[37] | 1 | function model = mpt_parbb(Matrices,options) |
---|
| 2 | |
---|
| 3 | % For simple development, the code is currently implemented in high-level |
---|
| 4 | % YALMIP and MPT code. Hence, a substantial part of the computation time is |
---|
| 5 | % stupid over-head. |
---|
| 6 | |
---|
| 7 | [Matrices.lb,Matrices.ub] = mpt_detect_and_improve_bounds(Matrices,Matrices.lb,Matrices.ub,Matrices.binary_var_index,options); |
---|
| 8 | |
---|
| 9 | U = sdpvar(Matrices.nu,1); |
---|
| 10 | x = sdpvar(Matrices.nx,1); |
---|
| 11 | F = set(Matrices.G*U < Matrices.W + Matrices.E*x); |
---|
| 12 | F = F + set(Matrices.lb < [U;x] < Matrices.ub); |
---|
| 13 | F = F + set(binary(U(Matrices.binary_var_index))); |
---|
| 14 | F = F + set(Matrices.Aeq*U + Matrices.Beq*x == Matrices.beq); |
---|
| 15 | h = Matrices.H*U + Matrices.F*x; |
---|
| 16 | |
---|
| 17 | Universe = polytope(set(Matrices.lb(end-Matrices.nx+1:end) <= x <= Matrices.ub(end-Matrices.nx+1:end))); |
---|
| 18 | |
---|
| 19 | model = parametric_bb(F,h,options,x,Universe); |
---|
| 20 | |
---|
| 21 | function sol = parametric_bb(F,obj,ops,x,Universe) |
---|
| 22 | |
---|
| 23 | % F : All constraints |
---|
| 24 | % obj : Objective |
---|
| 25 | % x : parametric variables |
---|
| 26 | % y : all binary variables |
---|
| 27 | |
---|
| 28 | if isempty(ops) |
---|
| 29 | ops = sdpsettings; |
---|
| 30 | end |
---|
| 31 | ops.mp.algorithm = 1; |
---|
| 32 | ops.cachesolvers = 0; |
---|
| 33 | ops.mp.presolve=1; |
---|
| 34 | ops.solver = ''; |
---|
| 35 | |
---|
| 36 | % Expand nonlinear operators only once |
---|
| 37 | F = expandmodel(F,obj); |
---|
| 38 | ops.expand = 0; |
---|
| 39 | |
---|
| 40 | % Gather all binary variables |
---|
| 41 | y = unique([depends(F) depends(obj)]); |
---|
| 42 | n = length(y)-length(x); |
---|
| 43 | y = intersect(y,[yalmip('binvariables') depends(F(find(is(F,'binary'))))]); |
---|
| 44 | y = recover(y); |
---|
| 45 | |
---|
| 46 | % Make sure binary relaxations satisfy 0-1 constraints |
---|
| 47 | F = F + set(0 <= y <= 1); |
---|
| 48 | |
---|
| 49 | % recursive, starting in maximum universe |
---|
| 50 | sol = sub_bb(F,obj,ops,x,y,Universe); |
---|
| 51 | |
---|
| 52 | % Nice, however, we have introduced variables along the process, so the |
---|
| 53 | % parametric solutions contain variables we don't care about |
---|
| 54 | for i = 1:length(sol) |
---|
| 55 | for j = 1:length(sol{i}.Fi) |
---|
| 56 | sol{i}.Fi{j} = sol{i}.Fi{j}(1:n,:); |
---|
| 57 | sol{i}.Gi{j} = sol{i}.Gi{j}(1:n,:); |
---|
| 58 | end |
---|
| 59 | end |
---|
| 60 | |
---|
| 61 | function sol = sub_bb(F,obj,ops,x,y,Universe) |
---|
| 62 | |
---|
| 63 | sol = {}; |
---|
| 64 | |
---|
| 65 | % Find a feasible point in this region. Note that it may be the case that a |
---|
| 66 | % point is feasible, but the feasible space is flat. This will cause the |
---|
| 67 | % mplp solver to return an empty solution, and we have to pick a new |
---|
| 68 | % binary solution. |
---|
| 69 | |
---|
| 70 | localsol = {[]}; |
---|
| 71 | intsol.problem = 0; |
---|
| 72 | |
---|
| 73 | if 1%while intsol.problem == 0 |
---|
| 74 | localsol = {[]}; |
---|
| 75 | while isempty(localsol{1}) & (intsol.problem == 0) |
---|
| 76 | ops.verbose = ops.verbose-1; |
---|
| 77 | intsol = solvesdp(F,obj,sdpsettings(ops,'solver','glpk')); |
---|
| 78 | ops.verbose = ops.verbose+1; |
---|
| 79 | if intsol.problem == 0 |
---|
