1 | // $Id: gear.cpp 2469 2019-01-06 23:17:46Z forrest $ |
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2 | // Copyright (C) 2005, International Business Machines |
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3 | // Corporation and others. All Rights Reserved. |
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4 | // This code is licensed under the terms of the Eclipse Public License (EPL). |
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5 | |
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6 | #include <cassert> |
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7 | #include <iomanip> |
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8 | |
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9 | #include "CoinPragma.hpp" |
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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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19 | #include "CoinTime.hpp" |
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20 | |
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21 | /************************************************************************ |
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22 | |
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23 | This shows how we can define a new branching method to solve problems with |
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24 | nonlinearities and discontinuities. |
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25 | |
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26 | We are going to solve the problem |
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27 | |
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28 | minimize abs ( 1.0/6.931 - x1*x4/x2*x3) |
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29 | |
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30 | where the variables are integral between 12 and 60. |
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31 | See E.Sangren, "Nonlinear Integer and Discrete Programming in |
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32 | Mechanical Design Optimization". Trans. ASME, J. Mech Design 112, 223-229, 1990 |
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33 | |
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34 | One could try to use logarithms to make the problem separable but that leads to a |
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35 | weak formulation. Instaed we are going to use linked |
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36 | special ordered sets. The generalization with column generation can be even more powerful |
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37 | but is not yet in CBC. |
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38 | |
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39 | The idea is simple: |
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40 | |
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41 | A linear variable is a convex combination of its lower bound and upper bound! |
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42 | 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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43 | xl + xu == 1.0. At first this looks cumbersome but if we have xl12, xl13, ... xl60 and corresponding |
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44 | xu and yl and yu then we can write: |
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45 | |
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46 | x == sum 12.0*xl[i] + 60.0* xu[i] where sum xl[i] + xu[i] == 1.0 |
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47 | and |
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48 | 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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49 | + 12.0*60*.0xl60 + 60.0*60.0*xu60 |
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50 | |
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51 | 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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52 | Note that this would have worked just as easily for y**2 or any clean function of y. |
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53 | |
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54 | So this is just like a special ordered set of type 1 but on two sets simultaneously. |
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55 | The idea is even more powerful if we want other functions on y as we can branch on all |
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56 | sets simultaneously. |
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57 | Also note that convexity requirements for any non-linear functions are not needed. |
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58 | |
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59 | So we need a new branching method to do that - see CbcBranchLink.?pp |
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60 | |
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61 | We are going to need a CbcBranchLink method to see whether we are satisfied etc and also to |
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62 | create another branching object which knows how to fix variables. We might be able to use an |
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63 | existing method for the latter but let us create two methods CbcLink and |
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64 | CbcLinkBranchingObject. |
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65 | |
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66 | For CbcLink we will need the following methods: |
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67 | Constructot/Destructor |
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68 | infeasibility - returns 0.0 if feasible otherwise some measure of infeasibility |
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69 | feasibleRegion - sets bounds to contain current solution |
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70 | createBranch - creates a CbcLinkBranchingObject |
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71 | |
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72 | For CbcLinkBranchingObject we need: |
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73 | Constructor/Destructor |
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74 | branch - does actual fixing |
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75 | print - optional for debug purposes. |
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76 | |
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77 | The easiest way to do this is to cut and paste from CbcBranchActual to get current |
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78 | SOS stuff and then modify that. |
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79 | |
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80 | ************************************************************************/ |
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81 | |
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82 | int main(int argc, const char *argv[]) |
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83 | { |
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84 | |
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85 | OsiClpSolverInterface solver1; |
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86 | |
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87 | /* |
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88 | We are going to treat x1 and x2 as integer and x3 and x4 as a set. |
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89 | We define two new variables y1 == x1*x4 and y2 == x2*x3. |
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90 | We define a variable z == x1*x4/x2*x3 so y2*z == y1 |
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91 | (we will treat y2 as a set) |
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92 | Then we have objective - minimize w1 + w2 where |
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93 | w1 - w2 = 1.0/6.931 - z |
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94 | |
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95 | The model would be a lot smaller if we had column generation. |
