遗传算法解TSP问题的C++源码

《智能优化算法》课的一次作业。报着学点东西的态度，没有从网上下载（网上好像都是那个VC6的MFC程序），纯C++，从零写起，顺便学习了一下如何用STL。

 

#include <iostream> #include <iomanip> #include <vector> #include <iterator> #include <algorithm> #include <fstream> #include <math.h> #include <time.h> const int NCITY = 51; struct CityCoor { int sn, x, y; }; struct Sequence { double distance; std::vector<int> vSeqnc; }; std::vector<CityCoor> vCityCoors(NCITY); std::vector<std::vector<double>> vDistanceMatrix(NCITY); double computDistance( const std::vector<int>& v ); namespace ga { const int POPSIZE = NCITY*5; const int GENERATION = 5000; //在变化显著的情况下为5000代 const int SIMILAR_TIMES = 200; const double DIFF = 1e-15; //量化变化不显著 const double P_CROSSOVER = 0.3; //交叉概率 const double P_MUTATION = 0.1; //变异概率 int nGen = 0; std::vector<int> vCitySequence(NCITY); std::vector<Sequence> vChromsome(POPSIZE+1); //第一个染色体只记录上一代遗传的最优解而不参与遗传运算 std::vector<double> vProbability(POPSIZE+1); namespace itor { inline void printSequence(int sn) {std::cout << sn << " ";} inline void printCityCoors(const CityCoor& cc) {std::cout << cc.sn << " " << cc.x << " " << cc.y << "/n";} inline void printChromsome(const Sequence &s) {std::cout << s.distance << " ";} inline void itorDistance( Sequence& se ) {se.distance = computDistance(se.vSeqnc);} inline void initChromsome(Sequence& v); inline void testPrintSeqLen(const Sequence &s) {std::cout << s.vSeqnc.size() << " ";} }//itor:: inline bool less_second(const Sequence &a, const Sequence &b) {return a.distance < b.distance;} }//ga:: ////////////////////////////////////////////////////////////////////////// //迭代器 typedef std::vector<CityCoor>::iterator vitorCityCoor; typedef std::vector<int>::iterator vitorSn; typedef std::vector<int>::size_type vintSize; typedef std::vector<CityCoor>::const_iterator cvitorCityCoor; typedef std::vector<int>::const_iterator cvitorSn; typedef std::vector<Sequence>::const_iterator cvitorChromsome; ////////////////////////////////////////////////////////////////////////// std::vector<Sequence> vTemp(ga::POPSIZE+1); ////////////////////////////////////////////////////////////////////////// //全局函数，具体作用可见Definition bool readTSP_Data(); inline double myrand(double, double); void crossover(); void mutation(); void selection(); void calcDistanceMatrix(); bool isValid(std::vector<int> v) { sort(v.begin(), v.end()); for (std::vector<int>::size_type i=0; i<v.size()-1; ++i) if (v[i] == v[i+1]) { std::cout << "序列出错!!!!!!!!!/n"; std::cout << "v[" << i << "]" << "=v[" << i+1 << "]/n"; for_each(v.begin(), v.end(), ga::itor::printSequence); system("pause"); return false; } std::cout << "序列正确/n"; return true; } int main() { ////////////////////////////////////////////////////////////////////////// std::cout<<"#读入数据"; if (!readTSP_Data()) { std::cerr << "---读入城市坐标出错!"; exit(1); } std::cout<<" OK/n"; clock_t startTime = clock(); std::cout<<"#计算城市距离矩阵"; calcDistanceMatrix(); std::cout<<" OK/n"; //求适应函数 ga::vProbability[0] = 0.05; double a = 0.05; for (int i=1; i<=ga::POPSIZE; ++i) { a *= 0.95; ga::vProbability[i] = ga::vProbability[i-1] + a; } ////////////////////////////////////////////////////////////////////////// std::cout<<"#初始化" << ga::POPSIZE << "个染色体："; for_each(ga::vChromsome.begin()+1, ga::vChromsome.end(), ga::itor::initChromsome); std::cout<<" OK/n"; ga::vChromsome[0] = ga::vChromsome[1]; //先淘汰一次，以优化初值 sort(ga::vChromsome.begin()+1, ga::vChromsome.end(), ga::less_second); ////////////////////////////////////////////////////////////////////////// std::cout<<"/n#开始遗传算法，结束条件为连续" << ga::SIMILAR_TIMES <<"代变化小于" << ga::DIFF <<""; int generWidth = static_cast<int>(ceil(log10(static_cast<double>(ga::GENERATION)))); for (int i=1; i<=ga::GENERATION; ++i) { selection(); double