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on a 9×9 board where I penalise prohibited configuration by a factor 1.2 (a wee bit more than empty nodes). The perimeter of the 9×9 board is filled with ones and never actualised. (In the above convoluted products, the goal is to count how many neighbours of the entries equal to one are also equal to one. More than 2 is penalised.) The simulated annealing move is then updating the 9×9 grid gridz:

temp=1
maxarg=curarg=targ(gridz)
for (t in 1:1e3){
for (v in 1:1e4){
i=sample(2:8,1);j=sample(2:8,1)
newgrid=gridz;newgrid[i,j]=1-gridz[i,j]
newarg=targ(newgrid)
if (log(runif(1))

and calls to the procedure always return 28 entries as the optimum, as in

As it happens, I had misread the wording of the original puzzle, which considered a dynamic placement of the units on the board, one at a time with two free neighbours imposed.

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