为什么这个两行更改会破坏这个 minizinc set-cover 程序？

Question

下面的程序（改编自 http://www.hakank.org/minizinc/set_covering4b.mzn ）是集合覆盖问题的解决方案（问题末尾提供的示例数据）。这运行正确。

int: num_alternatives;
int: num_objects;
par set of int: ALTERNATIVES = 1..num_alternatives;

% costs for the alternatives
array[ALTERNATIVES] of int: costs; 

% objects covered by the alternatives
array[ALTERNATIVES] of var set of 1..num_objects: a;

% decision variable: which alternative to choose
array[ALTERNATIVES] of var bool: x; 

% the objective to minimize
var int: z = sum(i in 1..num_alternatives) (x[i]*costs[i]); 
solve minimize z;

constraint
   forall(j in 1..num_objects) (
     sum(i in 1..num_alternatives) (x[i] * bool2int(j in a[i])) >= 1
   )
;

output
[
  "x: " ++ show(x) ++ "\n" ++ 
  "a: " ++ show(a) ++ "\n"
];

但是，如果我替换上面的 a 定义：

array[ALTERNATIVES] of var set of 1..num_objects: a;

这两行在我看来是等价的：

var set of int: OBJECTS = 1..num_objects;  
array[ALTERNATIVES] of OBJECTS: a;

...突然出现以下错误：

MiniZinc: type error: type-inst must be par set but is `var set of int'

这让我很困惑。我什至改变了什么？在每种情况下，a 都是一个整数集数组。类型实例在每种情况下都是 var set of int ，但是第二个会抛出错误而第一个不会因为某种原因抛出错误？

这里有一些数据可以放在 .mzn 代码文件的底部，以生成一个独立的、可运行的示例：

% data
num_alternatives =  10;
costs = [ 19, 16, 18, 13, 15, 19, 15, 17, 16, 15];
num_objects = 8;

% the alternatives and the objects they contain
a = [
  {1,6},
  {2,6,8},
  {1,4,7},
  {2,3,5},
  {2,5},
  {2,3},
  {2,3,4},
  {4,5,8},
  {3,6,8},
  {1,6,7}
];

Answer 1

你可以这样写：

int: num_alternatives;
int: num_objects;
set of int: ALTERNATIVES = 1..num_alternatives;
set of int: OBJECTS = 1..num_objects;

% costs for the alternatives
array[ALTERNATIVES] of int: costs; 

% objects covered by the alternatives
array[ALTERNATIVES] of var set of OBJECTS: a;

% decision variable: which alternative to choose
array[ALTERNATIVES] of var bool: x; 

% the objective to minimize
var int: z = sum(i in ALTERNATIVES) (x[i]*costs[i]); 
solve minimize z;

constraint
   forall(j in OBJECTS) (
     sum(i in ALTERNATIVES) (x[i] * (j in a[i])) >= 1
   )
;

output
[
  "x: " ++ show(x) ++ "\n" ++ 
  "a: " ++ show(a) ++ "\n"
];

在你的实验中

var set of int: OBJECTS = 1..num_objects;  
array[ALTERNATIVES] of OBJECTS: a;

a 是 array 范围内的整数 1..num_objects。但是您想要 array 个该范围内的整数集。

为什么这个两行更改会破坏这个 minizinc set-cover 程序？

Why does this two-line change break this minizinc set-cover program?

constraint-programming

minizinc

operations-research

set-cover