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C++实现的基本遗传算法框架来解决多边形套料的示例代码
下面是一个使用C++实现的遗传算法框架,用于解决多边形套料问题。这个示例将展示如何使用遗传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。
由于多边形套料问题是一个非常复杂的优化问题,涉及多个约束条件(如多边形不能重叠,必须完全位于原材料内部等),下面的示例代码将简化一些细节,仅提供一个基本的框架。实际应用中可能需要更复杂的碰撞检测算法、适应度函数以及编码方式。
```cpp
#include <iostream>
#include <vector>
#include <algorithm>
#include <random>
#include <cassert>
// Define a polygon as a vector of points
struct Point {
int x, y;
};
struct Polygon {
std::vector<Point> points;
};
// Genetic Algorithm parameters
const int POPULATION_SIZE = 100;
const int GENERATIONS = 1000;
const double MUTATION_RATE = 0.05;
const double CROSSOVER_RATE = 0.7;
// Material parameters
const int MATERIAL_WIDTH = 100;
const int MATERIAL_HEIGHT = 100;
// A simple chromosome represents an arrangement of polygons on the material
class Chromosome {
public:
std::vector<Polygon> polygons;
double fitness;
Chromosome(const std::vector<Polygon>& _polygons) : polygons(_polygons), fitness(0) {}
void calculateFitness() {
// Simplified fitness calculation based on the total area covered by polygons
int totalArea = 0;
for (const auto& p : polygons) {
totalArea += p.points.back().x * p.points.back().y;
}
fitness = static_cast<double>(totalArea) / (MATERIAL_WIDTH * MATERIAL_HEIGHT);
}
};
// Function to generate an initial population
std::vector<Chromosome> generatePopulation(const std::vector<Polygon>& polygons) {
std::vector<Chromosome> population;
for (int i = 0; i < POPULATION_SIZE; ++i) {
std::vector<Polygon> shuffledPolygons = polygons;
std::random_shuffle(shuffledPolygons.begin(), shuffledPolygons.end());
population.emplace_back(shuffledPolygons);
}
return population;
}
// Function to perform crossover between two chromosomes
Chromosome crossover(const Chromosome& parent1, const Chromosome& parent2) {
Chromosome child(parent1.polygons);
int crossoverPoint = std::rand() % parent1.polygons.size();
child.polygons = std::vector<Polygon>(parent1.polygons.begin(), parent1.polygons.begin() + crossoverPoint);
child.polygons.insert(child.polygons.end(), parent2.polygons.begin() + crossoverPoint, parent2.polygons.end());
return child;
}
// Function to mutate a chromosome
void mutate(Chromosome& chromosome) {
if (std::rand() / static_cast<double>(RAND_MAX) < MUTATION_RATE) {
std::swap(chromosome.polygons[std::rand() % chromosome.polygons.size()],
chromosome.polygons[std::rand() % chromosome.polygons.size()]);
}
}
// Function to run the Genetic Algorithm
Chromosome geneticAlgorithm(const std::vector<Polygon>& polygons) {
std::vector<Chromosome> population = generatePopulation(polygons);
for (int generation = 0; generation < GENERATIONS; ++generation) {
// Calculate fitness for each chromosome
for (auto& chromosome : population) {
chromosome.calculateFitness();
}
// Sort the population by fitness
std::sort(population.begin(), population.end(), [](const Chromosome& a, const Chromosome& b) {
return a.fitness > b.fitness;
});
// Select top chromosomes for reproduction
std::vector<Chromosome> selected;
for (int i = 0; i < POPULATION_SIZE / 2; ++i) {
selected.push_back(population[i]);
}
// Create new population through crossover and mutation
std::vector<Chromosome> newPopulation;
while (newPopulation.size() < POPULATION_SIZE) {
if (std::rand() / static_cast<double>(RAND_MAX) < CROSSOVER_RATE) {
Chromosome child = crossover(selected[std::rand() % selected.size()],
selected[std::rand() % selected.size()]);
mutate(child);
newPopulation.push_back(child);
} else {
newPopulation.push_back(selected[std::rand() % selected.size()]);
}
}
population = newPopulation;
}
// Return the best chromosome found
return *std::max_element(population.begin(), population.end(), [](const Chromosome& a, const Chromosome& b) {
return a.fitness < b.fitness;
});
}
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}}
};
// Run the Genetic Algorithm
Chromosome bestSolution = geneticAlgorithm(polygons);
// Print results
std::cout << "Best solution fitness: " << bestSolution.fitness << std::endl;
return 0;
}
```
这个示例代码提供了遗传算法的基本框架,包括种群初始化、适应度计算、交叉、变异等步骤。然而,实际的多边形套料问题涉及到复杂的碰撞检测和位置优化,这在上述代码中没有体现。在真实的应用场景中,可能需要引入更高级的数据结构和算法来处理这些细节,例如使用空间划分数据结构来加速碰撞检测,以及采用更精细的编码方式和适应度评估方法。此外,遗传算法的参数(如种群大小、交叉率、突变率等)也需要根据具体问题进行适当的调整。 |
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