问题
I want to implement this Summations as Objective and Constraints(1-6) Could anyone help me that how I can Implement them?
OBJ: Min ∑(i=1..N)∑(j=1..N) Cij * ∑(k=1..K)Xijk
constraint : ∑(k=1..K) Yik=1 (for all i in N)
回答1:
The following answer is specific to ECLiPSe (it uses loops, array and array slice notation, which are not part of standard Prolog).
I assume that N and K (and presumably C) are given, and your matrices are declared as
dim(C, [N,N]),
dim(X, [N,N,K]),
dim(Y, [N,K]),
You can then set up the constraints in a loop:
constraint : ∑(k=1..K) Yik=1 (for all i in N)
( for(I,1,N), param(Y) do
sum(Y[I,*]) $= 1
),
Note that the notation sum(Y[I,*]) here is a shorthand for sum([Y[I,1],Y[I,2],...,Y[I,K]]) when K is the size of this array dimension.
For your objective, because of the nested sum, an auxiliary loop/list is still necessary:
OBJ: Min ∑(i=1..N)∑(j=1..N) Cij * ∑(k=1..K)Xijk
( multifor([I,J],1,N), foreach(Term,Terms), param(C,X) do
Term = (C[I,J] * sum(X[I,J,*]))
),
Objective = sum(Terms),
...
You then have to pass this objective expression to the solver -- the details depend on which solver you use (e.g. eplex, ic).
来源：https://stackoverflow.com/questions/55778381/how-to-implement-this-mp-problem-in-eclipse-clp-or-prolog