1 | /* $Id: AbcSimplexDual.hpp 1910 2013-01-27 02:00:13Z forrest $ */ |
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2 | // Copyright (C) 2002, International Business Machines |
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3 | // Corporation and others, Copyright (C) 2012, FasterCoin. 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 | Authors |
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7 | |
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8 | John Forrest |
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9 | |
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10 | */ |
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11 | #ifndef AbcSimplexDual_H |
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12 | #define AbcSimplexDual_H |
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13 | |
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14 | #include "AbcSimplex.hpp" |
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15 | #if 0 |
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16 | #undef ABC_PARALLEL |
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17 | #define ABC_PARALLEL 2 |
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18 | #undef cilk_for |
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19 | #undef cilk_spawn |
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20 | #undef cilk_sync |
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21 | #include <cilk/cilk.h> |
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22 | #endif |
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23 | typedef struct { |
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24 | double theta; |
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25 | double totalThru; |
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26 | double useThru; |
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27 | double bestEverPivot; |
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28 | double increaseInObjective; |
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29 | double tentativeTheta; |
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30 | double lastPivotValue; |
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31 | double thisPivotValue; |
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32 | double thruThis; |
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33 | double increaseInThis; |
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34 | int lastSequence; |
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35 | int sequence; |
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36 | int block; |
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37 | int numberSwapped; |
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38 | int numberRemaining; |
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39 | int numberLastSwapped; |
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40 | bool modifyCosts; |
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41 | } dualColumnResult; |
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42 | /** This solves LPs using the dual simplex method |
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43 | |
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44 | It inherits from AbcSimplex. It has no data of its own and |
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45 | is never created - only cast from a AbcSimplex object at algorithm time. |
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46 | |
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47 | */ |
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48 | |
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49 | class AbcSimplexDual : public AbcSimplex { |
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50 | |
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51 | public: |
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52 | |
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53 | /**@name Description of algorithm */ |
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54 | //@{ |
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55 | /** Dual algorithm |
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56 | |
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57 | Method |
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58 | |
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59 | It tries to be a single phase approach with a weight of 1.0 being |
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60 | given to getting optimal and a weight of updatedDualBound_ being |
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61 | given to getting dual feasible. In this version I have used the |
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62 | idea that this weight can be thought of as a fake bound. If the |
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63 | distance between the lower and upper bounds on a variable is less |
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64 | than the feasibility weight then we are always better off flipping |
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65 | to other bound to make dual feasible. If the distance is greater |
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66 | then we make up a fake bound updatedDualBound_ away from one bound. |
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67 | If we end up optimal or primal infeasible, we check to see if |
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68 | bounds okay. If so we have finished, if not we increase updatedDualBound_ |
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69 | and continue (after checking if unbounded). I am undecided about |
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70 | free variables - there is coding but I am not sure about it. At |
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71 | present I put them in basis anyway. |
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72 | |
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73 | The code is designed to take advantage of sparsity so arrays are |
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74 | seldom zeroed out from scratch or gone over in their entirety. |
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75 | The only exception is a full scan to find outgoing variable for |
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76 | Dantzig row choice. For steepest edge we keep an updated list |
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77 | of infeasibilities (actually squares). |
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78 | On easy problems we don't need full scan - just |
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79 | pick first reasonable. |
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80 | |
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81 | One problem is how to tackle degeneracy and accuracy. At present |
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82 | I am using the modification of costs which I put in OSL and some |
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83 | of what I think is the dual analog of Gill et al. |
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84 | I am still not sure of the exact details. |
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85 | |
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86 | The flow of dual is three while loops as follows: |
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87 | |
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88 | while (not finished) { |
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89 | |
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90 | while (not clean solution) { |
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91 | |
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92 | Factorize and/or clean up solution by flipping variables so |
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93 | dual feasible. If looks finished check fake dual bounds. |
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94 | Repeat until status is iterating (-1) or finished (0,1,2) |
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95 | |
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96 | } |
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97 | |
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98 | while (status==-1) { |
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99 | |
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100 | Iterate until no pivot in or out or time to re-factorize. |
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101 | |
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102 | Flow is: |
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103 | |
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104 | choose pivot row (outgoing variable). if none then |
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105 | we are primal feasible so looks as if done but we need to |
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106 | break and check bounds etc. |
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107 | |
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108 | Get pivot row in tableau |
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109 | |
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110 | Choose incoming column. If we don't find one then we look |
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111 | primal infeasible so break and check bounds etc. (Also the |
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112 | pivot tolerance is larger after any iterations so that may be |
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113 | reason) |
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114 | |
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115 | If we do find incoming column, we may have to adjust costs to |
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116 | keep going forwards (anti-degeneracy). Check pivot will be stable |
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117 | and if unstable throw away iteration and break to re-factorize. |
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118 | If minor error re-factorize after iteration. |