prevDistance = ga::vChromsome[0].distance; srand(static_cast<unsigned>(time(NULL))); crossover(); mutation(); //对每个染色体求距离 for_each(ga::vChromsome.begin()+1, ga::vChromsome.end(), ga::itor::itorDistance); //进化，好解(小)在前，上一代的最优解也带入 sort(ga::vChromsome.begin(), ga::vChromsome.end(), ga::less_second); std::cout << "/n 第" ; std::cout << std::setfill(' ') << std::setw(generWidth) << i; std::cout << "代 最短距离="<< ga::vChromsome[0].distance; if (prevDistance - ga::vChromsome[0].distance < ga::DIFF) ++ga::nGen; else ga::nGen = 0; if (ga::SIMILAR_TIMES < ga::nGen) break; } std::cout<<"/n/n#检验结果->"; isValid(ga::vChromsome[0].vSeqnc); for_each(ga::vChromsome[0].vSeqnc.begin(), ga::vChromsome[0].vSeqnc.end(), ga::itor::printSequence); std::cout<<"/n"; std::cout<<"/n共使用时间: " << static_cast<double>(clock()-startTime) / CLOCKS_PER_SEC<< "秒/n"; system("pause"); return 0; } bool readTSP_Data() { try { std::ifstream fin("TSP.data"); for (vitorCityCoor i=vCityCoors.begin(); i != vCityCoors.end(); ++i) { fin >> (*i).sn >> (*i).x >> (*i).y; } fin.close(); } catch (...) { return false; } return true; } //贪婪算法Right int GreedyRight( std::vector<int> &cityrouter, int nCity ) { bool bFindCity = false; vitorSn iter_city; for(iter_city=cityrouter.begin();iter_city!=cityrouter.end(); ++iter_city) if( *iter_city == nCity ) { bFindCity = true; break; } if( bFindCity ) { ++iter_city; if( iter_city == cityrouter.end() ) iter_city = cityrouter.begin(); return *iter_city; } else return -1; } //贪婪算法Left int GreedyLeft( std::vector<int> &cityrouter, int nCity ) { bool bFindCity = false; vitorSn iter_city; for( iter_city=cityrouter.begin();iter_city!=cityrouter.end(); ++iter_city ) if( *iter_city == nCity ) { bFindCity = true; break; } if( bFindCity ) { if( iter_city == cityrouter.begin() ) return cityrouter.back(); else { --iter_city; return *iter_city; } } else return -1; } void GreedyErase( std::vector<int> &cityrouter, int ndelcity ) { bool bFindCity = false; vitorSn iter_city; for( iter_city=cityrouter.begin();iter_city!=cityrouter.end(); ++iter_city ) if( *iter_city == ndelcity ) { bFindCity = true; break; } if( bFindCity ) cityrouter.erase( iter_city ); } //************************************ // Method: doCrossover // FullName: doCrossover // Access: public // Returns: void // Parameter: int nFatherA // Parameter: int nFatherB // Qualifier: 贪心交叉方式（Greedy Crossover）， // 具体算法可参见 谢胜利,等.求解TSP问题的一种改进的遗传算法[J].计算机工程与应用,2002(8):58～245。见下载目录 //************************************ void doCrossover(int nFatherA, int nFatherB) { int randomcity, nowopcity, nextopcity, rightA, rightB, leftA, leftB; std::vector<int> SonA, SonB; randomcity = static_cast<int>(myrand(1, NCITY)); nowopcity = randomcity; SonA.push_back( nowopcity ); std::vector<int> FatherA = ga::vChromsome[nFatherA].vSeqnc; std::vector<int> FatherB = ga::vChromsome[nFatherB].vSeqnc; while( FatherA.size() > 1 && FatherB.size() > 1 ) { rightA = GreedyRight( FatherA, nowopcity ); rightB = GreedyRight( FatherB, nowopcity ); if( vDistanceMatrix[nowopcity-1][rightA-1] < vDistanceMatrix[nowopcity-1][rightB-1] ) { SonA.push_back( rightA ); nextopcity = rightA; } else { SonA.push_back( rightB ); nextopcity = rightB; } GreedyErase( FatherA, nowopcity ); GreedyErase( FatherB, nowopcity ); nowopcity = nextopcity; } nowopcity = randomcity; SonB.push_back( nowopcity ); FatherA = ga::vChromsome[nFatherA].vSeqnc; FatherB = ga::vChromsome[nFatherB].vSeqnc; while( FatherA.size() > 1 && FatherB.size() > 1 ) { leftA = GreedyLeft( FatherA, nowopcity ); leftB = GreedyLeft( FatherB, nowopcity ); if( vDistanceMatrix[nowopcity-1][leftA-1] < vDistanceMatrix[nowopcity-1][leftB-1]) { SonB.push_back( leftA ); nextopcity = leftA; } else { SonB.push_back( leftB ); nextopcity = leftB; } GreedyErase( FatherA, nowopcity ); GreedyErase( FatherB, nowopcity ); nowopcity = nextopcity; } swap(ga::vChromsome[nFatherA].vSeqnc, SonA); swap(ga::vChromsome[nFatherB].vSeqnc, SonB); } //************************************ // Method: crossover // FullName: crossover // Access: public // Returns: void // Qualifier: 交配 //************************************ void crossover() { std::vector<int> vecCrossoverIndexs; double random; for( int i=1;i<=ga::POPSIZE;i++ ) { random = static_cast<double>(myrand(0,1)); if( random < ga::P_CROSSOVER ) vecCrossoverIndexs.push_back( i ); } size_t CrossoverNumber = vecCrossoverIndexs.size(); if( CrossoverNumber%2 != 0 ) vecCrossoverIndexs.pop_back(); CrossoverNumber = vecCrossoverIndexs.size(); for(size_t i=0; i<CrossoverNumber; i+=2) { int nFatherA = vecCrossoverIndexs[i]; int nFatherB = vecCrossoverIndexs[i+1]; doCrossover( nFatherA, nFatherB); } } void ga::itor::initChromsome(Sequence& v) { v.vSeqnc.resize(NCITY); for (int i=1; i <= NCITY; ++i) v.vSeqnc[i-1] = i; std::random_shuffle(v.vSeqnc.begin(), v.vSeqnc.end()); v.distance = computDistance(v.vSeqnc); std::cout << "."; } //************************************ // Method: myrand // FullName: myrand // Access: public // Returns: double // Qualifier: // Parameter: double a // Parameter: double b // Uniform Distribution // return a random num in area [a,b] //************************************ double myrand(double a, double b) { double y; if(a>b) { printf("/nThe first parameter should be less than the second!"); exit(1); } ////////////////////////////////////////////////////////////////////////// //rand() can reture a number in [0, RAND_MAX] y = static_cast<double>(rand())/RAND_MAX; return (a+(b-a)*y); } //************************************ // Method: mutation // FullName: mutation // Access: public // Returns: void // Qualifier: 变异，对两个随机位置之间的城市随机重排 //************************************ void mutation() { vitorSn it; for (int i=1; i <= ga::POPSIZE; ++i) if (ga::P_MUTATION > myrand(0,1)) { int left = static_cast<int>(myrand(0, NCITY/2)); int right = static_cast<int>(myrand(NCITY/2, NCITY)); it = ga::vChromsome[i].vSeqnc.begin(); std::random_shuffle(it+left, it+right); } } double computDistance( const std::vector<int>& v ) { double tmp = 0.0; for (int it=0; it<NCITY-1; ++it) tmp += vDistanceMatrix[v[it]-1][v[it+1]-1]; tmp += vDistanceMatrix[v[NCITY-1]-1][v[0]-1]; return tmp; } //************************************ // Method: selection // FullName: selection // Access: public // Returns: void // Qualifier: 选择，轮盘赌，让前面的解（好解）以较大概率被选中 //************************************ void selection() { double r; int label; vTemp[0] = ga::vChromsome[0]; //第一个仅仅作记录用 for (int i=1; i <= ga::POPSIZE; ++i) { r = myrand(0, ga::vProbability[ga::POPSIZE]); label = 0; for (int j=0; j <= ga::POPSIZE; ++j) { if (r <= ga::vProbability[j]) { label = j; break; } } vTemp[i] = ga::vChromsome[label]; } swap(ga::vChromsome, vTemp); } //************************************ // Method: calcDistanceMatrix // FullName: calcDistanceMatrix // Access: public // Returns: void // Qualifier: 预先计算出城市间的距离矩阵供后面查询，典型的空间换时间 //************************************ void calcDistanceMatrix() { double dltX, dltY; std::vector<std::vector<double>>::iterator it = vDistanceMatrix.begin(); for(; it != vDistanceMatrix.end(); ++it) (*it).resize(NCITY); for (int i=0; i<NCITY; ++i) for (int j=i; j<NCITY; ++j) if (i == j) vDistanceMatrix[i][j] = 0.0; else { dltX = vCityCoors[i].x - vCityCoors[j].x; dltY = vCityCoors[i].y - vCityCoors[j].y; vDistanceMatrix[i][j] = sqrt(static_cast<double>(dltX*dltX + dltY*dltY)); vDistanceMatrix[j][i] = vDistanceMatrix[i][j]; } }

