[1574] | 1 | // $Id: gear.cpp 1898 2013-04-09 18:06:04Z forrest $ |
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[125] | 2 | // Copyright (C) 2005, International Business Machines |
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| 3 | // Corporation and others. All Rights Reserved. |
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[1574] | 4 | // This code is licensed under the terms of the Eclipse Public License (EPL). |
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| 5 | |
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[125] | 6 | #include <cassert> |
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| 7 | #include <iomanip> |
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| 8 | |
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[1898] | 9 | #include "CoinPragma.hpp" |
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[125] | 10 | |
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| 11 | // For Branch and bound |
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| 12 | #include "OsiSolverInterface.hpp" |
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| 13 | #include "CbcModel.hpp" |
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| 14 | #include "CoinModel.hpp" |
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| 15 | // For Linked Ordered Sets |
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| 16 | #include "CbcBranchLink.hpp" |
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| 17 | #include "OsiClpSolverInterface.hpp" |
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| 18 | |
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[1898] | 19 | #include "CoinTime.hpp" |
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[125] | 20 | |
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| 21 | |
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| 22 | /************************************************************************ |
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| 23 | |
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| 24 | This shows how we can define a new branching method to solve problems with |
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| 25 | nonlinearities and discontinuities. |
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| 26 | |
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| 27 | We are going to solve the problem |
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| 28 | |
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| 29 | minimize abs ( 1.0/6.931 - x1*x4/x2*x3) |
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| 30 | |
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| 31 | where the variables are integral between 12 and 60. |
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[128] | 32 | See E.Sangren, "Nonlinear Integer and Discrete Programming in |
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| 33 | Mechanical Design Optimization". Trans. ASME, J. Mech Design 112, 223-229, 1990 |
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[125] | 34 | |
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| 35 | One could try to use logarithms to make the problem separable but that leads to a |
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| 36 | weak formulation. Instaed we are going to use linked |
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| 37 | special ordered sets. The generalization with column generation can be even more powerful |
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| 38 | but is not yet in CBC. |
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| 39 | |
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| 40 | The idea is simple: |
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| 41 | |
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| 42 | A linear variable is a convex combination of its lower bound and upper bound! |
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| 43 | If x must lie between 12 and 60 then we can substitute for x as x == 12.0*xl + 60.0*xu where |
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| 44 | xl + xu == 1.0. At first this looks cumbersome but if we have xl12, xl13, ... xl60 and corresponding |
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| 45 | xu and yl and yu then we can write: |
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| 46 | |
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| 47 | x == sum 12.0*xl[i] + 60.0* xu[i] where sum xl[i] + xu[i] == 1.0 |
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| 48 | and |
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| 49 | x*y == 12.0*12.0*xl12 + 12.0*60.0*xu12 + 13.0*12.0*xl13 + 13.0*60.0*x13 .... |
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| 50 | + 12.0*60*.0xl60 + 60.0*60.0*xu60 |
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| 51 | |
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| 52 | And now x*y is correct if x is integer and xl[i], xu[i] are only nonzero for one i. |
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| 53 | Note that this would have worked just as easily for y**2 or any clean function of y. |
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| 54 | |
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| 55 | So this is just like a special ordered set of type 1 but on two sets simultaneously. |
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| 56 | The idea is even more powerful if we want other functions on y as we can branch on all |
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| 57 | sets simultaneously. |
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| 58 | Also note that convexity requirements for any non-linear functions are not needed. |
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| 59 | |
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| 60 | So we need a new branching method to do that - see CbcBranchLink.?pp |
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| 61 | |
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| 62 | We are going to need a CbcBranchLink method to see whether we are satisfied etc and also to |
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| 63 | create another branching object which knows how to fix variables. We might be able to use an |
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| 64 | existing method for the latter but let us create two methods CbcLink and |
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| 65 | CbcLinkBranchingObject. |
