从线性编程解决方案中检索顶点路径

我一直在努力解决路由问题，比如 TSP （旅行商问题），但有一些曲折 . 我使用线性编程（ CPlex library ）和有向图（带有原点顶点）（ Coin-Or::Lemon library ）对问题进行了建模 .

线性程序找到解决方案，但我的问题在于如何检索路径 . 我可以迭代图形的每个顶点和边缘以找出线性程序正在使用的内容，所以我想我只是从Origin开始并使用所选边缘到达下一个节点，直到我再次到达Origin .

问题是CPlex路径可能会多次遍历任何顶点 . 所以我决定使用递归算法 . 但我无法弄明白 . 这是我尝试过的：

FindPath ( node N, path P)
    AddedAnyPath <- false
    for each edge E out of N that hasn't been used yet
        T is the target of E
        add T to P

        if findPath ( E, P )
            AddedAnyPath = true
    end for each

    if AddedAnyPath 
        if all edges were used
            return true
        else
            return false
        end if
    endif
end

该算法无法找到路径 . 如果你能指出我的任何方向，我将非常感激 .

编辑

提供的答案帮助我找到了答案 . 这是 C++ 中的代码：

bool findPath2 ( Store_Instance &T, DiNode &current, list <DiNode> &path, ListDigraph::ArcMap<bool> &usedArcs, IloCplex &cplex, ListDigraph::ArcMap<IloNumVar> &x) {
DiNode currentNode = current;
bool success = false;
int positionToInsert = 1;
while (true) {
    //Find an unvisited edge E whose value is 1.
    Arc unvisitedArc = INVALID;
    for(Digraph::OutArcIt a(T.g, currentNode); a != INVALID; ++a) {
        if(cplex.getValue(x[a]) >= 1-EPS && !usedArcs[a]) {
            unvisitedArc = a;
            break;
        }
    }
    if (unvisitedArc != INVALID) {
        //Mark edge as visited
        usedArcs[unvisitedArc] = true;
        //Get the target T of the edge
        DiNode target = T.g.target(unvisitedArc);
        //Add Edge E to the path
        list<DiNode>::iterator iterator = path.begin();
        advance(iterator, positionToInsert);
        path.insert(iterator, target);
        //Increase the iterator
        positionToInsert++;
        //If all the edges whose value is 1 are visited, stop
        bool usedAllEdges = true;
        for (ArcIt a(T.g); a != INVALID; ++a){
            if (cplex.getValue(x[a]) > 1-EPS && usedArcs[a] == false) {
                usedAllEdges = false;
                break;
            }
        }
        if (usedAllEdges) {
            success = true;
            break;
        }
        //Else, Set N to be T and repeat
        else currentNode = target;
    } else {
        //No arcs were found. Find a node from the path that has unvisited Arc
        positionToInsert = 0;
        DiNode target = INVALID;
        for (list<DiNode>::const_iterator iterator = path.begin(), end = path.end(); iterator != end; ++iterator) {
            DiNode v = *iterator;
            for(Digraph::OutArcIt a(T.g, v); a != INVALID; ++a) {
                if(cplex.getValue(x[a]) >= 1-EPS && !usedArcs[a]) {
                    target = v;
                    break;
                }
            }
            positionToInsert ++;
            if (target != INVALID) break;
        }

        if (target != INVALID) {
            //cout << "found lost node" << endl;
            currentNode = target;
        } else {
            success = false;
            break;
        }
    }
}
return success;
}