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
' T4 C* E0 Q# h. Q6 Nsets:
* X" {/ T+ w7 V! D  _# ?& B7 Mnodes/A,B,C,D,E,F,G,H,I,J,K,L/;
4 w0 }% X$ s) u1 e5 ?- F/ i0 }arcs(nodes,nodes)/
A,B A,E
1 d9 C" Q! _% j, cB,C B,E B,F
) f. \% T* t6 L, Y7 f% k$ m8 @C,B C,D
D,C D,H
E,A E,F
F,B F,E F,G F,I F,J
4 o# _) i2 a. WG,C G,F G,H G,K
H,D H,K H,L
' G' F! ]9 H" v6 H! g! R# S- ^- e* iI,E I,J
J,F J,G
K,G K,J
L,K
3 L8 Y9 {7 a9 A; r4 p; M) R: S/: c, x;
endsets
data:
c=
$ r* o/ b9 T; W+ Z- [150 165
6 y' [- v3 S/ _, D130 230 160
: K+ U0 _. t: z' }6 h" y6 n140 100
100 190
165 144
0 C3 a! ?3 ~) ?170 144 128 218 174
200 122 109 185
180 141 190
194 148
174 233
$ p2 A0 q* h, H7 k* F5 w2 M7 i; E! L185 135
6 ~8 s2 V+ o  Q8 V2 C! y4 e110;
enddata
+ L/ f7 x' L! q* q& In = @size(nodes);
min = @sum(arcs: c * x);
@for(nodes(i):
3 u% I$ C9 o6 g' m@sum(arcs(i,j):x(i,j))=@sum(arcs(k,i):x(k,i))
);
: U5 y9 w" V9 t& d# v@for(arcs: @bnd(1,x,9));

4 T6 Z" R: B# Z4 W& I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：

7 D& C/ k7 ?) k* {6 @

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];

% X# I: Q/ d5 x! i% Q5 [1 t

open[1000]