在Minizinc中声明一个变量以使其最大化

Question

我有一个问题，就是确定一组骑士在棋盘内可以进行的最大移动长度，条件是：

• 共有4名骑士，他们的移动顺序为：A->B->C->D.他们的第一个位置是角落
• 有些细胞无法访问，而其他细胞只能访问k次。第一个位置不算数
• 结果应该是骑士在棋盘上可以做的一系列动作

这是我的代码，但我不知道如何修改程序以最大化路径(t(的值：

include "globals.mzn";
int: n=4; %nxnxt board
int: k=1; %k times visited cell
var 0..100: t; %Lenth of the path
%Initial board
array[1..t, 1..n, 1..n] of var 0..k:b;
% Decision variables (*CHANGED*)
array[1..t,1..4] of var 1..n: r;% The sequence of moves in the path
array[1..t,1..4] of var 1..n: c;% (row and column of each move).
%%% Always the same order A -> B -> C -> D knights
%Constraints
% Forcing the first moves.
constraint r[1,1] = 1;%A
constraint c[1,1] = 1;
constraint r[1,2] = 1;%B
constraint c[1,2] = n;
constraint r[1,3] = n;%C
constraint c[1,3] = 1;
constraint r[1,4] = n;%D
constraint c[1,4] = n;
constraint b[1,1,2] = k;
constraint b[1,1,3] = k;
constraint b[1,2,1] = k;
constraint b[1,3,1] = k;
constraint b[1,2,4] = k;
constraint b[1,3,4] = k;
constraint b[1,4,2] = k;
constraint b[1,4,3] = k;
% LIMIT ON VISITS (*ADDED*)
constraint
forall (i in 1..t, j in 1..n, l in 1..n) (
b[i,j,l] <= k
);
% SUCCESSOR (STEP OF THE KNIGHT)
constraint
forall (i in 1..t-1, j in 1..4) (
c[i,j] != c[i+1,j] /%Each movement has to be diferent than the previous one
r[i,j] != r[i+1,j] /
abs(c[i,j] - c[i+1,j]) + abs(r[i,j] - r[i+1,j]) = 3
);

% NEVER TWO QUEENS ON THE SAME CELL
constraint forall(i in 1..t, j in 1..3, p in 2..4 where p > j )(
r[i,j] != r[i,p] /     
c[i,j] != c[i,p]);

constraint forall(i in 2..t, j in 1..n, l in 1..n)(
if b[i-1,j,l] = k then  
b[i, j, l] = k
endif
);
% APPLY THE MOVE IN THE MATRIX
constraint
forall (i in 2..t, j in 1..4) ( 
exists(w in {-2, 2}, q in {-1, 1}) ( % Set up the possible moviments.
if  1 <= r[i-1,j]+w / r[i-1,j]+w <= n / 
1 <= c[i-1,j]+q / c[i-1,j]+q <= n / 
b[i-1, r[i-1, j]+w, c[i-1, j]+q] < k then
(r[i,j] = r[i-1, j] + w /
c[i,j] = c[i-1, j] + q)
endif
/
if  1 <= r[i-1,j]+q / r[i-1,j]+q <= n / 
1 <= c[i-1,j]+w / c[i-1,j]+w <= n / 
b[i-1, r[i-1,j]+q, c[i-1,j]+w] < k then
(r[i,j] = r[i-1, j] + q /
c[i,j] = c[i-1, j] + w) 
endif) /
b[i, r[i,j], c[i,j]] = b[i-1, r[i,j], c[i,j]] + 1
);     
solve maximize t;
output["r"]++[
if j = 1 then "n" else "" endif ++
show(r[i,j]) ++ " "
| i in 1..t, j in 1..n   
]++["nnc"]++
[
if j = 1 then "n" else "" endif ++
show(c[i,j]) ++ " "
| i in 1..t, j in 1..n  
]++["n"] ++
[ if l = 1 then "n" else "" endif ++  
show(b[i,j,l]) ++ " " 
|i in 1..t, j in 1..n, l in 1..n];
include "globals.mzn";
int: n=4; %nxnxt board
int: k=1; %k times visited cell
var 0..100: t; %Lenth of the path
l in 1..n];

Answer 1

规划风格问题的一种通用方法是首先设置可能步骤数的上限。然后对模型进行修改，以便可以应用一些哨兵无移动移动，但只能在移动结束时应用。最后，你可以通过计算没有移动的次数并从固定上限中减去它来计算使用的移动次数。