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96 | */ |
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97 | // Create model |
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98 | CoinModel build; |
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99 | // Keep values of all variables for reporting purposes even if not necessary |
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100 | /* |
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101 | z is first, then x then y1,y2 then w1,w2 |
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102 | then y1 stuff, y2 stuff and finally y2 -> z stuff. |
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103 | For rows same but 2 per y then rest of z stuff |
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104 | */ |
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105 | int loInt = 12; |
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106 | int hiInt = 60; |
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107 | int ybaseA = 5, ybaseB = 9, ylen = hiInt - loInt + 1; |
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108 | int base = ybaseB + 2 * 2 * ylen; |
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109 | int yylen = hiInt * hiInt - loInt * loInt + 1; |
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110 | int zbase = 10; |
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111 | int i; |
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112 | // Do single variables |
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113 | double value[] = { 1.0, 1.0 }; |
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114 | int row[2]; |
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115 | /* z - obviously we can't choose bounds too tight but we need bounds |
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116 | so choose 20% off as obviously feasible. |
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117 | fastest way to solve would be too run for a few seconds to get |
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118 | tighter bounds then re-formulate and solve. */ |
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119 | double loose = 0.2; |
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120 | double loZ = (1 - loose) * (1.0 / 6.931), hiZ = (1 + loose) * (1.0 / 6.931); |
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121 | row[0] = 0; // for reporting |
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122 | row[1] = zbase + 1; // for real use |
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123 | build.addColumn(2, row, value, loZ, hiZ, 0.0); |
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124 | // x |
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125 | for (i = 0; i < 4; i++) { |
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126 | row[0] = i + 1; |
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127 | build.addColumn(1, row, value, loInt, hiInt, 0.0); |
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128 | // we don't need to say x2, x3 integer but won't hurt |
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129 | build.setInteger(i + 1); |
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130 | } |
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131 | // y |
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132 | for (i = 0; i < 2; i++) { |
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133 | // y from x*x, and convexity |
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134 | row[0] = ybaseA + 2 * i; |
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135 | if (i == 0) |
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136 | row[1] = zbase + 2; // yb*z == ya |
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137 | else |
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138 | row[1] = zbase - 1; // to feed into z |
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139 | build.addColumn(2, row, value, loInt * loInt, hiInt * hiInt, 0.0); |
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140 | // we don't need to say integer but won't hurt |
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141 | build.setInteger(ybaseA + i); |
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142 | } |
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143 | // skip z convexity put w in final equation |
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144 | row[0] = zbase + 1; |
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145 | build.addColumn(1, row, value, 0.0, 1.0, 1.0); |
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146 | value[0] = -1.0; |
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147 | build.addColumn(1, row, value, 0.0, 1.0, 1.0); |
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148 | // Do columns so we know where each is |
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149 | for (i = ybaseB; i < base + (2 * yylen); i++) |
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150 | build.setColumnBounds(i, 0.0, 1.0); |
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151 | // Now do rows |
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152 | // z definition |
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153 | build.setRowBounds(0, 0.0, 0.0); |
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154 | for (i = 0; i < yylen; i++) { |
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155 | // l |
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156 | build.setElement(0, base + 2 * i, -loZ); |
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157 | // u |
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158 | build.setElement(0, base + 2 * i + 1, -hiZ); |
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159 | } |
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160 | // x |
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161 | for (i = 0; i < 2; i++) { |
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162 | int iVarRow = 1 + i; |
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163 | int iSetRow = 4 - i; // as it is x1*x4 and x2*x3 |
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164 | build.setRowBounds(iVarRow, 0.0, 0.0); |
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165 | build.setRowBounds(iSetRow, 0.0, 0.0); |
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166 | int j; |
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167 | int base2 = ybaseB + 2 * ylen * i; |
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168 | for (j = 0; j < ylen; j++) { |
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169 | // l |
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170 | build.setElement(iVarRow, base2 + 2 * j, -loInt); |
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171 | build.setElement(iSetRow, base2 + 2 * j, -loInt - j); |
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172 | // u |
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173 | build.setElement(iVarRow, base2 + 2 * j + 1, -hiInt); |
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174 | build.setElement(iSetRow, base2 + 2 * j + 1, -loInt - j); |
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175 | } |
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176 | } |
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177 | // y |
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178 | for (i = 0; i < 2; i++) { |
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179 | int iRow = 5 + 2 * i; |
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180 | int iConvex = iRow + 1; |
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181 | build.setRowBounds(iRow, 0.0, 0.0); |
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182 | build.setRowBounds(iConvex, 1.0, 1.0); |
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183 | int j; |
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184 | int base2 = ybaseB + 2 * ylen * i; |
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185 | for (j = 0; j < ylen; j++) { |
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186 | // l |
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187 | build.setElement(iRow, base2 + 2 * j, -loInt * (j + loInt)); |
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188 | build.setElement(iConvex, base2 + 2 * j, 1.0); |
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189 | // u |
