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/* Any Wolfram elementary CA in 6D eucl. Neumann CA grid emulator generator */
/* Implemented, inspected, written and converted to GNU MathProg by NASZVADI, Peter, 2016-2017 <vuk@cs.elte.hu> */
/* see background info and more details in wolfra6d.lp */
/* each axis has this two endpoints */set V := 0..1;
/* this model processes a hypercube in 6d, so 6+1 parallel planes intersect */set H := 0..6;
/* denoting all vertices in the 6d unit hypercube */set Cells := V cross V cross V cross V cross V cross V;
/* input parameters, bup/bdn = number of upper/lower neighbour 6d cells of a (cyclic) segment */param bup{i in H}, default 1;param bdn{i in H}, default 2;
/* boolean meaning if a vertex is chosen */var x{Cells}, binary;
/* temporary calculations to enforce bup/bdn */var up{Cells}, >=0;var dn{Cells}, >=0;
/* the total weight of selected cells near the main diagonal */var obj;
/* up/dn vars denote the number of selected upper/lower neighbours */s.t. cup{(v1,v2,v3,v4,v5,v6) in Cells: v1+v2+v3+v4+v5+v6<6}: sum{(w1,w2,w3,w4,w5,w6) in Cells: max(v1-w1,v2-w2,v3-w3,v4-w4,v5-w5,v6-w6)<=0} if (w1+w2+w3+w4+w5+w6) = (1+v1+v2+v3+v4+v5+v6) then x[w1,w2,w3,w4,w5,w6] else 0 = up[v1,v2,v3,v4,v5,v6];
s.t. cdn{(v1,v2,v3,v4,v5,v6) in Cells: v1+v2+v3+v4+v5+v6>0}: sum{(w1,w2,w3,w4,w5,w6) in Cells: min(v1-w1,v2-w2,v3-w3,v4-w4,v5-w5,v6-w6)>=0} if (w1+w2+w3+w4+w5+w6) = (-1+v1+v2+v3+v4+v5+v6) then x[w1,w2,w3,w4,w5,w6] else 0 = dn[v1,v2,v3,v4,v5,v6];
/* 4 helper constraints, hences the leading "c" */s.t. cbup1{(v1,v2,v3,v4,v5,v6) in Cells: v1+v2+v3+v4+v5+v6<6}: up[v1,v2,v3,v4,v5,v6] >= bup[v1+v2+v3+v4+v5+v6] * x[v1,v2,v3,v4,v5,v6];
s.t. cbup2{(v1,v2,v3,v4,v5,v6) in Cells: v1+v2+v3+v4+v5+v6<6}: up[v1,v2,v3,v4,v5,v6] + (2**6) * x[v1,v2,v3,v4,v5,v6] <= (2**6) + bup[v1+v2+v3+v4+v5+v6];
s.t. cbdn1{(v1,v2,v3,v4,v5,v6) in Cells: v1+v2+v3+v4+v5+v6>0}: dn[v1,v2,v3,v4,v5,v6] >= bdn[v1+v2+v3+v4+v5+v6] * x[v1,v2,v3,v4,v5,v6];
s.t. cbdn2{(v1,v2,v3,v4,v5,v6) in Cells: v1+v2+v3+v4+v5+v6>0}: dn[v1,v2,v3,v4,v5,v6] + (2**6) * x[v1,v2,v3,v4,v5,v6] <= (2**6) + bdn[v1+v2+v3+v4+v5+v6];
/* these two promoted points should be selected */s.t. initdiag: x[0,0,0,0,0,0] + x[1,1,1,1,1,1] = 2;
/* obvious */s.t. sumx: sum{(v1,v2,v3,v4,v5,v6) in Cells} x[v1,v2,v3,v4,v5,v6] = obj;
minimize cobj: obj;
solve;
/* pretty-printing hopefully nontrivial solution */printf "\nChosen vertex subset:\n";for{i in H}: { printf "Weight=%s\n", i; printf{(v1,v2,v3,v4,v5,v6) in Cells: v1+v2+v3+v4+v5+v6 = i+(8-8*x[v1,v2,v3,v4,v5,v6])} " %s%s%s%s%s%s\n",v1,v2,v3,v4,v5,v6;}printf "\nTotal number of selected cells in the hypercube: %g\n\n", obj;
data;
/* these parameters were chosen in the first run that yielded a solution */param bup := 0 6 1 2 2 3 3 2 4 1 5 1 6 6;
param bdn := 0 3 1 1 2 2 3 1 4 4 5 3 6 3;
end;
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