% % Problem: % % From: marco % Newsgroups: comp.lang.prolog % Subject: CLP-FD suggestions % Date: Wed, 9 Dec 2009 05:20:12 -0800 (PST) % % I would like to solve a simple problem in CLP: assign 26 groups of % people of various sizes to 6 slots respecting the capacity of each % slot and minimizing the conflicts among the preferences of people. % Preferences are expressed, for each group, as a list of distances from % optimum. % ... % % Solution: % % This solution uses a finite domain solver (ic). % Using a naive predefined search procedure is very slow. % Using a greedy heuristic guided by the preferences finds % good solutions quickly, but struggles to prove optimality. % This is because the boolean model does not give a good cost % bound with CP techniques. % % See also hybrid ic/eplex solution, and the modified ic model % using extra integer variables and element constraints. % % Joachim Schimpf, Monash University, Dec 2009. % This code may be freely used for any purpose. % :- lib(ic). :- lib(branch_and_bound). solve(Cost, Slots) :- data(Pref, Cap, Size), model(Pref, Cap, Size, Slots, Obj), Cost #= eval(Obj), % a standard search routine is very slow % minimize(search(Slots,0,input_order,indomain_max,complete,[]), Cost), % use a problem-specific heuristic bb_min(heuristic_search(Slots,Pref), Cost, bb_options{timeout:10}), ( foreacharg(Slot,Slots) do writeln(Slot) ). heuristic_search(Slots, Pref) :- dim(Pref, [NSlots,NGroups]), % pair the decision variables with their preferences ( multifor([T,G],1,[NSlots,NGroups]), foreach(P-X,PXs), param(Pref,Slots) do P is Pref[T,G], X is Slots[T,G] ), % sort them in descending order sort(1, >=, PXs, SPXs), % label left-to-right, trying zeros first ( foreach(_-X,SPXs) do indomain(X, min) ). model(Pref, Cap, Size, Slots, Obj) :- dim(Cap, [NSlots]), dim(Size, [NGroups]), dim(Slots, [NSlots,NGroups]), Slots[1..NSlots,1..NGroups] \$:: 0.0..1.0, integers(Slots[1..NSlots,1..NGroups]), ( for(T,1,NSlots), param(Slots,Cap,Size,NGroups) do ( for(G,1,NGroups), foreach(U,Used), param(Slots,Size,T) do U = Size[G] * Slots[T,G] ), sum(Used) \$=< Cap[T] ), ( for(G,1,NGroups), param(Slots,NSlots) do sum(Slots[1..NSlots,G]) \$= 1 ), ( multifor([T,G],1,[NSlots,NGroups]), foreach(C,Cs), param(Pref,Slots) do C = Pref[T,G] * Slots[T,G] ), Obj = sum(Cs). %data(Prefs, Capac, Compon) :- % Prefs = []([](0, 1, 1), [](1, 0, 0)), % slot 1 is the first choice for group 1, a second choice for groups 2 and 3 % Capac = [](8, 6), % the first slot can receive 8 people, the second 6 % Compon = [](5, 3, 4). % the first group has 5 people, the second 3, the third 4 data(Prefs, Capac, Compon) :- Prefs = []( [](1, 2, 6, 5, 6, 6, 3, 4, 4, 1, 2, 4, 4, 3, 1, 5, 1, 4, 5, 6, 5, 2, 5, 5, 3, 2), [](2, 3, 3, 2, 1, 4, 4, 2, 2, 6, 3, 1, 5, 5, 5, 6, 4, 2, 6, 4, 4, 5, 6, 2, 2, 1), [](5, 1, 1, 6, 3, 5, 5, 3, 6, 5, 5, 3, 6, 2, 4, 1, 6, 3, 2, 5, 1, 1, 2, 6, 4, 3), [](3, 6, 5, 3, 5, 3, 2, 1, 3, 3, 4, 2, 1, 1, 6, 2, 3, 5, 1, 3, 6, 3, 4, 3, 6, 5), [](4, 4, 4, 4, 2, 2, 1, 6, 1, 4, 6, 5, 2, 4, 2, 3, 5, 6, 4, 2, 3, 6, 1, 1, 1, 6), [](6, 5, 2, 1, 4, 1, 6, 5, 5, 2, 1, 6, 3, 6, 3, 4, 2, 1, 3, 1, 2, 4, 3, 4, 5, 4) ), Capac = [](18, 18, 18, 18, 18, 18), Compon = [](5, 4, 4, 4, 3, 3, 3, 3, 3, 4, 4, 5, 5, 2, 5, 3, 4, 4, 3, 3, 3, 5, 2, 4, 4, 5).