退火模拟的SAW板材开料优化,要求C#编写,计算余料,堆积开料,切宽度

好的，SAW板材开料优化是一个经典的组合优化问题，可以采用退火模拟算法来求解。下面是一个简单的 C# 代码实现：

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace SimulatedAnnealing
{
    class Program
    {
        static Random random = new Random();

        static void Main(string[] args)
        {
            int[] lengths = { 100, 200, 300, 400, 500 }; // 可供选择的板材长度
            int[] widths = { 50, 100, 150, 200 }; // 可供选择的板材宽度

            int targetLength = 1000; // 目标板材长度
            int targetWidth = 500; // 目标板材宽度

            List<Plate> initialPlates = GenerateInitialPlates(lengths, widths, targetLength, targetWidth);

            double temperature = 100.0; // 初始温度
            double coolingRate = 0.001; // 降温速率

            List<Plate> bestPlates = simulatedAnnealing(initialPlates, temperature, coolingRate);

            Console.WriteLine("最佳方案：");
            foreach (Plate plate in bestPlates)
            {
                Console.WriteLine(plate);
            }

            Console.ReadLine();
        }

        static List<Plate> GenerateInitialPlates(int[] lengths, int[] widths, int targetLength, int targetWidth)
        {
            List<Plate> plates = new List<Plate>();

            while (true)
            {
                int length = lengths[random.Next(lengths.Length)];
                int width = widths[random.Next(widths.Length)];

                if (length <= targetLength && width <= targetWidth)
                {
                    plates.Add(new Plate(length, width));
                    targetLength -= length;
                    targetWidth -= width;

                    if (targetLength == 0 && targetWidth == 0)
                    {
                        break;
                    }
                }
            }

            return plates;
        }

        static List<Plate> simulatedAnnealing(List<Plate> initialPlates, double temperature, double coolingRate)
        {
            List<Plate> currentPlates = initialPlates;
            List<Plate> bestPlates = currentPlates;
            double bestScore = GetScore(bestPlates);

            while (temperature > 1.0)
            {
                List<Plate> newPlates = Mutate(currentPlates);
                double newScore = GetScore(newPlates);

                if (newScore > bestScore || Math.Exp((newScore - bestScore) / temperature) > random.NextDouble())
                {
                    currentPlates = newPlates;
                    bestScore = newScore;

                    if (bestScore > GetScore(bestPlates))
                    {
                        bestPlates = currentPlates;
                    }
                }

                temperature *= 1 - coolingRate;
            }

            return bestPlates;
        }

        static List<Plate> Mutate(List<Plate> plates)
        {
            List<Plate> newPlates = new List<Plate>(plates);

            int index1 = random.Next(newPlates.Count);
            int index2 = random.Next(newPlates.Count);

            Plate temp = newPlates[index1];
            newPlates[index1] = newPlates[index2];
            newPlates[index2] = temp;

            return newPlates;
        }

        static double GetScore(List<Plate> plates)
        {
            double score = 0.0;
            int currentWidth = 0;

            foreach (Plate plate in plates)
            {
                currentWidth += plate.Width;

                if (currentWidth > plate.Length)
                {
                    score += currentWidth - plate.Length;
                    currentWidth = plate.Width;
                }
            }

            score += currentWidth;

            return score;
        }
    }

    class Plate
    {
        public int Length { get; set; }
        public int Width { get; set; }

        public Plate(int length, int width)
        {
            Length = length;
            Width = width;
        }

        public override string ToString()
        {
            return string.Format("[{0}, {1}]", Length, Width);
        }
    }
}

代码中的 `Plate` 类表示一块板材，包含长度和宽度两个属性。`GenerateInitialPlates` 方法用于生成初始的板材方案，通过随机选择可供选择的板材长度和宽度来生成，直到目标板材长度和宽度都减为 0。`simulatedAnnealing` 方法是退火模拟算法的主体部分，其中的 `Mutate` 方法用于对当前的板材方案进行变异，即随机交换两个板材的位置。`GetScore` 方法用于计算当前板材方案的得分，即计算余料、堆积开料和切宽度的总和。最终的最佳方案通过比较得分来确定。

这里采用的温度调度方式是指数退火，即每次降温后温度乘以一个小于 1 的系数，这里取 0.999。温度越高时，接受劣解的概率越大，随着温度的降低，接受劣解的概率逐渐减小。最终的温度越低时，得到的解越可能是全局最优解。