA-PLS — Genetic Algorithm variable selection
_Group_: **Variable selector** · _Registry tolerance_: `1e-06`
## Description
GA-PLS genetic algorithm selection
From the `pls4all.sklearn.GASelector` docstring:
> Genetic Algorithm feature selection.
> **Registry note** — R `plsVarSel::ga_pls` genetic-algorithm variable selection. Default `_ga_select_pls4all` path mirrors the same R call with seed=11 (iters=5, popSize=20, GA.threshold=3), giving bit-exact mask parity. The C++ splitmix64 GA kernel is opt-in via `legacy=True`.
### Parameters
| Name | Type | Default | Notes |
|------|------|---------|-------|
| `n_components` | `int` | `2` | Number of latent components extracted (k). |
| `n_generations` | `int` | `30` | Number of GA generations to evolve. |
| `population_size` | `int` | `40` | Number of candidate feature subsets per generation. |
| `min_features` | `int | None` | `None` | Minimum number of variables the selector is allowed to keep (defaults to `n_components`). |
| `max_features` | `int | None` | `None` | Upper bound on the GA chromosome cardinality (defaults to all features). |
| `mutation_rate` | `float` | `0.05` | Per-bit mutation probability applied to GA chromosomes. |
| `n_folds` | `int` | `3` | Number of cross-validation folds used inside the selector. |
| `seed` | `int` | `0` | Random seed for reproducible sampling/initialization. |
## Explanations
### Bibliographic source
Leardi, R. (2000). *Application of genetic algorithm–PLS for feature selection in spectral data sets*. Journal of Chemometrics 14(5–6), 643–655.
### Mathematical principle
Wrap a binary genetic algorithm around PLS CV-RMSE. Each chromosome is a $p$-bit binary mask encoding which features to include; fitness is $-\mathrm{CV\text{-}RMSE}$ from PLS on the masked subset; standard GA operators (single-point crossover, bit-flip mutation, elitism) drive the population.
Cost is high — every fitness evaluation is a full PLS fit — but GA-PLS handles non-convex fitness landscapes (non-additive interactions between selected features) that greedy methods miss. Recommended population sizes: 30–100; generations: 100–500.
Stochastic by construction: results vary across RNG seeds. For deterministic comparisons against this selector the benchmark widens the parity tolerance and fixes the seed; in production use a small ensemble of GA runs and take the consensus.
### Implementation
`n4m_ga_select`. Reference: R `plsVarSel`.
### Usage
Every pls4all binding tab dispatches into the same C kernel; the external libraries listed at the bottom of the page are the parity references registered in `benchmarks.parity_timing.registry`. Switch tabs to read the same fit in your language. The R package now ships drop-in-compatible facades for the CRAN `pls` package (`plsr`, `pcr`, `mvr`) and for the `mdatools::pls(x, y, ...)` matrix idiom — those tabs appear only on the methods that have a meaningful equivalence.
**pls4all bindings**
::::{tab-set}
:class: pls4all-bindings
:::{tab-item} C ABI · libn4m
:sync: c
:class-label: lang-c
```c
/* C ABI — libn4m */
n4m_context_t* ctx = n4m_context_create();
n4m_config_t* cfg = n4m_config_create();
n4m_method_result_t* res = NULL;
n4m_ga_select_fit(ctx, cfg, &x_view, &y_view, /* hyperparams */, &res);
/* … read coefficients / mask / scores via */
/* n4m_method_result_get_double_matrix / vector / scalar … */
n4m_method_result_destroy(res);
n4m_config_destroy(cfg);
n4m_context_destroy(ctx);
```
:::
:::{tab-item} Python · pls4all (raw)
:sync: python-raw
:class-label: lang-python
```python
import pls4all
from pls4all._methods import ga_select_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = ga_select_fit(ctx, cfg, X, y, n_components=4)
# then: res.matrix("predictions"), res.matrix("coefficients"),
# res.vector("mask"), res.scalar("intercept"), …
```
:::
:::{tab-item} Python · pls4all.sklearn
:sync: python-sklearn
:class-label: lang-python
```python
from pls4all.sklearn import GASelector
mdl = GASelector(n_components=2, n_generations=30, population_size=40, min_features=None, max_features=None, mutation_rate=0.05, n_folds=3, seed=0)
mdl.fit(X, y)
y_hat = mdl.predict(X_test)
```
:::
:::{tab-item} R · pls4all_method()
:sync: r-dispatcher
:class-label: lang-r
```r
library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("ga_select", X, y,
n_components = 4L, params = list(n_generations = 5L, population_size = 12L, min_features = 5L, max_features = 20L, mutation_rate = 0.1, seed = 11L))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.
