Mathematica 能否完全替代Lingo？

入戏太深丶

要求从1开始，最终回到1，且路径有方向，要求所有路径都经过。
以下是lingo的代码
, ~, W& V0 O' A" U' o  Ysets:
nodes/A,B,C,D,E,F,G,H,I,J,K,L/;
arcs(nodes,nodes)/
0 b* J" i" I8 P+ v8 M3 ?  [A,B A,E
B,C B,E B,F
C,B C,D
D,C D,H
4 a% v" [$ H- Y9 zE,A E,F
1 P* H5 \+ Z' [+ XF,B F,E F,G F,I F,J
$ F3 j( c! _! a" lG,C G,F G,H G,K
- [) ^9 n# s+ {, y8 I: l1 LH,D H,K H,L
I,E I,J
2 C) C7 N3 l1 Q& E  eJ,F J,G
K,G K,J
L,K
/: c, x;
endsets
data:
9 P8 D1 C  v+ O; V! h+ H8 S1 _; hc=
6 @! f- ]" a" b) \9 N5 M150 165
2 S+ G% z/ b3 d% U! ?/ Z, Q130 230 160
140 100
( E4 X7 b4 L' ]" d100 190
4 C# u7 m$ m- s' Q# }165 144
7 }8 z3 s) \7 c* \. f8 h0 N170 144 128 218 174
2 X9 N  I% P( E! O. w3 r200 122 109 185
2 {$ R8 B3 b( p180 141 190
194 148
174 233
' N5 e8 L% A: v/ t185 135
110;
enddata
n = @size(nodes);
min = @sum(arcs: c * x);
@for(nodes(i):
% ~3 B) C3 M' D@sum(arcs(i,j):x(i,j))=@sum(arcs(k,i):x(k,i))
% G/ J& A$ ^6 C7 P);
" S0 C; d7 q& r3 x@for(arcs: @bnd(1,x,9));
1 V5 A$ u9 ~8 o$ ?1 R
它只能算出路径的步数和路程，并不能得到线路。希望能用mma解决这个问题。

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自己用mma写的程序对于四点还可以，但是扩展到12点实在繁琐：

P11 = {2, 5}; P12 = {150, 165};

P21 = {5, 6}; P22 = {230, 160};

P51 = {1, 6}; P52 = {165, 144};

P61 = {2, 5}; P62 = {170, 144};(*只考虑1、2、5、6四点，P11为第一点“可去往的点”，P12表述对应的路程*)

open[q_] :=

Module[{i = 1, randomD, randomP, D, randomreal, p1, p2, p5, p6, c, u,

Df = 80000, uf, path = {1}, pathf = {1}, pb},(*随机搜索*)

For[r = 0, r < q, r++,

{p1 = {}; p2 = {}; p5 = {}; p6 = {}; u = 0; D = 0; i = 1;

randomP = P11; randomD = P12;

While[

Length[p1] != 2 || Length[p2] != 2 || Length[p5] != 2 ||

Length[p6] != 2 || i != 1,

randomreal = RandomInteger[{1, Length[randomP]}];

c = randomP[[randomreal]]; AppendTo[path, c];(*Print[path];*)

Which[

i == 1 &&

Product[If[p1[] != c, 1, 0], {i, 1, Length[p1]}] ==

1, {AppendTo[p1, c]},

i == 2 &&

Product[If[p2[] != c, 1, 0], {i, 1, Length[p2]}] ==

1, {AppendTo[p2, c]},

i == 5 &&

Product[If[p5[] != c, 1, 0], {i, 1, Length[p5]}] ==

1, {AppendTo[p5, c]},

i == 6 &&

Product[If[p6[] != c, 1, 0], {i, 1, Length[p6]}] ==

1, {AppendTo[p6, c]}];

i = c;

D = D + randomD[[randomreal]];

Which[i == 1, {randomP = P11, randomD = P12},

i == 2, {randomP = P21, randomD = P22},

i == 5, {randomP = P51, randomD = P52},

i == 6, {randomP = P61, randomD = P62}];

u = u + 1; If[u > 11, Break[]];

If[Df > D, {Df = D, uf = u, pathf = path, path = {1}},

path = {1}];

}

];

Print[Df, ",", uf, ",", pathf];

open[1000]

. g0 Y8 K' V1 Q9 _