*QUESTION: How can I solve the following problem for anything but toy
examples?*
Say, I have the following sets:
All : {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}
subA: {0,1,2,3,4}
subB: {5,6,7,8,9}
If I ask for a subset of "All" which contains 4 elements, of which 2
elements are from "subA" and 2 elements are from "subB", I get a variety of
results, such as
{0,1,5,6}
{0,1,5,7}
...
{3,4,8,9}
...
etc.
This works perfectly fine.
Now, for cases where subA, and subB are not strictly sequential (i.e.
sorted but non-consecutive numbers)
subA: {4,8,14,16,17}
subB: {0,3,5,10,12}
The system quickly runs out of steam (maybe not for the toy example here,
but for |All| = 100, |subA| = |subB| = 20, asking for 10 items -- see
attached code). Gecode just keeps computing and never seems to find a
solution.
Given that the sub-sets are disjoint a solution should really be trivial in
any case (take 50% of one subset and 50% of the other). However, I don't
want to make the assumption that they are disjoint.
I have attached some demo code for what I am talking about, so you can
experiment with it.
Thanks for your help!
Holger.
#include <gecode/set.hh>
#include <gecode/support.hh>
#include <gecode/kernel.hh>
#include <gecode/search.hh>
#include <vector>
#include <algorithm>
using namespace std;
using namespace Gecode;
#define BROKEN_PROBLEM 1 // will not finish
//#define BROKEN_PROBLEM 0 // works just fine
// A "Minimal" space definition for the problem
class MiniSpace: public Space
{
SetVarArray mSetStore;
void CreateAndRequestCategory(int numItemsInCategories, int
requestFromEachCategory, vector<int>& allItems)
{
vector<int> data (numItemsInCategories); // space to hold items
for(int i=0; i<numItemsInCategories; ++i) // fill data from
allItems
{
data[i] = allItems.back();
allItems.pop_back();
}
// sort the items before loading them into Gecode -- not sure
if this is necessary
sort(data.begin(), data.end());
// 1.) Create a new set domain that holds the "special" items
IntSet specialSet(&data[0], (int)data.size());
// 2.) Create a set variable that we'll associate with that set
later on
SetVar specialSelected(*this);
// 3.) Set "specialSelected" to the intersection of whatever a
possible solution is, and
// the "specialSet". This ensures that we can talk about
items that are included
// in the solution, but also belong to the special set
rel(*this, mSetStore[0], SOT_INTER, specialSet, SRT_EQ,
specialSelected);
// 4.) Now ensure that we only have "requestFromEachCategory"
of these overlapping items
cardinality(*this, specialSelected, requestFromEachCategory,
requestFromEachCategory);
}
public:
MiniSpace(int problemSize, int numItemsInCategories, int
numRequestedSize)
{
puts("Setting up problem...");
// Create a SetVariable array (only need one element really,
but this allows me to define the domain in one step)
mSetStore = SetVarArray(*this, 1, IntSet::empty, 0,
problemSize);
SetVar resultSet = mSetStore[0]; // get the one variable that
was defined in the above line
// impose the constraint that we only want "numRequestedSize"
items in the result set
cardinality(*this, resultSet, numRequestedSize,
numRequestedSize);
// Create two sets of random non-overlapping items from
inventory
vector<int> allItems (problemSize);
for(int i=0; i<problemSize; ++i) allItems[i] = problemSize-1-i;
// init items
#if BROKEN_PROBLEM
random_shuffle(allItems.begin(), allItems.end()); // shuffle
items
#endif
int requestFromEachCategory = numRequestedSize * 4 / 10;
CreateAndRequestCategory(numItemsInCategories,
requestFromEachCategory, allItems); // one category
// Create another set of items and request elements from it
CreateAndRequestCategory(numItemsInCategories,
requestFromEachCategory, allItems); // another category
// Given these constraints, branch
branch(*this, mSetStore, SET_VAR_NONE, SET_VAL_MIN_INC);
}
MiniSpace(bool share, MiniSpace& s) : Space(share, s)
{mSetStore.update(*this, share, s.mSetStore);}
virtual Space* copy(bool share) {return new MiniSpace(share, *this);}
void print() const
{
for(SetVarGlbValues d(mSetStore[0]);d();++d)
std::cout << d.val() << " ";
}
};
int main(int argc, char* argv[])
{
// Run the problem
//MiniSpace problem (
// 3000, // total number of items in inventory
// 200, // several sub-inventories (non-overlapping) with X
elements each
// 20 // requesting X items
//); // space instance
MiniSpace problem (
100, // total number of items in inventory
20, // several sub-inventories (non-overlapping)
with X elements each
10 // requesting X items
); // space instance
DFS<MiniSpace> solver (&problem);
int count=0;
puts("Looking for solutions...");
while(true){
MiniSpace* solution = solver.next();
if(!solution) break;
std::cout << "Solution Nr." << count++ << std::endl;
solution->print();
std::cout << std::endl;
delete solution;
}
std::cout << "Done..." << std::endl;
system("pause");
return 0;
}
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