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119 | |
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120 | Update everything (this may involve flipping variables to stay |
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121 | dual feasible. |
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122 | |
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123 | } |
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124 | |
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125 | } |
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126 | |
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127 | TODO's (or maybe not) |
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128 | |
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129 | At present we never check we are going forwards. I overdid that in |
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130 | OSL so will try and make a last resort. |
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131 | |
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132 | Needs partial scan pivot out option. |
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133 | |
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134 | May need other anti-degeneracy measures, especially if we try and use |
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135 | loose tolerances as a way to solve in fewer iterations. |
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136 | |
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137 | I like idea of dynamic scaling. This gives opportunity to decouple |
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138 | different implications of scaling for accuracy, iteration count and |
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139 | feasibility tolerance. |
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140 | |
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141 | for use of exotic parameter startFinishoptions see Abcsimplex.hpp |
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142 | */ |
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143 | |
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144 | int dual(); |
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145 | /** For strong branching. On input lower and upper are new bounds |
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146 | while on output they are change in objective function values |
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147 | (>1.0e50 infeasible). |
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148 | Return code is 0 if nothing interesting, -1 if infeasible both |
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149 | ways and +1 if infeasible one way (check values to see which one(s)) |
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150 | Solutions are filled in as well - even down, odd up - also |
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151 | status and number of iterations |
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152 | */ |
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153 | int strongBranching(int numberVariables, const int * variables, |
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154 | double * newLower, double * newUpper, |
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155 | double ** outputSolution, |
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156 | int * outputStatus, int * outputIterations, |
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157 | bool stopOnFirstInfeasible = true, |
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158 | bool alwaysFinish = false, |
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159 | int startFinishOptions = 0); |
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160 | /// This does first part of StrongBranching |
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161 | AbcSimplexFactorization * setupForStrongBranching(char * arrays, int numberRows, |
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162 | int numberColumns, bool solveLp = false); |
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163 | /// This cleans up after strong branching |
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164 | void cleanupAfterStrongBranching(AbcSimplexFactorization * factorization); |
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165 | //@} |
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166 | |
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167 | /**@name Functions used in dual */ |
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168 | //@{ |
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169 | /** This has the flow between re-factorizations |
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170 | Broken out for clarity and will be used by strong branching |
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171 | |
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172 | Reasons to come out: |
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173 | -1 iterations etc |
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174 | -2 inaccuracy |
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175 | -3 slight inaccuracy (and done iterations) |
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176 | +0 looks optimal (might be unbounded - but we will investigate) |
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177 | +1 looks infeasible |
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178 | +3 max iterations |
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179 | |
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180 | If givenPi not NULL then in values pass (copy from ClpSimplexDual) |
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181 | */ |
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182 | int whileIteratingSerial(); |
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183 | #if ABC_PARALLEL==1 |
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184 | int whileIteratingThread(); |
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185 | #endif |
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186 | #if ABC_PARALLEL==2 |
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187 | int whileIteratingCilk(); |
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188 | #endif |
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189 | void whileIterating2(); |
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190 | int whileIteratingParallel(int numberIterations); |
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191 | int whileIterating3(); |
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192 | void updatePrimalSolution(); |
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193 | int noPivotRow(); |
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194 | int noPivotColumn(); |
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195 | void dualPivotColumn(); |
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196 | /// Create dual pricing vector |
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197 | void createDualPricingVectorSerial(); |
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198 | int getTableauColumnFlipAndStartReplaceSerial(); |
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199 | void getTableauColumnPart1Serial(); |
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200 | #if ABC_PARALLEL==1 |
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201 | /// Create dual pricing vector |
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202 | void createDualPricingVectorThread(); |
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203 | int getTableauColumnFlipAndStartReplaceThread(); |
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204 | void getTableauColumnPart1Thread(); |
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205 | #endif |
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206 | #if ABC_PARALLEL==2 |
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207 | /// Create dual pricing vector |
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208 | void createDualPricingVectorCilk(); |
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209 | int getTableauColumnFlipAndStartReplaceCilk(); |
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210 | void getTableauColumnPart1Cilk(); |
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211 | #endif |
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212 | void getTableauColumnPart2(); |
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213 | int checkReplace(); |
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214 | void replaceColumnPart3(); |
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215 | void checkReplacePart1(); |
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216 | void checkReplacePart1a(); |
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217 | void checkReplacePart1b(); |
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218 | /// The duals are updated |
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219 | void updateDualsInDual(); |
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220 | /** The duals are updated by the given arrays. |
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221 | This is in values pass - so no changes to primal is made |
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222 | */ |
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223 | //void updateDualsInValuesPass(CoinIndexedVector * array, |
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224 | // double theta); |
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225 | /** While dualColumn gets flips |
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226 | this does actual flipping. |
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227 | returns number flipped |
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228 | */ |
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229 | int flipBounds(); |
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230 | /** Undo a flip |
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231 | */ |
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232 | void flipBack(int number); |
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233 | /** |
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234 | Array has tableau row (row section) |