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190 | build.setElement(iRow, base2 + 2 * j + 1, -hiInt * (j + loInt)); |
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191 | build.setElement(iConvex, base2 + 2 * j + 1, 1.0); |
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192 | } |
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193 | } |
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194 | // row that feeds into z and convexity |
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195 | build.setRowBounds(zbase - 1, 0.0, 0.0); |
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196 | build.setRowBounds(zbase, 1.0, 1.0); |
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197 | for (i = 0; i < yylen; i++) { |
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198 | // l |
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199 | build.setElement(zbase - 1, base + 2 * i, -(i + loInt * loInt)); |
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200 | build.setElement(zbase, base + 2 * i, 1.0); |
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201 | // u |
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202 | build.setElement(zbase - 1, base + 2 * i + 1, -(i + loInt * loInt)); |
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203 | build.setElement(zbase, base + 2 * i + 1, 1.0); |
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204 | } |
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205 | // and real equation rhs |
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206 | build.setRowBounds(zbase + 1, 1.0 / 6.931, 1.0 / 6.931); |
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207 | // z*y |
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208 | build.setRowBounds(zbase + 2, 0.0, 0.0); |
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209 | for (i = 0; i < yylen; i++) { |
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210 | // l |
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211 | build.setElement(zbase + 2, base + 2 * i, -(i + loInt * loInt) * loZ); |
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212 | // u |
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213 | build.setElement(zbase + 2, base + 2 * i + 1, -(i + loInt * loInt) * hiZ); |
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214 | } |
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215 | // And finally two more rows to break symmetry |
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216 | build.setRowBounds(zbase + 3, -COIN_DBL_MAX, 0.0); |
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217 | build.setElement(zbase + 3, 1, 1.0); |
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218 | build.setElement(zbase + 3, 4, -1.0); |
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219 | build.setRowBounds(zbase + 4, -COIN_DBL_MAX, 0.0); |
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220 | build.setElement(zbase + 4, 2, 1.0); |
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221 | build.setElement(zbase + 4, 3, -1.0); |
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222 | solver1.loadFromCoinModel(build); |
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223 | // To make CbcBranchLink simpler assume that all variables with same i are consecutive |
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224 | |
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225 | double time1 = CoinCpuTime(); |
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226 | solver1.initialSolve(); |
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227 | solver1.writeMps("bad"); |
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228 | CbcModel model(solver1); |
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229 | model.solver()->setHintParam(OsiDoReducePrint, true, OsiHintTry); |
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230 | model.solver()->setHintParam(OsiDoScale, false, OsiHintTry); |
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231 | |
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232 | CbcObject **objects = new CbcObject *[3]; |
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233 | /* Format is number in sets, number in each link, first variable in matrix) |
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234 | and then a weight for each in set to say where to branch. |
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235 | In this case use NULL to say 0,1,2 ... |
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236 | Finally a set number as ID. |
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237 | */ |
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238 | objects[0] = new CbcLink(&model, ylen, 2, ybaseB, NULL, 0); |
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239 | objects[0]->setPriority(10); |
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240 | objects[1] = new CbcLink(&model, ylen, 2, ybaseB + 2 * ylen, NULL, 0); |
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241 | objects[1]->setPriority(20); |
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242 | objects[2] = new CbcLink(&model, yylen, 2, base, NULL, 0); |
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243 | objects[2]->setPriority(1); |
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244 | model.addObjects(3, objects); |
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245 | for (i = 0; i < 3; i++) |
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246 | delete objects[i]; |
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247 | delete[] objects; |
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248 | model.messageHandler()->setLogLevel(1); |
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249 | // Do complete search |
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250 | |
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251 | model.setDblParam(CbcModel::CbcMaximumSeconds, 1200.0); |
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252 | model.setDblParam(CbcModel::CbcCutoffIncrement, 1.0e-8); |
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253 | model.branchAndBound(); |
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254 | |
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255 | std::cout << "took " << CoinCpuTime() - time1 << " seconds, " |
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256 | << model.getNodeCount() << " nodes with objective " |
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257 | << model.getObjValue() |
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258 | << (!model.status() ? " Finished" : " Not finished") |
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259 | << std::endl; |
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260 | |
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261 | if (model.getMinimizationObjValue() < 1.0e50) { |
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262 | |
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263 | const double *solution = model.bestSolution(); |
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264 | int numberColumns = model.solver()->getNumCols(); |
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265 | double x1 = solution[1]; |
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266 | double x2 = solution[2]; |
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267 | double x3 = solution[3]; |
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268 | double x4 = solution[4]; |
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269 | printf("Optimal solution %g %g %g %g\n", x1, x2, x3, x4); |
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270 | for (int iColumn = 0; iColumn < numberColumns; iColumn++) { |
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271 | double value = solution[iColumn]; |
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272 | if (fabs(value) > 1.0e-7) |
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273 | std::cout << iColumn << " " << value << std::endl; |
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274 | } |
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275 | } |
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276 | return 0; |
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277 | } |
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