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我正在解决 AMPL 中的一个小问题,我遇到了一个小问题。我有 4 组ABCD 维数 3和 1 个变量x{A,B} binaryy{B,C} binary

D的子集的元素都来自A

A 的每个元素都必须从B中分配一个元素。[这部分完成]

B的指定值中的每个元素都必须从C中指定一个元素。【问题来了】

出于这个原因,我必须定义一个新变量map{A},它将元素从A映射到B(这意味着如果 x[a,b] = 1 则 map[a] = b)。

我想写这样的东西:y[ map[a],c]where {a in A, c in C} 这意味着 A in B的映射 b在A但是 cplex 给了我错误"continuous variable in index expression"

反正有这样做吗?提前致谢。感谢您的帮助。

进一步说明:

假设以下代码:

set A;
set B;
set C;
set D dimen 3; #elements are from A

var x{A,B} binary;
var y{B,C} binary;
var map{A};

forall{a in A} sum {b in B} x[a,b] = 1; #every element from A must have a mapping to B
forall{b in B} sum {c in C} y[b,c] <= 1; #for each element from B, there can be max of 1 mapping to C

subject to mapAtoB{a in A, b in B}: x[a,b] = 1 ==> map[a] = b;
subject to constr{ (i,j,k) in D, c in C }: y[ map[i],c ] + y[ map[j],c ] + y[ map[k],c] = 2; #here is the problem .. I want to be able to say map[i] which is supposed to be equal to some element in B which was assigned to A

data;
set A:= 1 2 3 4;
set B:= a b c;
set C:= i ii iii;
set D: 1 2 3:= (1,2,3) (1,2,4);
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1 回答 1

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您正在尝试使用变量索引变量。这更像是约束编程的风格。您可以通过添加指示 B 的元素是否分配给 A 的元素的变量来执行您在 AMPL 和 cplex 中尝试的操作。

var active{B} binary;
forall {A in A} sum {b in B} x[a,b] = 1
forall {b in B, a in A} x[a,b] <= active[b]
forall {b in B} sum {c in C} y[b,c] = active[b]

因此,如果没有将 A 的元素分配给bb则不会将其分配给 C 的元素。

于 2014-08-08T15:22:15.150 回答