| 80 | y_feasible = round(double(y)); |
---|
| 81 | ops.relax = 1; |
---|
| 82 | localsol = solvemp(F+set(y == y_feasible),obj,ops,x); |
---|
| 83 | ops.relax = 0; |
---|
| 84 | if isempty(localsol{1}) |
---|
| 85 | F = F + not_equal(y,y_feasible); |
---|
| 86 | end |
---|
| 87 | F = F + not_equal(y,y_feasible); |
---|
| 88 | |
---|
| 89 | end |
---|
| 90 | end |
---|
| 91 | if ~isempty(localsol{1}) |
---|
| 92 | |
---|
| 93 | % YALMIP syntax... |
---|
| 94 | if isa(localsol,'cell') |
---|
| 95 | localsol = localsol{1}; |
---|
| 96 | end |
---|
| 97 | |
---|
| 98 | % Now we want to find solutions with other binary combinations, in |
---|
| 99 | % order to find the best one. Cut away the current bionary using |
---|
| 100 | % overloaded not equal |
---|
| 101 | F = F + not_equal(y,y_feasible); |
---|
| 102 | |
---|
| 103 | % Could be that the binary was feasible, but the feasible space in the |
---|
| 104 | % other variables is empty/lower-dimensional |
---|
| 105 | if ~isempty(localsol) |
---|
| 106 | % Dig into this solution. Try to find another feasible binary |
---|
| 107 | % combination, with a better cost, in each of the regions |
---|
| 108 | for i = 1:length(localsol.Pn) |
---|
| 109 | G = F; |
---|
| 110 | % Better cost |
---|
| 111 | G = G + set(obj <= localsol.Bi{i}*x + localsol.Ci{i}); |
---|
| 112 | % In this region |
---|
| 113 | [H,K] = double(localsol.Pn(i)); |
---|
| 114 | G = G + set(H*x <= K); |
---|
| 115 | % Recurse |
---|
| 116 | diggsol{i} = sub_bb(G,obj,ops,x,y,localsol.Pn(i)); |
---|
| 117 | end |
---|
| 118 | |
---|
| 119 | % Create all neighbour regions, and compute solutions in them too |
---|
| 120 | flipped = regiondiff(union(Universe),union(localsol.Pn)); |
---|
| 121 | flipsol={}; |
---|
| 122 | for i = 1:length(flipped) |
---|
| 123 | [H,K] = double(flipped(i)); |
---|
| 124 | flipsol{i} = sub_bb(F+ set(H*x <= K),obj,ops,x,y,flipped(i)); |
---|
| 125 | end |
---|
| 126 | |
---|
| 127 | % Just place all solutions in one big cell. We should do some |
---|
| 128 | % intersect and compare already here, but I am lazy now. |
---|
| 129 | sol = appendlists(sol,localsol,diggsol,flipsol); |
---|
| 130 | end |
---|
| 131 | end |
---|
| 132 | end |
---|
| 133 | |
---|
| 134 | function sol = appendlists(sol,localsol,diggsol,flipsol) |
---|
| 135 | |
---|
| 136 | sol{end+1} = localsol; |
---|
| 137 | for i = 1:length(diggsol) |
---|
| 138 | if ~isempty(diggsol{i}) |
---|
| 139 | if isa(diggsol{i},'cell') |
---|
| 140 | for j = 1:length(diggsol{i}) |
---|
| 141 | sol{end+1} = diggsol{i}{j}; |
---|
| 142 | end |
---|
| 143 | else |
---|
| 144 | sol{end+1} = diggsol{i}; |
---|
| 145 | end |
---|
| 146 | end |
---|
| 147 | end |
---|
| 148 | for i = 1:length(flipsol) |
---|
| 149 | if ~isempty(flipsol{i}) |
---|
| 150 | if isa(flipsol{i},'cell') |
---|
| 151 | for j = 1:length(flipsol{i}) |
---|
| 152 | sol{end+1} = flipsol{i}{j}; |
---|
| 153 | end |
---|
| 154 | else |
---|
| 155 | sol{end+1} = flipsol{i}; |
---|
| 156 | end |
---|
| 157 | end |
---|
| 158 | end |
---|
| 159 | |
---|
| 160 | |
---|
| 161 | function F = not_equal(X,Y) |
---|
| 162 | zv = find((Y == 0)); |
---|
| 163 | ov = find((Y == 1)); |
---|
| 164 | lhs = 0; |
---|
| 165 | if ~isempty(zv) |
---|
| 166 | lhs = lhs + sum(extsubsref(X,zv)); |
---|
| 167 | end |
---|
| 168 | if ~isempty(ov) |
---|
| 169 | lhs = lhs + sum(1-extsubsref(X,ov)); |
---|
| 170 | end |
---|
| 171 | F = set(lhs >=1); |
---|