1 | /* |
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2 | * TSPSG: TSP Solver and Generator |
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3 | * Copyright (C) 2007-2016 Oleksii Serdiuk <contacts[at]oleksii[dot]name> |
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4 | * |
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5 | * $Id: $Format:%h %ai %an$ $ |
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6 | * $URL: http://tspsg.info/ $ |
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7 | * |
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8 | * This file is part of TSPSG. |
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9 | * |
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10 | * TSPSG is free software: you can redistribute it and/or modify |
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11 | * it under the terms of the GNU General Public License as published by |
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12 | * the Free Software Foundation, either version 2 of the License, or |
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13 | * (at your option) any later version. |
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14 | * |
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15 | * TSPSG is distributed in the hope that it will be useful, |
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16 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 | * GNU General Public License for more details. |
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19 | * |
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20 | * You should have received a copy of the GNU General Public License |
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21 | * along with TSPSG. If not, see <http://www.gnu.org/licenses/>. |
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22 | */ |
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23 | |
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24 | #include "tspsolver.h" |
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25 | |
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26 | #include <QCoreApplication> |
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27 | |
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28 | #ifdef DEBUG |
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29 | # include <QDebug> |
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30 | #endif |
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31 | |
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32 | //! \internal \brief A short for maximum double, used internally in the solution algorithm. |
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33 | #define MAX_DOUBLE std::numeric_limits<double>::max() |
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34 | |
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35 | namespace TSPSolver { |
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36 | |
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37 | /*! |
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38 | * \brief Returns CTSPSolver's version ID. |
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39 | * \return A string: <b>\$Id: $Format:%h %ai %an$ $</b>. |
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40 | */ |
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41 | QString CTSPSolver::getVersionId() |
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42 | { |
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43 | return QString("$Id: $Format:%h %ai %an$ $"); |
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44 | } |
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45 | |
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46 | /*! |
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47 | * \brief Constructs CTSPSolver object. |
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48 | * \param parent A parent object. |
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49 | */ |
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50 | CTSPSolver::CTSPSolver(QObject *parent) |
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51 | : QObject(parent), cc(true), nCities(0), total(0), root(NULL) {} |
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52 | |
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53 | /*! |
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54 | * \brief Cleans up the object and frees up memory used by the solution tree. |
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55 | * \param processEvents If set to \c true then \link QCoreApplication::processEvents() QCoreApplication::processEvents(QEventLoop::ExcludeUserInputEvents)\endlink will be called from time to time while cleaning up. |
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56 | * \warning After call to this function a solution tree returned by the solve() function is no longer valid. |
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57 | * \note It is not required to call this function manually. This function is always called by solve() at the beginning of the solution process. |
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58 | * |
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59 | * \sa solve(), setCleanupOnCancel() |
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60 | */ |
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61 | void CTSPSolver::cleanup(bool processEvents) |
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62 | { |
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63 | route.clear(); |
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64 | mayNotBeOptimal = false; |
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65 | if (root != NULL) |
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66 | deleteTree(root, processEvents); |
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67 | } |
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68 | |
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69 | /*! |
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70 | * \brief Returns the sorted optimal path, starting from City 1. |
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71 | * \param city A string that represents city elements in the path. |
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72 | * \param separator A string that represents separators between cities in the path. |
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73 | * \return A string, containing sorted optimal path. |
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74 | * |
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75 | * The resulting path will be in the form \a city+\a separator+\a city+...+\a separator+\a city. |
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76 | * \c \%1 in \a city will be replaced by the city number. |
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77 | */ |
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78 | QString CTSPSolver::getSortedPath(const QString &city, const QString &separator) const |
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79 | { |
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80 | if (!root || route.isEmpty() || (route.size() != nCities)) |
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81 | return QString(); |
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82 | |
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83 | int i = 0; // We start from City 1 |
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84 | QStringList path; |
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85 | path << city.arg(1); |
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86 | while ((i = route[i]) != 0) { |
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87 | path << city.arg(i + 1); |
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88 | } |
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89 | // And finish in City 1, too |
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90 | path << city.arg(1); |
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91 | |
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92 | return path.join(separator); |
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93 | } |
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94 | |
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95 | /*! |
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96 | * \brief Returns a total number of steps in the current solution. |
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97 | * \return A total number of steps or \c 0 if no solution. |
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98 | * \note This is not always the same as the number of cities. |
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99 | */ |
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100 | int CTSPSolver::getTotalSteps() const |
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101 | { |
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102 | return total; |
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103 | } |
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104 | |
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105 | /*! |
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106 | * \brief Indicates whether or not the solution is definitely optimal. |
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107 | * \return \c true if the solution is definitely optimal, otherwise \c false. |
