遗传算法的SAW板材开料优化,要求C#编写,计算余料,堆积开料,切割宽度,切割顺序,切割路径,转向次数

遗传算法是一种常用的优化算法，可以应用于板材开料问题。以下是一个简单的SAW板材开料优化的C#实现。

首先定义一个板材类，包含板材的长度、宽度和剩余面积等信息：

class Plate
{
    public int Length { get; set; }
    public int Width { get; set; }
    public int Area { get; set; }
    public List<Cut> Cuts { get; set; }
    public Plate(int length, int width)
    {
        Length = length;
        Width = width;
        Area = length * width;
        Cuts = new List<Cut>();
    }
}

接着定义一个切割类，包含切割的长度、宽度和位置等信息：

class Cut
{
    public int Length { get; set; }
    public int Width { get; set; }
    public int X { get; set; }
    public int Y { get; set; }
    public Cut(int length, int width, int x, int y)
    {
        Length = length;
        Width = width;
        X = x;
        Y = y;
    }
}

然后定义一个遗传算法类，包含种群、交叉率、变异率等参数：

class GeneticAlgorithm
{
    private List<Plate> population;
    private float crossoverRate = 0.8f;
    private float mutationRate = 0.05f;
    public GeneticAlgorithm(int populationSize)
    {
        population = new List<Plate>();
        for (int i = 0; i < populationSize; i++)
        {
            population.Add(new Plate(4000, 2000)); // 初始化种群，每个个体为一块 4000x2000 的板材
        }
    }
    public void Evolve(int generations)
    {
        for (int i = 0; i < generations; i++)
        {
            // 计算适应度
            foreach (Plate plate in population)
            {
                plate.Area = plate.Length * plate.Width;
                int usedArea = 0;
                for (int j = 0; j < plate.Cuts.Count; j++)
                {
                    Cut cut = plate.Cuts[j];
                    usedArea += cut.Length * cut.Width;
                    if (j > 0) // 计算转向次数
                    {
                        Cut prevCut = plate.Cuts[j - 1];
                        if (cut.X == prevCut.X)
                        {
                            if (prevCut.Y + prevCut.Width != cut.Y)
                            {
                                plate.Area += 100;
                            }
                        }
                        else
                        {
                            if (prevCut.X + prevCut.Length != cut.X)
                            {
                                plate.Area += 100;
                            }
                        }
                    }
                }
                plate.Area -= usedArea; // 计算余料
            }

            // 选择父母
            List<Plate> parents = new List<Plate>();
            while (parents.Count < population.Count)
            {
                Plate parent1 = SelectParent();
                Plate parent2 = SelectParent();
                parents.Add(parent1);
                parents.Add(parent2);
            }

            // 交叉
            for (int j = 0; j < parents.Count; j += 2)
            {
                if (Random.NextDouble() < crossoverRate)
                {
                    CrossOver(parents[j], parents[j + 1]);
                }
            }

            // 变异
            foreach (Plate plate in population)
            {
                if (Random.NextDouble() < mutationRate)
                {
                    Mutate(plate);
                }
            }
        }
    }
    private Plate SelectParent()
    {
        // 采用轮盘赌选择父母
        float sumFitness = population.Sum(p => p.Area);
        float rand = (float)Random.NextDouble() * sumFitness;
        float partialSum = 0;
        foreach (Plate plate in population)
        {
            partialSum += plate.Area;
            if (partialSum >= rand)
            {
                return plate;
            }
        }
        return population[population.Count - 1];
    }
    private void CrossOver(Plate parent1, Plate parent2)
    {
        // 采用单点交叉
        int cutPoint = Random.Next(1, Math.Min(parent1.Cuts.Count - 1, parent2.Cuts.Count - 1));
        List<Cut> tempCuts = new List<Cut>(parent1.Cuts.GetRange(0, cutPoint));
        parent1.Cuts.RemoveRange(0, cutPoint);
        parent1.Cuts.AddRange(parent2.Cuts.GetRange(cutPoint, parent2.Cuts.Count - cutPoint));
        parent2.Cuts.RemoveRange(cutPoint, parent2.Cuts.Count - cutPoint);
        parent2.Cuts.InsertRange(0, tempCuts);
    }
    private void Mutate(Plate plate)
    {
        // 采用插入变异
        int cutIndex = Random.Next(0, plate.Cuts.Count);
        Cut cut = plate.Cuts[cutIndex];
        plate.Cuts.RemoveAt(cutIndex);
        int x = Random.Next(0, plate.Length - cut.Length);
        int y = Random.Next(0, plate.Width - cut.Width);
        Cut newCut = new Cut(cut.Length, cut.Width, x, y);
        plate.Cuts.Add(newCut);
    }
}

最后在主函数中使用遗传算法求解：

static void Main(string[] args)
{
    // 初始化切割方案
    List<Cut> cuts = new List<Cut>();
    cuts.Add(new Cut(500, 100, 0, 0));
    cuts.Add(new Cut(500, 100, 0, 100));
    cuts.Add(new Cut(500, 100, 0, 200));
    cuts.Add(new Cut(500, 100, 0, 300));
    cuts.Add(new Cut(500, 100, 0, 400));
    cuts.Add(new Cut(500, 100, 0, 500));
    cuts.Add(new Cut(500, 100, 0, 600));
    cuts.Add(new Cut(500, 100, 0, 700));
    cuts.Add(new Cut(500, 100, 0, 800));
    cuts.Add(new Cut(500, 100, 0, 900));
    cuts.Add(new Cut(2000, 500, 500, 0));
    cuts.Add(new Cut(2000, 500, 500, 500));
    cuts.Add(new Cut(2000, 500, 500, 1000));

    // 定义种群大小和迭代次数
    int populationSize = 100;
    int generations = 100;

    // 初始化遗传算法
    GeneticAlgorithm ga = new GeneticAlgorithm(populationSize);

    // 进化
    ga.Evolve(generations);

    // 打印最优解
    Plate bestPlate = ga.population.OrderBy(p => p.Area).First();
    Console.WriteLine("余料：{0}", bestPlate.Area);
    Console.WriteLine("切割顺序：");
    for (int i = 0; i < bestPlate.Cuts.Count; i++)
    {
        Console.WriteLine("{0}. ({1}, {2})", i + 1, bestPlate.Cuts[i].X, bestPlate.Cuts[i].Y);
    }
}

上述代码中，切割方案为一个包含若干个切割的列表，每个切割包含长度、宽度和位置等信息。种群大小和迭代次数可以根据实际情况进行调整。在遗传算法的进化过程中，首先计算每个个体的适应度，然后采用轮盘赌选择父母，进行单点交叉和插入变异，得到新一代个体。最后，选择最优个体作为最终方案。