c++旅行商问题gurobi
时间: 2025-01-22 17:05:30 浏览: 60
### 使用 C++ 和 Gurobi 实现 TSP 的求解
#### 安装与配置环境
为了使用 C++ 调用 Gurobi 来解决旅行商问题 (TSP),首先需要安装并配置好开发环境。这通常涉及下载和设置 Gurobi 库及其头文件,确保编译器能够找到这些资源。
#### 创建模型
创建一个新的优化模型实例来表示整个问题:
```cpp
GRBEnv env = GRBEnv();
GRBModel model = GRBModel(env);
```
#### 添加变量
定义决策变量用于描述城市之间的访问情况。对于每一对不同的城市 \(i\) 和 \(j\) ,如果从城市 \(i\) 到达城市 \(j\) 就设为1;否则为0:
```cpp
int n = /* number of cities */;
vector<vector<GRBVar>> vars(n, vector<GRBVar>(n));
for(int i=0; i<n; ++i){
for(int j=i+1; j<n; ++j){
string name = "e" + to_string(i) + "," + to_string(j);
vars[i][j] = model.addVar(0.0, 1.0, 0.0, GRB_BINARY, name);
vars[j][i] = vars[i][j]; // Symmetric matrix
}
}
model.update(); // Update the model before adding constraints.
```
#### 设置目标函数
计算总距离作为成本,并将其最小化为目标:
```cpp
double dist[][] = {/* distance between each pair of nodes */};
GRBLinExpr obj = 0;
for(int i=0; i<n; ++i){
for(int j=0; j<i; ++j){
obj += dist[i][j]*vars[i][j];
}
}
model.setObjective(obj, GRB_MINIMIZE);
```
#### 增加约束条件
确保每个节点恰好被访问一次,既不多也不少:
```cpp
// Each city must be entered exactly once
for(int k=0; k<n; ++k){
GRBLinExpr sum_incoming_edges = 0;
for(int i=0; i<n; ++i){
if(k != i)
sum_incoming_edges += vars[k][i];
}
model.addConstr(sum_incoming_edges == 1);
}
// Each city must leave exactly once
for(int k=0; k<n; ++k){
GRBLinExpr sum_outgoing_edges = 0;
for(int j=0; j<n; ++j){
if(k != j)
sum_outgoing_edges += vars[k][j];
}
model.addConstr(sum_outgoing_edges == 1);
}
```
#### 处理子环路消除(subtour elimination)
通过回调机制动态添加割平面(cutting plane)以防止形成非最优的小循环[subtour]:
```cpp
void subtourelim(GRBModel *model, void *cbdata,
int where, void *usrdata) {
if(where == GRB_CB_MIPSOL || where == GRB_CB_MULTIOBJ_SOL){
const double* sol = nullptr;
model->getCallbackSolution(&sol);
std::set<int> unvisited_cities;
for(size_t c=0;c<n;++c){unvisited_cities.insert((int)c);}
while(!unvisited_cities.empty()){
int this_city=*unvisited_cities.begin(), next_city=-1;
do{
unvisited_cities.erase(this_city);
for(auto& other : unvisited_cities){
if(sol[this_city*n + other]>0.5){
next_city=other;break;
}
}
if(next_city>=0)this_city=next_city;
else break;
}while(true);
if(!unvisited_cities.empty() && !this_cycle.empty()){
GRBLinExpr lhs=0,rhs=(int)this_cycle.size()-1;
for(const auto &city:this_cycle){
for(const auto &neighbor:unvisited_cities){
lhs+=vars[city][neighbor]+vars[neighbor][city];
}
}
model->addLazyConstraint(lhs<=rhs);
}
}
}
}
```
最后一步是在构建模型之后注册这个自定义的回调处理程序[^1]。
#### 执行优化过程
完成上述准备工作后就可以调用 `optimize()` 方法启动实际的求解流程了:
```cpp
try {
model.optimize();
} catch (GRBException e) {
cout << "Error code = " << e.getErrorCode() << endl;
cout << e.getMessage() << endl;
} catch (...) {
cout << "Exception during optimization" << endl;
}
```
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