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C++实现的蚁群算法框架来解决多边形套料的示例代码
蚁群算法(Ant Colony Optimization, ACO)在解决多边形套料问题时,可以通过模拟蚂蚁在寻找食物过程中留下的信息素来寻找最优解。然而,与一维或多维背包问题、旅行商问题(TSP)等相比,多边形套料问题更为复杂,因为它不仅涉及到尺寸的匹配,还涉及到形状的匹配和空间的布局,因此直接应用ACO可能需要更复杂的实现。
下面是一个简化版的蚁群算法框架,用于解决多边形套料问题的示例代码。这个示例将展示如何使用蚁群算法来优化多个不同形状和尺寸的多边形在一块原材料上的布局,以最大化利用率和减少浪费。请注意,这个示例代码进行了大量的简化,主要关注算法的核心概念和流程,而未涵盖所有细节,尤其是碰撞检测和空间布局优化。
```cpp
#include <iostream>
#include <vector>
#include <random>
#include <algorithm>
#include <map>
// Define a polygon as a vector of points
struct Point {
int x, y;
};
struct Polygon {
std::vector<Point> points;
int id;
};
// Ant Colony Optimization parameters
const int NUM_ANTS = 100;
const int MAX_ITERATIONS = 100;
const double EVAPORATION_RATE = 0.1;
const double ALPHA = 1.0; // pheromone importance
const double BETA = 5.0; // heuristic information importance
// Material parameters
const int MATERIAL_WIDTH = 100;
const int MATERIAL_HEIGHT = 100;
// Pheromone trail representation
struct PheromoneTrail {
std::map<int, double> trail;
void init() {
for (const auto& polygon : polygons) {
trail[polygon.id] = 1.0; // initial pheromone value
}
}
void evaporate() {
for (auto& entry : trail) {
entry.second *= (1.0 - EVAPORATION_RATE);
}
}
};
// Ant class
class Ant {
public:
std::vector<Polygon> layout;
double fitness;
Ant() : fitness(0) {}
void buildLayout(const std::vector<Polygon>& polygons, const PheromoneTrail& pheromones) {
std::vector<bool> used(polygons.size(), false);
std::vector<double> probabilities(polygons.size(), 0.0);
double total = 0.0;
while (!layoutFull()) {
for (size_t i = 0; i < polygons.size(); ++i) {
if (!used[i]) {
double pheromone = pow(pheromones.trail[polygons[i].id], ALPHA);
double heuristic = pow(calculateHeuristic(polygons[i]), BETA);
probabilities[i] = pheromone * heuristic;
total += pheromone * heuristic;
}
}
// Normalize probabilities
for (size_t i = 0; i < polygons.size(); ++i) {
if (!used[i]) {
probabilities[i] /= total;
}
}
// Select next polygon
double r = static_cast<double>(rand()) / RAND_MAX;
int selectedPolygon = -1;
for (size_t i = 0; i < polygons.size(); ++i) {
if (!used[i]) {
r -= probabilities[i];
if (r <= 0.0) {
selectedPolygon = i;
break;
}
}
}
if (selectedPolygon != -1) {
layout.push_back(polygons[selectedPolygon]);
used[selectedPolygon] = true;
}
}
calculateFitness();
}
private:
bool layoutFull() {
int totalWidth = 0;
int totalHeight = 0;
for (const auto& polygon : layout) {
totalWidth += polygon.points.back().x;
totalHeight = std::max(totalHeight, polygon.points.back().y);
}
return totalWidth >= MATERIAL_WIDTH && totalHeight >= MATERIAL_HEIGHT;
}
double calculateHeuristic(const Polygon& polygon) {
// Simplified heuristic based on polygon area
return polygon.points.back().x * polygon.points.back().y;
}
void calculateFitness() {
int totalWidth = 0;
int totalHeight = 0;
for (const auto& polygon : layout) {
totalWidth += polygon.points.back().x;
totalHeight = std::max(totalHeight, polygon.points.back().y);
}
fitness = 1.0 / (totalWidth * totalHeight);
}
};
// Function to run the Ant Colony Optimization algorithm
void antColonyOptimization(std::vector<Polygon>& polygons) {
PheromoneTrail pheromones;
pheromones.init();
for (int iteration = 0; iteration < MAX_ITERATIONS; ++iteration) {
std::vector<Ant> ants;
ants.reserve(NUM_ANTS);
for (int i = 0; i < NUM_ANTS; ++i) {
Ant ant;
ant.buildLayout(polygons, pheromones);
ants.push_back(ant);
}
// Update pheromones based on ants' layouts
for (const auto& ant : ants) {
for (const auto& polygon : ant.layout) {
pheromones.trail[polygon.id] += 1.0 / ant.layout.size();
}
}
pheromones.evaporate();
}
}
int main() {
std::srand(std::chrono::system_clock::now().time_since_epoch().count());
// Example polygons
std::vector<Polygon> polygons = {
{{0, 0}, {10, 0}, {10, 10}, {0, 10}},
{{0, 0}, {15, 0}, {15, 15}, {0, 15}},
{{0, 0}, {20, 0}, {20, 10}, {0, 10}}
};
for (size_t i = 0; i < polygons.size(); ++i) {
polygons[i].id = i;
}
// Run the Ant Colony Optimization algorithm
antColonyOptimization(polygons);
// Note: The actual best solution is not extracted from the ants in this simplified example.
return 0;
}
```
这个示例代码提供了一个简化版的蚁群算法框架,用于解决多边形套料问题。在实际应用中,你可能需要引入更复杂的碰撞检测算法、更精细的适应度函数以及更准确的布局优化策略。例如,你可以使用AABB树或四叉树等数据结构来加速碰撞检测,使用局部搜索算法来优化每个蚂蚁的布局,以及使用更复杂的编码方式和信息素更新策略来提高算法的性能。
此外,这个示例代码中的信息素更新策略较为简单,只基于蚂蚁的数量和布局的大小。在实际应用中,你可能需要根据布局的实际效果(如材料利用率、布局的紧凑度等)来动态调整信息素的更新规则,以更好地引导搜索过程。同时,你也需要仔细调整算法的参数,如蚂蚁数量、迭代次数、信息素挥发率等,以平衡算法的探索与利用能力,从而获得更优的解决方案。 |
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