10.1 - 遗传算法（旅行商问题C#求解）

        遗传算法是模拟自然界生物进化过程的随机优化算法，通过模拟"自然选择"和"遗传机制"来寻找最优解，其中遗传机制主要依靠突变、交叉、选择这些仿生算子。

适应度	生存能力	解决方案的质量评分
选择	自然选择	选择优秀的个体进行繁殖
交叉	有性繁殖	组合两个个体的基因
变异	基因突变	随机改变个体的某些基因

一、旅行商问题

给定一系列城市和每对城市之间的距离，求解访问每一座城市一次并回到起始城市的最短回路

        为了简单起见：以直线上等间距的10个城市为例。最短距离就是18. 

        编程思路是：

        1. 先随机生成比如20条路线；

        2. 然后按距离排序，丢掉最长的10条；

       3. 剩下（被选择）的10条通过突变因子和交叉因子再生成10条。

       4.  （当迭代次数未完成时）返回到2. 完成一次迭代。 

【备注】如果按照50个人口来，差不多几次就可以得到最好的结果

1.1 突变因子

        把两座随机指定的城市交换位置。

 public Solution Mutate(Random random)
{
var i=random.Next(0,CityList.Count);
var j= random.Next(0, CityList.Count);
if (i == j)
{
return this;
}
var newCityList = new List<int>(CityList);
var temp = newCityList[i];
newCityList[i] = newCityList[j];
newCityList[j]= temp;
return new Solution(newCityList);
}

2.交叉算子

        由父A母B的各一部分交叉组成；思路是：随机从B中取一段放到child中，然后把A中的所有不在子类的按顺序填充到child中。作为进化后的        

//把另外一个的城市序列的一段拷贝过来，并且把本序列的其余部分按顺序拷贝到child中

 public Solution CrossOver(Random random,Solution solution)
{
int length = this.CityList.Count;
// 随机选择两个交叉点
int point1 = random.Next(0, length - 1);
int point2 = random.Next(point1 + 1, length);
int[] child1 = new int[length];
FillArray(child1, -1);
// 复制中间段
for (int i = point1; i <= point2; i++)
{
child1[i] = solution.CityList[i];

     }
FillRemainingPositions(this.CityList,  child1, point1, point2);
return new Solution(child1);

 }        

//按顺序把parent中不在child中的元素填充过来。

 private static void FillRemainingPositions(List<int> parent,
int[] child, int start, int end)
{

     var remainElement = parent.Where(x => child.Contains(x) == false).Select(x => x).ToList();
if (remainElement.Any() == false)
return;

     int j = 0;
for (int i = 0; i < child.Length; i++)
{
if (i >= start && i <= end) continue;
child[i] = remainElement[j++];