运行结果：

#读入数据 OK
#计算城市距离矩阵 OK
#初始化255个染色体：............................................................................................................................................
................................................................................................................... OK

#开始遗传算法，结束条件为连续200代变化小于1e-015
    第   1代       最短距离=971.792
    第   2代       最短距离=892.135
    第   3代       最短距离=713.293
    第   4代       最短距离=670.46
    第   5代       最短距离=621.353
    第   6代       最短距离=597.599
    第   7代       最短距离=553.647
    第   8代       最短距离=523.755
    第   9代       最短距离=519.167
    第  10代       最短距离=494.994
    第  11代       最短距离=484.889
    第  12代       最短距离=477.425
    第  13代       最短距离=468.237
    第  14代       最短距离=449.349
    第  15代       最短距离=449.349
    第  16代       最短距离=446.246
    第  17代       最短距离=446.246
    第  18代       最短距离=446.246
    第  19代       最短距离=446.246
    第  20代       最短距离=445.269
    第  21代       最短距离=441.656
    第  22代       最短距离=440.679
    第  23代       最短距离=436.875
    （第  24代 到 第 225代 最短距离的小数点后三位相等，这里不一一列出）
    第 226代       最短距离=436.875

#检验结果->序列正确
1 22 2 21 29 20 35 36 3 28 31 26 8 48 6 23 7 43 24 14 25 13 41 40 19 42 44 15 45
 33 39 10 30 34 50 16 11 38 9 49 5 37 17 4 18 47 12 46 51 27 32

共使用时间: 1.931秒
Press any key to continue . . .

使用了谢胜利的贪心交叉方式（Greedy Crossover），极大地提高了收敛速度。