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108 | * |
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109 | * The solution may need some further iterations to determine whether or not it is optimal. |
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110 | * In such cases this function returns \c false. |
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111 | */ |
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112 | bool CTSPSolver::isOptimal() const |
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113 | { |
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114 | return !mayNotBeOptimal; |
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115 | } |
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116 | |
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117 | /*! |
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118 | * \brief Sets whether or not to call cleanup() on solution cancel. |
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119 | * \param enable Set to \c true to enable clenup (default). |
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120 | * |
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121 | * This may be useful if you want to make cleanup yourself or provide indication of clenup to user. |
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122 | * |
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123 | * \note Please, note that cleanup() is explicitly called at the start of each solution. |
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124 | * Disabling cleanup and forgetting to do it manually may considerably increase the solution time for large tasks (with more than 15 cities). |
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125 | * \sa cleanup() |
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126 | */ |
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127 | void CTSPSolver::setCleanupOnCancel(bool enable) |
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128 | { |
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129 | cc = enable; |
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130 | } |
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131 | |
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132 | /*! |
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133 | * \brief Solves the given task. |
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134 | * \param numCities Number of cities in the task. |
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135 | * \param task The matrix of city-to-city travel costs. |
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136 | * \return Pointer to the root of the solution tree. |
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137 | * |
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138 | * \todo TODO: Comment the algorithm. |
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139 | */ |
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140 | SStep *CTSPSolver::solve(int numCities, const TMatrix &task) |
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141 | { |
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142 | if (numCities < 3) |
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143 | return NULL; |
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144 | |
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145 | QMutexLocker locker(&mutex); |
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146 | cleanup(); |
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147 | canceled = false; |
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148 | locker.unlock(); |
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149 | |
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150 | nCities = numCities; |
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151 | |
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152 | SStep *step = new SStep(); |
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153 | step->matrix = task; |
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154 | // We need to distinguish the values forbidden by the user |
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155 | // from the values forbidden by the algorithm. |
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156 | // So we replace user's infinities by the maximum available double value. |
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157 | normalize(step->matrix); |
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158 | #ifdef DEBUG |
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159 | qDebug() << step->matrix; |
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160 | #endif // DEBUG |
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161 | step->price = align(step->matrix); |
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162 | root = step; |
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163 | |
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164 | SStep *left, *right; |
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165 | int nRow, nCol; |
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166 | bool firstStep = true; |
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167 | double check = INFINITY; |
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168 | total = 0; |
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169 | while (route.size() < nCities) { |
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170 | step->alts = findCandidate(step->matrix,nRow,nCol); |
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171 | |
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172 | while (hasSubCycles(nRow,nCol)) { |
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173 | #ifdef DEBUG |
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174 | qDebug() << "Forbidden: (" << nRow << ";" << nCol << ")"; |
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175 | #endif // DEBUG |
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176 | step->matrix[nRow][nCol] = INFINITY; |
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177 | step->price += align(step->matrix); |
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178 | step->alts = findCandidate(step->matrix,nRow,nCol); |
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179 | } |
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180 | |
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181 | #ifdef DEBUG |
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182 | qDebug() /*<< step->matrix*/ << "Selected: (" << nRow << ";" << nCol << ")"; |
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183 | qDebug() << "Alternate:" << step->alts; |
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184 | qDebug() << "Step price:" << step->price << endl; |
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185 | #endif // DEBUG |
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186 | |
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187 | locker.relock(); |
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188 | if ((nRow == -1) || (nCol == -1) || canceled) { |
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189 | if (canceled && cc) |
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190 | cleanup(); |
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191 | return NULL; |
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192 | } |
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193 | locker.unlock(); |
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194 | |
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195 | // Route with (nRow,nCol) path |
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196 | right = new SStep(); |
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197 | right->pNode = step; |
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198 | right->matrix = step->matrix; |
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199 | for (int k = 0; k < nCities; k++) { |
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200 | if (k != nCol) |
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201 | right->matrix[nRow][k] = INFINITY; |
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202 | if (k != nRow) |
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203 | right->matrix[k][nCol] = INFINITY; |
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204 | } |
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205 | right->price = step->price + align(right->matrix); |
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206 | // Forbid the selected route to exclude its reuse in next steps. |
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207 | right->matrix[nCol][nRow] = INFINITY; |
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208 | right->matrix[nRow][nCol] = INFINITY; |
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209 | |
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210 | // Route without (nRow,nCol) path |
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211 | left = new SStep(); |
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212 | left->pNode = step; |
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213 | left->matrix = step->matrix; |
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214 | left->matrix[nRow][nCol] = INFINITY; |