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235 | Puts candidates for rows in list |
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236 | Returns guess at upper theta (infinite if no pivot) and may set sequenceIn_ if free |
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237 | Can do all (if tableauRow created) |
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238 | */ |
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239 | void dualColumn1(bool doAll=false); |
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240 | /** |
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241 | Array has tableau row (row section) |
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242 | Just does slack part |
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243 | Returns guess at upper theta (infinite if no pivot) and may set sequenceIn_ if free |
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244 | */ |
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245 | double dualColumn1A(); |
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246 | /// Do all given tableau row |
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247 | double dualColumn1B(); |
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248 | /** |
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249 | Chooses incoming |
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250 | Puts flipped ones in list |
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251 | If necessary will modify costs |
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252 | */ |
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253 | void dualColumn2(); |
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254 | void dualColumn2Most(dualColumnResult & result); |
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255 | void dualColumn2First(dualColumnResult & result); |
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256 | /** |
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257 | Chooses part of incoming |
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258 | Puts flipped ones in list |
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259 | If necessary will modify costs |
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260 | */ |
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261 | void dualColumn2(dualColumnResult & result); |
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262 | /** |
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263 | This sees what is best thing to do in branch and bound cleanup |
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264 | If sequenceIn_ < 0 then can't do anything |
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265 | */ |
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266 | void checkPossibleCleanup(CoinIndexedVector * array); |
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267 | /** |
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268 | Chooses dual pivot row |
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269 | Would be faster with separate region to scan |
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270 | and will have this (with square of infeasibility) when steepest |
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271 | For easy problems we can just choose one of the first rows we look at |
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272 | */ |
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273 | void dualPivotRow(); |
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274 | /** Checks if any fake bounds active - if so returns number and modifies |
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275 | updatedDualBound_ and everything. |
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276 | Free variables will be left as free |
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277 | Returns number of bounds changed if >=0 |
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278 | Returns -1 if not initialize and no effect |
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279 | fills cost of change vector |
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280 | */ |
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281 | int changeBounds(int initialize, double & changeCost); |
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282 | /** As changeBounds but just changes new bounds for a single variable. |
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283 | Returns true if change */ |
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284 | bool changeBound( int iSequence); |
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285 | /// Restores bound to original bound |
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286 | void originalBound(int iSequence); |
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287 | /** Checks if tentative optimal actually means unbounded in dual |
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288 | Returns -3 if not, 2 if is unbounded */ |
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289 | int checkUnbounded(CoinIndexedVector & ray, double changeCost); |
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290 | /** Refactorizes if necessary |
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291 | Checks if finished. Updates status. |
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292 | lastCleaned refers to iteration at which some objective/feasibility |
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293 | cleaning too place. |
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294 | |
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295 | type - 0 initial so set up save arrays etc |
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296 | - 1 normal -if good update save |
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297 | - 2 restoring from saved |
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298 | */ |
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299 | void statusOfProblemInDual(int type); |
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300 | /** Fast iterations. Misses out a lot of initialization. |
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301 | Normally stops on maximum iterations, first re-factorization |
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302 | or tentative optimum. If looks interesting then continues as |
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303 | normal. Returns 0 if finished properly, 1 otherwise. |
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304 | */ |
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305 | /// Gets tableau column - does flips and checks what to do next |
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306 | /// Knows tableau column in 1, flips in 2 and gets an array for flips (as serial here) |
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307 | int whatNext(); |
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308 | /// see if cutoff reached |
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309 | bool checkCutoff(bool computeObjective); |
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310 | /// Does something about fake tolerances |
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311 | int bounceTolerances(int type); |
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312 | /// Perturbs problem |
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313 | void perturb(double factor); |
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314 | /// Perturbs problem B |
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315 | void perturbB(double factor,int type); |
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316 | /// Make non free variables dual feasible by moving to a bound |
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317 | int makeNonFreeVariablesDualFeasible(bool changeCosts=false); |
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318 | int fastDual(bool alwaysFinish = false); |
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319 | /** Checks number of variables at fake bounds. This is used by fastDual |
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320 | so can exit gracefully before end */ |
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321 | int numberAtFakeBound(); |
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322 | |
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323 | /** Pivot in a variable and choose an outgoing one. Assumes dual |
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324 | feasible - will not go through a reduced cost. Returns step length in theta |
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325 | Return codes as before but -1 means no acceptable pivot |
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326 | */ |
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327 | int pivotResultPart1(); |
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328 | /** Get next free , -1 if none */ |
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329 | int nextSuperBasic(); |
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330 | /// Startup part of dual |
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331 | void startupSolve(); |
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332 | /// Ending part of dual |
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333 | void finishSolve(); |
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334 | void gutsOfDual(); |
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335 | //int dual2(int ifValuesPass,int startFinishOptions=0); |
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336 | int resetFakeBounds(int type); |
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337 | |
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338 | //@} |
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339 | }; |
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340 | #if ABC_PARALLEL==1 |
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341 | void * abc_parallelManager(void * simplex); |
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342 | #endif |
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343 | #endif |
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