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| 66 | |
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| 67 | For CbcLink we will need the following methods: |
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| 68 | Constructot/Destructor |
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| 69 | infeasibility - returns 0.0 if feasible otherwise some measure of infeasibility |
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| 70 | feasibleRegion - sets bounds to contain current solution |
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| 71 | createBranch - creates a CbcLinkBranchingObject |
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| 72 | |
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| 73 | For CbcLinkBranchingObject we need: |
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| 74 | Constructor/Destructor |
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| 75 | branch - does actual fixing |
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| 76 | print - optional for debug purposes. |
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| 77 | |
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| 78 | The easiest way to do this is to cut and paste from CbcBranchActual to get current |
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| 79 | SOS stuff and then modify that. |
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| 80 | |
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| 81 | ************************************************************************/ |
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| 82 | |
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| 83 | int main (int argc, const char *argv[]) |
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| 84 | { |
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| 85 | |
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| 86 | OsiClpSolverInterface solver1; |
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| 87 | |
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| 88 | /* |
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| 89 | We are going to treat x1 and x2 as integer and x3 and x4 as a set. |
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| 90 | We define two new variables y1 == x1*x4 and y2 == x2*x3. |
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| 91 | We define a variable z == x1*x4/x2*x3 so y2*z == y1 |
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| 92 | (we will treat y2 as a set) |
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| 93 | Then we have objective - minimize w1 + w2 where |
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| 94 | w1 - w2 = 1.0/6.931 - z |
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| 95 | |
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| 96 | The model would be a lot smaller if we had column generation. |
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| 97 | */ |
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| 98 | // Create model |
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| 99 | CoinModel build; |
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| 100 | // Keep values of all variables for reporting purposes even if not necessary |
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| 101 | /* |
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| 102 | z is first, then x then y1,y2 then w1,w2 |
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| 103 | then y1 stuff, y2 stuff and finally y2 -> z stuff. |
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| 104 | For rows same but 2 per y then rest of z stuff |
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| 105 | */ |
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| 106 | int loInt=12; |
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| 107 | int hiInt=60; |
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| 108 | int ybaseA=5, ybaseB=9, ylen=hiInt-loInt+1; |
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| 109 | int base = ybaseB+2*2*ylen; |
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| 110 | int yylen = hiInt*hiInt-loInt*loInt+1; |
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| 111 | int zbase = 10; |
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| 112 | int i; |
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| 113 | // Do single variables |
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| 114 | double value[] ={1.0,1.0}; |
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| 115 | int row[2]; |
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| 116 | /* z - obviously we can't choose bounds too tight but we need bounds |
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[126] | 117 | so choose 20% off as obviously feasible. |
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| 118 | fastest way to solve would be too run for a few seconds to get |
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| 119 | tighter bounds then re-formulate and solve. */ |
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| 120 | double loose=0.2; |
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| 121 | double loZ = (1-loose)*(1.0/6.931), hiZ = (1+loose)*(1.0/6.931); |
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[125] | 122 | row[0]=0; // for reporting |
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| 123 | row[1]=zbase+1; // for real use |
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| 124 | build.addColumn(2,row,value,loZ, hiZ, 0.0); |
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| 125 | // x |
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| 126 | for (i=0;i<4;i++) { |
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| 127 | row[0]=i+1; |
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| 128 | build.addColumn(1,row,value,loInt, hiInt,0.0); |
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| 129 | // we don't need to say x2, x3 integer but won't hurt |
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| 130 | build.setInteger(i+1); |
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| 131 | } |
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| 132 | // y |
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| 133 | for (i=0;i<2;i++) { |
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| 134 | // y from x*x, and convexity |
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| 135 | row[0]=ybaseA+2*i; |
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| 136 | if (i==0) |
