用Tabu Search（禁忌搜索）java代码实现图染色问题

//定义节点类
class Node{
int id; //节点ID
int color; //节点颜色
List<Node> neighbors; //邻居节点列表
public Node(int id){
this.id = id;
this.color = -1; //初始时节点颜色为-1
neighbors = new ArrayList<Node>();
}
//添加邻居节点
public void addNeighbor(Node neighbor){
neighbors.add(neighbor);
}
}

//定义图类
class Graph{
List<Node> nodes; //节点列表
int maxColors; //最大颜色数
public Graph(int maxColors){
this.maxColors = maxColors;
nodes = new ArrayList<Node>();
}
//添加节点
public void addNode(Node node){
nodes.add(node);
}
}

//定义禁忌搜索类
class TabuSearch{
int tabuTenure; //禁忌期
int maxIterations; //最大迭代次数
Graph graph; //图
int[][] tabuList; //禁忌表
int[] bestSolution; //最优解
int bestObjective; //最优目标函数值
public TabuSearch(int tabuTenure, int maxIterations, Graph graph){
this.tabuTenure = tabuTenure;
this.maxIterations = maxIterations;
this.graph = graph;
tabuList = new int[graph.nodes.size()][graph.maxColors];
bestSolution = new int[graph.nodes.size()];
bestObjective = Integer.MAX_VALUE;
}
//初始化解
private void initialSolution(){
for(Node node : graph.nodes){
int color = (int)(Math.random() * graph.maxColors); //随机分配颜色
node.color = color;
bestSolution[node.id] = color;
}
bestObjective = evaluateSolution(bestSolution); //计算目标函数值
}
//计算目标函数值
private int evaluateSolution(int[] solution){
int conflicts = 0;
for(Node node : graph.nodes){
for(Node neighbor : node.neighbors){
if(solution[node.id] == solution[neighbor.id]){ //如果节点颜色与邻居节点颜色相同
conflicts++;
}
}
}
return conflicts;
}
//选择邻域解
private int[] selectNeighbor(int[] solution, int[][] tabuList){
int[] bestNeighbor = null;
int bestNeighborObjective = Integer.MAX_VALUE;
for(int i = 0; i < graph.nodes.size(); i++){
Node node = graph.nodes.get(i);
for(int j = 0; j < graph.maxColors; j++){
if(solution[node.id] != j){ //尝试将节点颜色改为j
int[] neighbor = solution.clone();
neighbor[node.id] = j;
int neighborObjective = evaluateSolution(neighbor);
if(neighborObjective < bestNeighborObjective){ //选择目标函数值最小的邻域解
if(tabuList[node.id][j] == 0){ //如果邻域解不在禁忌表中，则直接选择该邻域解
bestNeighbor = neighbor;
bestNeighborObjective = neighborObjective;
}else{ //如果邻域解在禁忌表中，则选择禁忌期结束时间最早的邻域解
if(tabuList[node.id][j] < i){
bestNeighbor = neighbor;
bestNeighborObjective = neighborObjective;
}
}
}
}
}
}
return bestNeighbor;
}
//更新禁忌表
private void updateTabuList(int[] solution, int[][] tabuList, int iteration){
for(int i = 0; i < graph.nodes.size(); i++){
Node node = graph.nodes.get(i);
tabuList[node.id][solution[node.id]] = iteration + tabuTenure;
}
}
//禁忌搜索
public void search(){
initialSolution(); //初始化解
int[] currentSolution = bestSolution.clone(); //当前解
int currentObjective = bestObjective; //当前目标函数值
for(int i = 0; i < maxIterations; i++){
int[] neighbor = selectNeighbor(currentSolution, tabuList); //选择邻域解
int neighborObjective = evaluateSolution(neighbor); //计算邻域解的目标函数值
if(neighborObjective < currentObjective){ //如果邻域解的目标函数值优于当前解，则选择邻域解作为当前解
currentSolution = neighbor;
currentObjective = neighborObjective;
if(neighborObjective < bestObjective){ //如果邻域解的目标函数值优于最优解，则更新最优解
bestSolution = neighbor.clone();
bestObjective = neighborObjective;
}
}
updateTabuList(currentSolution, tabuList, i); //更新禁忌表
}
}
}

//测试代码
public class Test{
public static void main(String[] args){
Graph graph = new Graph(3); //创建一个最大颜色数为3的图
Node node1 = new Node(0);
Node node2 = new Node(1);
Node node3 = new Node(2);
Node node4 = new Node(3);
node1.addNeighbor(node2);
node1.addNeighbor(node3);
node2.addNeighbor(node1);
node2.addNeighbor(node3);
node2.addNeighbor(node4);
node3.addNeighbor(node1);
node3.addNeighbor(node2);
node3.addNeighbor(node4);
node4.addNeighbor(node2);
node4.addNeighbor(node3);
graph.addNode(node1);
graph.addNode(node2);
graph.addNode(node3);
graph.addNode(node4);
TabuSearch tabuSearch = new TabuSearch(5, 100, graph); //创建一个禁忌搜索对象，禁忌期为5，最大迭代次数为100
tabuSearch.search(); //执行禁忌搜索算法
for(Node node : graph.nodes){
System.out.println("Node " + node.id + " is assigned to color " + tabuSearch.bestSolution[node.id]);
}
System.out.println("The number of conflicts is " + tabuSearch.bestObjective);
}
}