/* Set covering problem in Picat. This is adapted from set_covering3.pi to handle scp41 problem: http://people.brunel.ac.uk/~mastjjb/jeb/orlib/files/scp41.txt Times: - mip: solves set_covering3/4 in in 0.18s (MinVal = 429) Model created by Hakan Kjellerstrand, hakank@gmail.com See also my Picat page: http://www.hakank.org/picat/ */ % import cp. % import sat. import mip. main => go. % % First find the optimal value (MinVal), then find all the solutions with that value. % go => println("Find the optimal solution"), costs(Costs), belongs(Belongs), NumGroups = Belongs.length, NumSenators = Belongs[1].length, Belongs2 = [], foreach(Group in Belongs) Senators = [ I : {S,I} in zip(Group,1..NumSenators), S == 1], Belongs2 := Belongs2 ++ [Senators] end, set_covering3(Belongs, Costs, MinVal,_), % set_covering3b(Belongs2, NumGroups, NumSenators, Costs, MinVal,_), % printf("\nFinding all optimal solutions with MinVal %d:\n", MinVal), % L = findall(X, set_covering3(Belongs,Costs, MinVal,X)), % Len = length(L), % printf("It was %d solutions\n", Len), nl. set_covering3b(Belongs, NumGroups, NumSenators, Costs, MinVal, X) => println([numGroups=NumGroups,numSenators=NumSenators]), % which senator to choose for this group X = new_list(NumGroups), X :: 1..NumSenators, % which senators was selected Selected = new_list(NumSenators), Selected :: 0..1, println("MinVal"), MinVal #= sum([Selected[I]*Costs[I] : I in 1..NumSenators]), println(minVal=MinVal), println("The Loop"), foreach(I in 1..NumGroups) element(J,Belongs[I],X[I]), element(X[I], Selected, 1), sum([X[I] #= BI : BI in Belongs[I]]) #= 1 end, println("Before solve"), Vars = X.vars() ++ Selected.vars() , solve($[min(MinVal),ff,down,report(printf("MinVal: %d Selected: %w\n",MinVal, Selected))], Vars), println(x=X), printf("These where are selected: %w\n", [I : I in 1..NumSenators, Selected[I] == 1]), println(minVal=MinVal). %%% %%% Original 0/1 version %%% set_covering3(Belongs, Costs, MinVal, X) => % The dimensions of Belongs matrix NumGroups = Belongs.length, NumSenators = Belongs[1].length, println([numGroups=NumGroups,numSenators=NumSenators]), % which senator to choose X = new_list(NumSenators), X :: 0..1, Selected = new_list(NumGroups), Selected :: 1..NumSenators, % cover all groups with the senators foreach(I in 1..NumGroups) sum([X[J]*Belongs[I,J]: J in 1..NumSenators]) #>= 1 end, % objective: minimize the number of senators % MinVal :: 0..sum(Costs), MinVal #= sum([Costs[I]*X[I] : I in 1..NumSenators]), % Either search for all solutions (for the minimum value) or % the optimal value. if ground(MinVal) then solve(X) else solve($[min(MinVal),constr,split,report(printf("MinVal: %d\n",MinVal))], X) end, println(x=X), printf("These where are selected: %w\n", [I : I in 1..NumSenators, X[I] == 1]), println(minVal=MinVal). costs(Costs) => Costs = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 16, 16, 17, 18, 18, 18, 18, 18, 19, 20, 22, 22, 23, 23, 24, 24, 25, 27, 27, 27, 28, 28, 29, 32, 34, 39, 43, 51, 57, 58]. belongs(Belongs) => Belongs = [ [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], 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