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| 137 | row[1]=zbase+2; // yb*z == ya |
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| 138 | else |
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| 139 | row[1]=zbase-1; // to feed into z |
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| 140 | build.addColumn(2,row,value,loInt*loInt, hiInt*hiInt,0.0); |
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| 141 | // we don't need to say integer but won't hurt |
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| 142 | build.setInteger(ybaseA+i); |
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| 143 | } |
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| 144 | // skip z convexity put w in final equation |
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| 145 | row[0]=zbase+1; |
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| 146 | build.addColumn(1,row,value,0.0,1.0,1.0); |
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| 147 | value[0]=-1.0; |
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| 148 | build.addColumn(1,row,value,0.0,1.0,1.0); |
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| 149 | // Do columns so we know where each is |
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| 150 | for (i=ybaseB;i<base+(2*yylen);i++) |
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| 151 | build.setColumnBounds(i,0.0,1.0); |
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| 152 | // Now do rows |
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| 153 | // z definition |
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| 154 | build.setRowBounds(0,0.0,0.0); |
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| 155 | for (i=0;i<yylen;i++) { |
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| 156 | // l |
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| 157 | build.setElement(0,base+2*i,-loZ); |
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| 158 | // u |
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| 159 | build.setElement(0,base+2*i+1,-hiZ); |
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| 160 | } |
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| 161 | // x |
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| 162 | for (i=0;i<2;i++) { |
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| 163 | int iVarRow = 1+i; |
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| 164 | int iSetRow = 4-i; // as it is x1*x4 and x2*x3 |
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| 165 | build.setRowBounds(iVarRow,0.0,0.0); |
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| 166 | build.setRowBounds(iSetRow,0.0,0.0); |
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| 167 | int j; |
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| 168 | int base2 = ybaseB + 2*ylen*i; |
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| 169 | for (j=0;j<ylen;j++) { |
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| 170 | // l |
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| 171 | build.setElement(iVarRow,base2+2*j,-loInt); |
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| 172 | build.setElement(iSetRow,base2+2*j,-loInt-j); |
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| 173 | // u |
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| 174 | build.setElement(iVarRow,base2+2*j+1,-hiInt); |
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| 175 | build.setElement(iSetRow,base2+2*j+1,-loInt-j); |
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| 176 | } |
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| 177 | } |
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| 178 | // y |
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| 179 | for (i=0;i<2;i++) { |
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| 180 | int iRow = 5+2*i; |
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| 181 | int iConvex = iRow+1; |
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| 182 | build.setRowBounds(iRow,0.0,0.0); |
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| 183 | build.setRowBounds(iConvex,1.0,1.0); |
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| 184 | int j; |
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| 185 | int base2 = ybaseB + 2*ylen*i; |
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| 186 | for (j=0;j<ylen;j++) { |
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| 187 | // l |
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| 188 | build.setElement(iRow,base2+2*j,-loInt*(j+loInt)); |
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| 189 | build.setElement(iConvex,base2+2*j,1.0); |
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| 190 | // u |
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| 191 | build.setElement(iRow,base2+2*j+1,-hiInt*(j+loInt)); |
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| 192 | build.setElement(iConvex,base2+2*j+1,1.0); |
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| 193 | } |
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| 194 | } |
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| 195 | // row that feeds into z and convexity |
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| 196 | build.setRowBounds(zbase-1,0.0,0.0); |
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| 197 | build.setRowBounds(zbase,1.0,1.0); |
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| 198 | for (i=0;i<yylen;i++) { |
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| 199 | // l |
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| 200 | build.setElement(zbase-1,base+2*i,-(i+loInt*loInt)); |
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| 201 | build.setElement(zbase,base+2*i,1.0); |
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| 202 | // u |
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| 203 | build.setElement(zbase-1,base+2*i+1,-(i+loInt*loInt)); |
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| 204 | build.setElement(zbase,base+2*i+1,1.0); |
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| 205 | } |
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| 206 | // and real equation rhs |
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| 207 | build.setRowBounds(zbase+1,1.0/6.931,1.0/6.931); |
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| 208 | // z*y |
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| 209 | build.setRowBounds(zbase+2,0.0,0.0); |
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| 210 | for (i=0;i<yylen;i++) { |