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215 | left->price = step->price + align(left->matrix); |
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216 | |
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217 | step->candidate.nRow = nRow; |
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218 | step->candidate.nCol = nCol; |
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219 | step->plNode = left; |
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220 | step->prNode = right; |
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221 | |
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222 | // This matrix is not used anymore. Restoring infinities back. |
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223 | denormalize(step->matrix); |
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224 | |
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225 | if (right->price <= left->price) { |
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226 | // Route with (nRow,nCol) path is cheaper |
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227 | step->next = SStep::RightBranch; |
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228 | step = right; |
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229 | route[nRow] = nCol; |
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230 | emit routePartFound(route.size()); |
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231 | if (firstStep) { |
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232 | check = left->price; |
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233 | firstStep = false; |
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234 | } |
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235 | } else { |
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236 | // Route without (nRow,nCol) path is cheaper |
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237 | step->next = SStep::LeftBranch; |
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238 | step = left; |
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239 | QCoreApplication::processEvents(); |
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240 | if (firstStep) { |
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241 | check = right->price; |
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242 | firstStep = false; |
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243 | } |
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244 | } |
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245 | total++; |
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246 | } |
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247 | |
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248 | mayNotBeOptimal = (check < step->price); |
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249 | |
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250 | return root; |
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251 | } |
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252 | |
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253 | /*! |
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254 | * \brief Indicates whether or not the solution process was canceled. |
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255 | * \return \c true if the solution process was canceled, otherwise \c false. |
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256 | */ |
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257 | bool CTSPSolver::wasCanceled() const |
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258 | { |
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259 | QMutexLocker locker(&mutex); |
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260 | return canceled; |
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261 | } |
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262 | |
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263 | /*! |
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264 | * \brief Cancels the solution process. |
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265 | */ |
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266 | void CTSPSolver::cancel() |
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267 | { |
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268 | QMutexLocker locker(&mutex); |
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269 | canceled = true; |
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270 | } |
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271 | |
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272 | CTSPSolver::~CTSPSolver() |
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273 | { |
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274 | if (root != NULL) |
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275 | deleteTree(root); |
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276 | } |
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277 | |
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278 | /* Privates **********************************************************/ |
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279 | |
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280 | double CTSPSolver::align(TMatrix &matrix) |
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281 | { |
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282 | double r = 0; |
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283 | double min; |
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284 | for (int k = 0; k < nCities; k++) { |
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285 | min = findMinInRow(k,matrix); |
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286 | if (min > 0) { |
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287 | r += min; |
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288 | if (min < MAX_DOUBLE) |
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289 | subRow(matrix,k,min); |
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290 | } |
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291 | } |
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292 | for (int k = 0; k < nCities; k++) { |
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293 | min = findMinInCol(k,matrix); |
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294 | if (min > 0) { |
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295 | r += min; |
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296 | if (min < MAX_DOUBLE) |
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297 | subCol(matrix,k,min); |
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298 | } |
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299 | } |
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300 | return (r != MAX_DOUBLE) ? r : INFINITY; |
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301 | } |
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302 | |
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303 | void CTSPSolver::deleteTree(SStep *&root, bool processEvents) |
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304 | { |
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305 | if (root == NULL) |
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306 | return; |
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307 | SStep *step = root; |
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308 | SStep *parent; |
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309 | forever { |
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310 | if (processEvents) |
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311 | QCoreApplication::processEvents(QEventLoop::ExcludeUserInputEvents); |
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312 | if (step->plNode != NULL) { |
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313 | // We have left child node - going inside it |
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314 | step = step->plNode; |
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315 | step->pNode->plNode = NULL; |
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316 | continue; |
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317 | } else if (step->prNode != NULL) { |
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318 | // We have right child node - going inside it |
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319 | step = step->prNode; |
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320 | step->pNode->prNode = NULL; |
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321 | continue; |
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322 | } else { |
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323 | // We have no child nodes. Deleting the current one. |
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324 | parent = step->pNode; |
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325 | delete step; |
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326 | if (parent != NULL) { |
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327 | // Going back to the parent node. |
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328 | step = parent; |
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329 | } else { |
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330 | // We came back to the root node. Finishing. |
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331 | root = NULL; |
