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C++实现的基本退火算法框架来解决一维套料的示例代码
模拟退火算法(Simulated Annealing, SA)可以有效地应用于一维套料问题,以寻找最优的切割方案。下面是使用C++实现的一个基本的模拟退火算法框架,用于解决一维套料问题的示例代码:
```cpp
#include <iostream>
#include <vector>
#include <algorithm>
#include <random>
#include <cmath>
#include <chrono>
// Problem parameters
const int RAW_LENGTH = 100; // Length of raw material
const std::vector<int> PIECES = {10, 20, 30}; // Desired piece lengths
// SA parameters
const int MAX_ITERATIONS = 1000;
const double INITIAL_TEMP = 1000.0;
const double COOLING_RATE = 0.99;
// Function to calculate the waste for a given cutting plan
int calculateWaste(const std::vector<int>& cuts)
{
int totalLength = 0;
for (int piece : cuts)
totalLength += piece;
return RAW_LENGTH * cuts.size() - totalLength;
}
// Function to generate a random cutting plan
std::vector<int> generateCuttingPlan()
{
std::vector<int> cuttingPlan;
int totalLength = 0;
while (totalLength < RAW_LENGTH)
{
int piece = PIECES[rand() % PIECES.size()];
if (totalLength + piece <= RAW_LENGTH)
{
cuttingPlan.push_back(piece);
totalLength += piece;
}
else
{
cuttingPlan.push_back(RAW_LENGTH - totalLength);
totalLength = RAW_LENGTH;
}
}
return cuttingPlan;
}
// Function to generate a neighbor cutting plan
std::vector<int> generateNeighborCuttingPlan(const std::vector<int>& currentPlan)
{
std::vector<int> neighborPlan = currentPlan;
int idx1 = rand() % neighborPlan.size();
int idx2 = rand() % neighborPlan.size();
std::swap(neighborPlan[idx1], neighborPlan[idx2]);
return neighborPlan;
}
// Function to run the Simulated Annealing algorithm
std::vector<int> simulatedAnnealing()
{
// Initialize with a random cutting plan
std::vector<int> currentPlan = generateCuttingPlan();
int currentWaste = calculateWaste(currentPlan);
double temperature = INITIAL_TEMP;
for (int i = 0; i < MAX_ITERATIONS; ++i)
{
std::vector<int> neighborPlan = generateNeighborCuttingPlan(currentPlan);
int neighborWaste = calculateWaste(neighborPlan);
// Calculate the change in energy (waste)
int deltaE = neighborWaste - currentWaste;
// If the new plan is better, or accepted probabilistically, accept it
if (deltaE < 0 || exp(-deltaE / temperature) > static_cast<double>(rand()) / RAND_MAX)
{
currentPlan = neighborPlan;
currentWaste = neighborWaste;
}
// Cool down the system
temperature *= COOLING_RATE;
}
return currentPlan;
}
int main()
{
std::srand(std::chrono::system_clock::now().time_since_epoch().count());
// Run the Simulated Annealing algorithm
std::vector<int> optimalCuttingPlan = simulatedAnnealing();
int optimalWaste = calculateWaste(optimalCuttingPlan);
std::cout << "Optimal Cutting Plan: ";
for (int piece : optimalCuttingPlan)
std::cout << piece << " ";
std::cout << "\nOptimal Waste: " << optimalWaste << std::endl;
return 0;
}
```
这个代码实现了一个基本的模拟退火算法,用于寻找最优的一维套料切割计划。算法从一个随机的切割计划开始,通过生成邻近的切割计划并根据当前温度和能量差(在这里是浪费的材料量)决定是否接受新的切割计划,逐步逼近最优解。
请注意,模拟退火算法是一种随机搜索算法,每次运行的结果可能会有所不同。此外,算法的性能和最终解的质量会受到参数(如初始温度、冷却率、最大迭代次数等)的影响。在实际应用中,可能需要通过实验来调整这些参数,以获得更好的结果。
在上面的代码中,生成切割计划和邻域切割计划的策略相对简单,即通过随机选择和交换两个切割点来生成新的切割计划。在处理更复杂的问题时,可能需要设计更复杂的策略,以确保算法的效率和解的质量。 |
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