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| 211 | // l |
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| 212 | build.setElement(zbase+2,base+2*i,-(i+loInt*loInt)*loZ); |
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| 213 | // u |
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| 214 | build.setElement(zbase+2,base+2*i+1,-(i+loInt*loInt)*hiZ); |
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| 215 | } |
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[126] | 216 | // And finally two more rows to break symmetry |
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| 217 | build.setRowBounds(zbase+3,-COIN_DBL_MAX,0.0); |
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| 218 | build.setElement(zbase+3,1,1.0); |
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| 219 | build.setElement(zbase+3,4,-1.0); |
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| 220 | build.setRowBounds(zbase+4,-COIN_DBL_MAX,0.0); |
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| 221 | build.setElement(zbase+4,2,1.0); |
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| 222 | build.setElement(zbase+4,3,-1.0); |
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[125] | 223 | solver1.loadFromCoinModel(build); |
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| 224 | // To make CbcBranchLink simpler assume that all variables with same i are consecutive |
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| 225 | |
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| 226 | double time1 = CoinCpuTime(); |
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| 227 | solver1.initialSolve(); |
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| 228 | solver1.writeMps("bad"); |
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| 229 | CbcModel model(solver1); |
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| 230 | model.solver()->setHintParam(OsiDoReducePrint,true,OsiHintTry); |
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[127] | 231 | model.solver()->setHintParam(OsiDoScale,false,OsiHintTry); |
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[125] | 232 | |
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| 233 | CbcObject ** objects = new CbcObject * [3]; |
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| 234 | /* Format is number in sets, number in each link, first variable in matrix) |
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| 235 | and then a weight for each in set to say where to branch. |
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| 236 | In this case use NULL to say 0,1,2 ... |
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| 237 | Finally a set number as ID. |
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| 238 | */ |
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| 239 | objects[0]=new CbcLink(&model,ylen,2,ybaseB,NULL,0); |
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| 240 | objects[0]->setPriority(10); |
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| 241 | objects[1]=new CbcLink(&model,ylen,2,ybaseB+2*ylen,NULL,0); |
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| 242 | objects[1]->setPriority(20); |
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| 243 | objects[2]=new CbcLink(&model,yylen,2,base,NULL,0); |
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| 244 | objects[2]->setPriority(1); |
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| 245 | model.addObjects(3,objects); |
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| 246 | for (i=0;i<3;i++) |
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| 247 | delete objects[i]; |
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| 248 | delete [] objects; |
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| 249 | model.messageHandler()->setLogLevel(1); |
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| 250 | // Do complete search |
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| 251 | |
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| 252 | model.setDblParam(CbcModel::CbcMaximumSeconds,1200.0); |
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| 253 | model.setDblParam(CbcModel::CbcCutoffIncrement,1.0e-8); |
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| 254 | model.branchAndBound(); |
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| 255 | |
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| 256 | std::cout<<"took "<<CoinCpuTime()-time1<<" seconds, " |
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| 257 | <<model.getNodeCount()<<" nodes with objective " |
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| 258 | <<model.getObjValue() |
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| 259 | <<(!model.status() ? " Finished" : " Not finished") |
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| 260 | <<std::endl; |
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| 261 | |
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| 262 | |
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| 263 | if (model.getMinimizationObjValue()<1.0e50) { |
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| 264 | |
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| 265 | const double * solution = model.bestSolution(); |
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| 266 | int numberColumns = model.solver()->getNumCols(); |
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| 267 | double x1=solution[1]; |
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| 268 | double x2=solution[2]; |
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| 269 | double x3=solution[3]; |
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| 270 | double x4=solution[4]; |
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| 271 | printf("Optimal solution %g %g %g %g\n",x1,x2,x3,x4); |
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| 272 | for (int iColumn=0;iColumn<numberColumns;iColumn++) { |
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| 273 | double value=solution[iColumn]; |
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| 274 | if (fabs(value)>1.0e-7) |
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| 275 | std::cout<<iColumn<<" "<<value<<std::endl; |
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| 276 | } |
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| 277 | } |
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| 278 | return 0; |
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| 279 | } |
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