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332 | break; |
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333 | } |
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334 | } |
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335 | } |
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336 | } |
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337 | |
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338 | void CTSPSolver::denormalize(TMatrix &matrix) const |
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339 | { |
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340 | for (int r = 0; r < nCities; r++) |
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341 | for (int c = 0; c < nCities; c++) |
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342 | if ((r != c) && (matrix.at(r).at(c) == MAX_DOUBLE)) |
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343 | matrix[r][c] = INFINITY; |
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344 | } |
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345 | |
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346 | QList<SStep::SCandidate> CTSPSolver::findCandidate(const TMatrix &matrix, int &nRow, int &nCol) const |
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347 | { |
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348 | nRow = -1; |
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349 | nCol = -1; |
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350 | QList<SStep::SCandidate> alts; |
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351 | SStep::SCandidate cand; |
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352 | double h = -1; |
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353 | double sum; |
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354 | for (int r = 0; r < nCities; r++) |
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355 | for (int c = 0; c < nCities; c++) |
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356 | if (matrix.at(r).at(c) == 0) { |
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357 | sum = findMinInRow(r,matrix,c) + findMinInCol(c,matrix,r); |
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358 | if (sum > h) { |
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359 | h = sum; |
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360 | nRow = r; |
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361 | nCol = c; |
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362 | alts.clear(); |
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363 | } else if ((sum == h) && !hasSubCycles(r,c)) { |
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364 | cand.nRow = r; |
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365 | cand.nCol = c; |
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366 | alts.append(cand); |
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367 | } |
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368 | } |
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369 | return alts; |
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370 | } |
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371 | |
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372 | double CTSPSolver::findMinInCol(int nCol, const TMatrix &matrix, int exr) const |
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373 | { |
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374 | double min = INFINITY; |
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375 | for (int k = 0; k < nCities; k++) |
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376 | if ((k != exr) && (min > matrix.at(k).at(nCol))) |
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377 | min = matrix.at(k).at(nCol); |
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378 | return (min == INFINITY) ? 0 : min; |
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379 | } |
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380 | |
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381 | double CTSPSolver::findMinInRow(int nRow, const TMatrix &matrix, int exc) const |
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382 | { |
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383 | double min = INFINITY; |
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384 | for (int k = 0; k < nCities; k++) { |
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385 | if (((k != exc)) && (min > matrix.at(nRow).at(k))) |
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386 | min = matrix.at(nRow).at(k); |
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387 | } |
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388 | return (min == INFINITY) ? 0 : min; |
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389 | } |
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390 | |
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391 | bool CTSPSolver::hasSubCycles(int nRow, int nCol) const |
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392 | { |
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393 | if ((nRow < 0) || (nCol < 0) || route.isEmpty() || !(route.size() < nCities - 1) || !route.contains(nCol)) |
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394 | return false; |
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395 | int i = nCol; |
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396 | forever { |
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397 | if ((i = route.value(i)) == nRow) |
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398 | return true; |
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399 | if (!route.contains(i)) |
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400 | return false; |
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401 | } |
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402 | return false; |
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403 | } |
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404 | |
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405 | void CTSPSolver::normalize(TMatrix &matrix) const |
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406 | { |
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407 | for (int r = 0; r < nCities; r++) |
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408 | for (int c = 0; c < nCities; c++) |
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409 | if ((r != c) && (matrix.at(r).at(c) == INFINITY)) |
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410 | matrix[r][c] = MAX_DOUBLE; |
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411 | } |
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412 | |
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413 | void CTSPSolver::subCol(TMatrix &matrix, int nCol, double val) |
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414 | { |
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415 | for (int k = 0; k < nCities; k++) |
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416 | if (k != nCol) |
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417 | matrix[k][nCol] -= val; |
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418 | } |
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419 | |
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420 | void CTSPSolver::subRow(TMatrix &matrix, int nRow, double val) |
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421 | { |
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422 | for (int k = 0; k < nCities; k++) |
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423 | if (k != nRow) |
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424 | matrix[nRow][k] -= val; |
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425 | } |
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426 | |
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427 | } |
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428 | |
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429 | #ifdef DEBUG |
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430 | QDebug operator<<(QDebug dbg, const TSPSolver::TMatrix &matrix) |
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431 | { |
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432 | for (int r = 0; r < matrix.count(); r++) { |
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433 | for (int c = 0; c < matrix.at(r).count(); c++) |
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434 | dbg.space() << QString::number(matrix.at(r).at(c)).leftJustified(5); |
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435 | dbg << endl; |
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436 | } |
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437 | return dbg; |
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438 | } |
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439 | |
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440 | QDebug operator<<(QDebug dbg, const TSPSolver::SStep::SCandidate &cand) |
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441 | { |
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442 | dbg.nospace() << "(" << cand.nRow << ";" << cand.nCol << ")"; |
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443 | return dbg; |
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444 | } |
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445 | #endif // DEBUG |
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