[37] | 1 | function sol = dua_test(F,obj,ops,x) |
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| 2 | |
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| 3 | % F : All constraints |
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| 4 | % obj : Objective |
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| 5 | % x : parametric variables |
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| 6 | % y : all binary variables |
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| 7 | |
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| 8 | if isempty(ops) |
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| 9 | ops = sdpsettings; |
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| 10 | end |
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| 11 | ops.mp.algorithm = 1; |
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| 12 | ops.cachesolvers = 0; |
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| 13 | ops.mp.presolve=1; |
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| 14 | ops.solver = ''; |
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| 15 | |
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| 16 | % Expand nonlinear operators only once |
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| 17 | F = expandmodel(F,obj); |
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| 18 | ops.expand = 0; |
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| 19 | |
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| 20 | % Gather all binary variables |
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| 21 | y = unique([depends(F) depends(obj)]); |
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| 22 | n = length(y)-length(x); |
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| 23 | y = intersect(y,[yalmip('binvariables') depends(F(find(is(F,'binary'))))]); |
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| 24 | y = recover(y); |
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| 25 | |
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| 26 | % Make sure binary relaxations satisfy 0-1 constraints |
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| 27 | F = F + set(0 <= y <= 1); |
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| 28 | |
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| 29 | % Bounded search-space |
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| 30 | Universe = unitbox(length(x),10); |
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| 31 | |
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| 32 | % recursive, starting in maximum universe |
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| 33 | sol = sub_dua(F,obj,ops,x,y,Universe); |
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| 34 | |
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| 35 | % Nice, however, we have introduced variables along the process, so the |
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| 36 | % parametric solutions contain variables we don't care about |
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| 37 | for i = 1:length(sol) |
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| 38 | for j = 1:length(sol{i}.Fi) |
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| 39 | sol{i}.Fi{j} = sol{i}.Fi{j}(1:n,:); |
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| 40 | sol{i}.Gi{j} = sol{i}.Gi{j}(1:n,:); |
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| 41 | end |
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| 42 | end |
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| 43 | |
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| 44 | |
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| 45 | function sol = sub_dua(F,obj,ops,x,y,Universe) |
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| 46 | |
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| 47 | sol = {}; |
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| 48 | |
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| 49 | % Find a feasible point in this region |
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| 50 | % ops.verbose = ops.verbose-1; |
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| 51 | % intsol = solvesdp(F,obj,ops); |
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| 52 | % ops.verbose = ops.verbose+1; |
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| 53 | |
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| 54 | y_feasible = 0; |
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| 55 | if 1 |
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| 56 | localsol = {[]}; |
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| 57 | intsol.problem = 0; |
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| 58 | while isempty(localsol{1}) & (intsol.problem == 0) |
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| 59 | ops.verbose = ops.verbose-1; |
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| 60 | intsol = solvesdp(F,obj,ops); |
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| 61 | ops.verbose = ops.verbose+1; |
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| 62 | if intsol.problem == 0 |
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| 63 | if isequal(y_feasible , round(double(y))) |
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| 64 | 1; |
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| 65 | end |
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| 66 | y_feasible = round(double(y)) |
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| 67 | 'start' |
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| 68 | localsol = solvemp(F+set(y == y_feasible),obj,sdpsettings(ops,'relax',1),x); |
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| 69 | 'end' |
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| 70 | if isempty(localsol{1}) |
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| 71 | F = F + not_equal(y,y_feasible); |
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| 72 | end |
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| 73 | end |
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| 74 | end |
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| 75 | else |
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| 76 | ops.verbose = ops.verbose-1; |
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| 77 | intsol = solvesdp(F,obj,ops); |
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| 78 | ops.verbose = ops.verbose+1; |
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| 79 | y_feasible = round(double(y)); |
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| 80 | end |
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| 81 | |
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| 82 | %if intsol.problem == 0 |
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| 83 | if ~isempty(localsol{1})%intsol.problem == 0 |
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| 84 | |
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| 85 | % Compute feasible mpLP solution for this binary combination |
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| 86 | %y_feasible = round(double(y)); |
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| 87 | %localsol = solvemp(F+set(y == y_feasible),obj,sdpsettings(ops,'relax',1),x); |
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| 88 | |
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| 89 | % YALMIP syntax... |
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| 90 | if isa(localsol,'cell') |
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| 91 | localsol = localsol{1}; |
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| 92 | end |
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| 93 | |
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| 94 | % Now we want to find solutions with other binary combinations, in |
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| 95 | % order to find the best one. Cut away the current bionary using |
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| 96 | % overloaded not equal |
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| 97 | F = F + not_equal(y , y_feasible); |
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| 98 | |
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| 99 | % Could be that the binary was feasible, but the feasible space in the |
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| 100 | % other variables is empty/lower-dimensional |
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| 101 | if ~isempty(localsol) |
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| 102 | % Dig into this solution. Try to find another feasible binary |
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| 103 | % combination, with a better cost, in each of the regions |
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| 104 | for i = 1:length(localsol.Pn) |
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| 105 | G = F; |
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| 106 | % Better cost |
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| 107 | G = G + set(obj <= localsol.Bi{i}*x + localsol.Ci{i}); |
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| 108 | % In this region |
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| 109 | [H,K] = double(localsol.Pn(i)); |
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| 110 | G = G + set(H*x <= K); |
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| 111 | % Recurse |
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| 112 | diggsol{i} = sub_dua(G,obj,ops,x,y,localsol.Pn(i)); |
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| 113 | end |
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| 114 | |
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| 115 | % Create all neighbour regions, and compute solutions in them too |
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| 116 | flipped = regiondiff(union(Universe),union(localsol.Pn)); |
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| 117 | flipsol={}; |
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| 118 | for i = 1:length(flipped) |
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| 119 | [H,K] = double(flipped(i)); |
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| 120 | flipsol{i} = sub_dua(F+ set(H*x <= K),obj,ops,x,y,flipped(i)); |
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| 121 | end |
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| 122 | |
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| 123 | % Just place all solutions in one big cell. We should do some |
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| 124 | % intersect and compare already here, but I am lazy now. |
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| 125 | sol = appendlists(sol,localsol,diggsol,flipsol); |
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| 126 | end |
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| 127 | end |
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| 128 | |
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| 129 | function sol = appendlists(sol,localsol,diggsol,flipsol) |
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| 130 | |
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| 131 | sol{end+1} = localsol; |
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| 132 | for i = 1:length(diggsol) |
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| 133 | if ~isempty(diggsol{i}) |
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| 134 | if isa(diggsol{i},'cell') |
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| 135 | for j = 1:length(diggsol{i}) |
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| 136 | sol{end+1} = diggsol{i}{j}; |
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| 137 | end |
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| 138 | else |
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| 139 | sol{end+1} = diggsol{i}; |
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| 140 | end |
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| 141 | end |
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| 142 | end |
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| 143 | for i = 1:length(flipsol) |
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| 144 | if ~isempty(flipsol{i}) |
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| 145 | if isa(flipsol{i},'cell') |
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| 146 | for j = 1:length(flipsol{i}) |
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| 147 | sol{end+1} = flipsol{i}{j}; |
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| 148 | end |
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| 149 | else |
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| 150 | sol{end+1} = flipsol{i}; |
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| 151 | end |
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| 152 | end |
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| 153 | end |
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| 154 | |
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