```
:::
:::{tab-item} MATLAB · pls4all (MEX)
:sync: matlab-mex
:class-label: lang-matlab
```matlab
res = pls4all.fit("ga_select", X, y, "NumComponents", 4);
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("ga_select", X, y, …)` directly from the unified MEX factory._
:::
::::
**Registry parity references** 📐
:::{card}
:class-card: external-refs
- 📐 **`ref.r_plsvarsel`** (R · r) — `plsVarSel` 0.10.0 · strict (rmse_rel ≤ 1e-06) — R `plsVarSel::ga_pls` — genetic-algorithm variable selection. RNG differs from pls4all's GA so set overlap is loose.
:::
### Benchmarks
Adaptive wall-clock per cell measured against [`full_matrix.csv`](../benchmarks/overview.md). Only backends that implement this method are listed; libraries without the method are omitted.
**Verdict** · ✓ ref / ≈ ref / ~ shape mark a reference-gate pass at strict / relaxed / qualitative tolerance · ✓ bind = pls4all binding agrees with the C++ baseline · ✗ divergent · ⚠ error · — not run. The fastest backend per column is marked 🏆.
**Reference gate**: strict — numeric equivalence (`rmse_rel_tol ≤ 1e-06`).
Rows tagged with **📐** are the canonical parity references for this method (declared in [`parity_timing.registry`](../benchmarks/methodology.md)). C++ and external rows show reference parity; pls4all language bindings show binding parity against the C++ backend. Hover the icon for role and tolerance band.
::::{tab-set}
:class: parity-tabs
:::{tab-item} 1 thread
:sync: threads-1
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ≈ | 768.4 ms | 4.0 s🏆 | 6.2 s | 18.3 s | 813.9 ms | 704.1 ms | 4.5 s🏆 | 16.1 s | 77.4 s | 9.6 s | 83.7 s | 521.9 s🏆 | 41.3 s | 444.6 s |
pls4all.cpp.blas+omp | ≈ | 767.8 ms | 4.3 s | 6.1 s🏆 | 16.4 s🏆 | 830.2 ms | 736.9 ms | 4.7 s | 16.1 s | 72.8 s🏆 | 10.4 s | 84.3 s | 530.3 s | 37.0 s🏆 | 440.7 s |
pls4all.cpp.omp | ≈ | 768.8 ms | 4.1 s | 6.4 s | 17.3 s | 813.7 ms | 726.1 ms | 4.7 s | 16.0 s🏆 | 83.2 s | 10.2 s | 82.8 s | 526.9 s | 39.2 s | 428.4 s |
pls4all.cpp.ref | ≈ | 746.9 ms | 4.1 s | 6.8 s | 19.3 s | 806.4 ms | 704.9 ms | 5.1 s | 16.3 s | 75.2 s | 9.6 s🏆 | 72.5 s🏆 | 526.1 s | 38.5 s | 428.4 s🏆 |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 768.0 ms | — | — | — | 807.6 ms | 705.2 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | 4.68 ms | — | — | — | 4.52 ms | 7.17 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | 15.9 ms | — | — | — | 8.87 ms | 14.2 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | 20.4 ms | — | — | — | 13.9 ms | 13.1 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | 20.1 ms | — | — | — | 10.5 ms | 13.8 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | 22.5 ms | — | — | — | 13.0 ms | 12.7 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | 6.07 ms | — | — | — | 5.13 ms | 7.55 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | 6.24 ms | — | — | — | 6.35 ms | 10.4 ms | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | 301.8 ms🏆 | — | — | — | 285.0 ms🏆 | 245.9 ms🏆 | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 3 threads
:sync: threads-3
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ✓ ref | — | — | — | — | 687.9 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 701.8 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 702.5 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 698.7 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 698.3 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 4.73 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 8.75 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 9.42 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 9.74 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 9.00 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 4.90 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 5.49 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | — | — | — | — | 247.7 ms🏆 | — | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 10 threads
:sync: threads-10
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ✓ ref | — | — | — | — | 574.2 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 567.0 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 574.4 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 571.0 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 560.3 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 3.73 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 6.54 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 7.50 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 7.38 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 7.37 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 4.53 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 4.80 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | — | — | — | — | 201.8 ms🏆 | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)