Nothing in the default objective discourages the same sub-plot arrangement repeating across whole plots

[rogerssam]

objective_function() scores adjacency and row/column balance only. A layout in which every whole plot carries the same sub-plot arrangement scores no worse than one where the arrangements vary. Where the input is systematic and already sits at a local optimum, speed() returns it essentially unchanged.

Row-spanning whole plots show it plainly:

wholeplot 1  a d c b      score 132
          2  b a d c
          3  c b a d
          4  a d c b   <- block 2 identical to block 1
          7  a d c b   <- block 3 identical

This is a genuine optimum (per-block rotations score 150; 200 random arrangements score 156–285) but not the only one: 40 random-restart steepest-descent runs also reach 132 with 10 distinct arrangements of 12. Varied layouts exist at the same score; the search just never reaches them from a systematic start, because the tied optima sit in basins single swaps can't cross.

Compact whole plots (2×2) come out varied but only because the systematic start isn't optimal for that geometry, so the search leaves it. Nothing prevents repetition there either; it's luck of the geometry.

Why it matters: repeated arrangements confound sub-plot treatment with position within whole plot, regardless of whether the whole plots share rows or columns. A positional effect not captured by row + col is then inseparable from treatment. It wouldn't pass review as a randomised split-plot.

Directions:

1. Add a repetition/concurrence-of-position penalty to the objective so varied layouts are strictly preferred, not merely tied.
2. Make random_initialisation usable for swap_all designs (currently breaks unit structure, see random_initialisation destroys nesting in swap_all = TRUE designs #141) so structure-preserving restarts can find the varied optima.
3. Post-process: randomly permute arrangements among tied whole plots. This would not change the score.

[rogerssam]

Related #141

[rogerssam]

Possibly related to #45