     }
}

3.实际的一段截图如下：

二、代码

   /// <summary>/// trip route,/// </summary>public class TripRoute{/// <summary>/// Map is distance between points, Map[2,3] means distance beween point2-point3./// </summary>public static double[,] Map { get;set; }public TripRoute(double[,] map){Map = map;}/// <summary>/// calculate the distance between the point series./// for example: 1-5-2-3;    1-5;5-2;2-3;/// </summary>/// <param name="solution"></param>public static void CalculateDistance(Solution solution){var result = 0.0;for(int i = 0; i <solution.CityList.Count-1; i++){result += Map[solution.CityList[i], solution.CityList[i + 1]];}result+= Map[0, solution.CityList.Count-1]; //最后回到原点solution.Distances = result;}}public class Solution :IComparable<Solution>{public List<int> CityList { get; set; }public double Distances { get; set; }/// <summary>/// Get a solution for travel route/// </summary>/// <param name="cityList"></param>public Solution(IEnumerable<int> cityList){CityList = new List<int>(cityList);TripRoute.CalculateDistance(this);}/// <summary>/// 变异\突变;/// 交换两个城市在序列中的位置/// </summary>/// <param name="random"></param>/// <returns></returns>public Solution Mutate(Random random){var i=random.Next(0,CityList.Count);var j= random.Next(0, CityList.Count);if (i == j){return this;}var newCityList = new List<int>(CityList);var temp = newCityList[i];newCityList[i] = newCityList[j];newCityList[j]= temp;return new Solution(newCityList);}/// <summary>/// 交叉算子，一个基因的前半部分和后一个基因的后一半部分组合/// </summary>/// <param name="random"></param>/// <param name="solution"></param>/// <returns></returns>public Solution CrossOver(Random random,Solution solution){int length = this.CityList.Count;// 随机选择两个交叉点int point1 = random.Next(0, length - 1);int point2 = random.Next(point1 + 1, length);int[] child1 = new int[length];FillArray(child1, -1);// 复制中间段for (int i = point1; i <= point2; i++){child1[i] = solution.CityList[i];}FillRemainingPositions(this.CityList,  child1, point1, point2);return new Solution(child1);}        /// <summary>/// 按顺序把parent中不在child中的元素填充过来。/// </summary>/// <param name="parent"></param>/// <param name="child"></param>/// <param name="start"></param>/// <param name="end"></param>private static void FillRemainingPositions(List<int> parent,int[] child, int start, int end){var remainElement = parent.Where(x => child.Contains(x) == false).Select(x => x).ToList();if (remainElement.Any() == false)return;int j = 0;for (int i = 0; i < child.Length; i++){if (i >= start && i <= end) continue;child[i] = remainElement[j++];}}public static void FillArray<T>(T[] array, T value){for (int i = 0; i < array.Length; i++){array[i] = value;}}public int CompareTo(Solution other){if (other == null) return 1;return this.Distances.CompareTo(other.Distances);}public override string ToString(){StringBuilder sb = new StringBuilder();foreach(int i in this.CityList){sb.Append( string.Format("{0}, ", i));}sb.Append("距离："+this.Distances.ToString());return sb.ToString();}}public class GeneticAlgorithmTsp{public int Iterations { get; set; }public TripRoute Tsp { get; set; }public List<Solution> Population { get; set; }public int Size;private static readonly Random random = new Random();public GeneticAlgorithmTsp(int iterations, TripRoute tsp, int size){Iterations = iterations;Tsp = tsp;Size = size;Population = new List<Solution>();}public Solution Execute(){InitPopulation();var i = 0;while(i<Iterations){var selected = ChooseBest();var newPopulation = Evolution(selected as List<Solution>);MergePopulation(newPopulation);i++;Logger.Record("----------------------");Logger.Record( string.Format("第{0}次迭代,种群数量{1},最优距离{2},种群如下", i,Population.Count , Population.First().Distances));foreach (var item in Population){Logger.Record(item.ToString());}Logger.Record("----------------------");}return Population.First();}/// <summary>/// 初始化种群/// </summary>private void InitPopulation(){var i = 0;while (i < Size){Population.Add(RandomSolution(TripRoute.Map.GetLength(0)));i++;}Logger.Record("初始化种群情况:");foreach(var item in Population){Logger.Record(item.ToString());}}/// <summary>/// 随机生成顺序/// </summary>/// <param name="n"></param>/// <returns></returns>private Solution RandomSolution(int n){var result = new List<int>();var range = Enumerable.Range(0, n).ToList();while (range.Count > 0){var index = random.Next(0, range.Count);result.Add(range[index]);range.RemoveAt(index);}return new Solution(result);}/// <summary>/// 人口合并/// </summary>/// <param name="newPopulation"></param>private void MergePopulation(IEnumerable<Solution> newPopulation){Population.AddRange(newPopulation);Population.Sort();Population = Population.GetRange(0, Size);}/// <summary>/// 使用交换或变异的办法产生新的元素/// </summary>/// <param name="selected"></param>/// <returns></returns>private IEnumerable<Solution> Evolution(List<Solution> selected){var result = new List<Solution>();for(var i=0;i<selected.Count;i++){result.Add(random.NextDouble() <= 0.4? selected[i].Mutate(random) : selected[i].CrossOver(random, selected[random.Next(0, selected.Count)]));}Logger.Record("-------------:");Logger.Record( string.Format("新进化出的人口，数量{0}，情况如下:",result.Count));foreach(Solution s in result){Logger.Record(s.ToString());}return result;}/// <summary>/// 选择表现好的，即总数的一半/// </summary>/// <returns></returns>private IEnumerable<Solution>   ChooseBest(){Population.Sort();Logger.Record("-------------:");Logger.Record("选择最好的一半，丢失的如下:");for(int i= Size / 2;i<Size;i++){Logger.Record(Population[i].ToString());}return Population.GetRange(0, Size / 2);}}static void Main(string[] args){var map = new double[,]{{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9  },	//城市距离矩阵{  1, 0, 1, 2, 3, 4, 5, 6, 7, 8  },{  2, 1, 0, 1, 2, 3, 4, 5, 6, 7  },{  3, 2, 1, 0, 1, 2, 3, 4, 5, 6  },{  4, 3, 2, 1, 0, 1, 2, 3, 4, 5  },{  5, 4, 3, 2, 1, 0, 1, 2, 3, 4  },{  6, 5, 4, 3, 2, 1, 0, 1, 2, 3  },{  7, 6, 5, 4, 3, 2, 1, 0, 1, 2  },{  8, 7, 6, 5, 4, 3, 2, 1, 0, 1  },{  9, 8, 7, 6, 5, 4, 3, 2, 1, 0  }};var ga = new GeneticAlgorithmTsp(100, new TripRoute(map), 20);var best = ga.Execute();Console.WriteLine("best solution:");foreach (var d in best.CityList)Console.Write("{0}, ", d);Console.WriteLine("\n" + "fitness:{0}", best.Distances);Console.Read();return;       }