启发式搜索实验
实验三 搜索推理技术
启发式搜索算法—A*算法
1(实验目的
,1,了解搜索推理的相关技术,
,2,掌握启发式搜索算法或者基于规则推理的分析方法。 2(实验内容,2个实验内容可以选择1个实现,
,1,启发式搜索算法。熟悉和掌握启发式搜索的定义、估价函数和算法过程～并求解博弈问题～理解求解流程和搜索顺序, ,2,产生式系统实验。熟悉和掌握产生式系统的运行机制～掌握基于规则推理的基本方法。
3(实验报告要求
,1,简述实验原理及方法～并请给出程序设计流程图。 ,A-Star)算法是一种静态路网中求解最短路最有效的直接搜索方法。
公式表示为: f(n)=g(n)+h(n),
其中 f(n) 是从初始点经由节点n到目标点的估价函数～ g(n) 是在状态空间中从初始节点到n节点的实际代价～ h(n) 是从n到目标节点最佳路径的估计代价。
保证找到最短路径,最优解的,条件～关键在于估价函数h(n)的选取:
估价值h(n)<= n到目标节点的距离实际值～这种情况下～搜索的点数多～搜索范围大～效率低。但能得到最优解。并且如果h(n)=d(n)～
即距离估计h(n)等于最短距离～那么搜索将严格沿着最短路径进行～ 此时的搜索效率是最高的。
然后我们通过图文结合的形式来解释下～如下图:
图中有这么几个要点先需要了解:
1、类似迷宫图～分开始节点(start)、障碍物、结束节点(end)～我们需要从start节点探寻一条到end节点的路线
2、对于探寻的每一步～都会以当前节点为基点～扫描其相邻的八个节点
3、计算当前节点与start节点及到end的距离
4、计算出最短路径
如果明白了上面的场景描述～下面就可以进行分析了。 在A*算法中～核心思想是一个公式～上面已经提到过:
f(n)=g(n)+h(n)
,2,源程序清单:
package com.itxxz.ui.suanfa.astar;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Queue;
import com.itxxz.ui.suanfa.astar.Point;
public class ItxxzAstar {
// 开始节点
private Point startPoint = null;
// 当前节点
private Point endPoint = null;
// 结束节点
private Point currentPoint = null;
// 最短距离坐标节点
private Point shortestFPoint = null;
// 迷宫数组地图
private static final int[][] mazeArray = {
{ 1, 0, 0, 0, 0 },
{ 1, 0, 2, 0, 0 },
{ 1, 0, 0, 0, 1 },
{ 1, 0, 0, 0, 0 },
{ 1, 1, 1, 1, 0 },
{ 1, 0, 0, 0, 0 },
{ 3, 0, 1, 1, 1 } };
// 迷宫坐标对象
private Point[][] mazePoint = null;
// 开启队列，用于存放待处理的节点
Queue
openQueue = null;
// 关闭队列，用于存放已经处理过的节点
Queue closedQueue = null;
// 起始节点到某个节点的距离
int[][] FList = null;
// 某个节点到目的节点的距离
int[][] GList = null;
// 起始节点经过某个节点到目的节点的距离
int[][] HList = null;
/**
* 构造函数
*
* @param maze
* 迷宫图
* @param startPoint
* 起始节点
* @param endPoint
* 结束节点
*/
public ItxxzAstar(Point[][] mazePoint, Point startPoint, Point endPoint) {
this.mazePoint = mazePoint;
this.startPoint = startPoint;
this.endPoint = endPoint;
openQueue = new LinkedList();
openQueue.offer(startPoint);
closedQueue = new LinkedList();
FList = new int[mazePoint.length][mazePoint[0].length];
GList = new int[mazePoint.length][mazePoint[0].length];
HList = new int[mazePoint.length][mazePoint[0].length];
for (int i = 0; i < mazePoint.length; i++) {
for (int j = 0; j < mazePoint[0].length; j++) {
FList[i][j] = Integer.MAX_VALUE;
GList[i][j] = Integer.MAX_VALUE;
HList[i][j] = Integer.MAX_VALUE;
}
}
// 起始节点到当前节点的距离
GList[startPoint.getX()][startPoint.getY()] = 0;
// 当前节点到目的节点的距离
HList[startPoint.getX()][startPoint.getY()] = getPointDistance(
startPoint.getX(), startPoint.getY(), endPoint.getX(),
endPoint.getY());
// f(x) = g(x) + h(x)
FList[startPoint.getX()][startPoint.getY()] = GList[startPoint.getX()][startPoint
.getY()] + HList[startPoint.getX()][startPoint.getY()];
}
/**
* 计算当前坐标与结束坐标之间的距离
*
* 计算方法为每向相信坐标移动一次算作一个距离单位
*
*/
private int getPointDistance(int current_x, int current_y, int end_x,
int end_y) {
return Math.abs(current_x - end_x) + Math.abs(current_y - end_y);
}
/**
* 数组迷宫地图
*
* 0、可通行 1、障碍 2、开始节点 3、结束节点
*
*/
public static void main(String[] args) {
// 创建节点迷宫图
Point[][] mazePoint = new Point[mazeArray.length][mazeArray[0].length];
for (int i = 0; i < mazePoint.length; i++) {
for (int j = 0; j < mazePoint[0].length; j++) {
mazePoint[i][j] = new Point(i, j, mazeArray[i][j]);
}
}
Point start = mazePoint[1][2];
Point end = mazePoint[6][0];
ItxxzAstar star = new ItxxzAstar(mazePoint, start, end);
star.start();
System.out.println(mazeArray.length + "," + mazeArray[0].length);
star.printPath();
}
/**
* 开始迷宫搜索
*
*/
public void start() {
while ((currentPoint = findShortestFPoint()) != null) {
if (currentPoint.getX() == endPoint.getX()
&& currentPoint.getY() == endPoint.getY())
return;
updateNeighborPoints(currentPoint);
}
}
/**
* 获取距离最短的坐标点
*
*/
public Point findShortestFPoint() {
currentPoint = null;
shortestFPoint = null;
int shortestFValue = Integer.MAX_VALUE;
Iterator it = openQueue.iterator();
while (it.hasNext()) {
currentPoint = it.next();
if (FList[currentPoint.getX()][currentPoint.getY()] <= shortestFValue) {
shortestFPoint = currentPoint;
shortestFValue = FList[currentPoint.getX()][currentPoint.getY()];
}
}
if (shortestFValue != Integer.MAX_VALUE) {
System.out
.println("【移除节点】:" + shortestFPoint.getValue() + "["
+ shortestFPoint.getX() + ","
+ shortestFPoint.getY() + "]");
openQueue.remove(shortestFPoint);
closedQueue.offer(shortestFPoint);
}
return shortestFPoint;
}
/**
* 更新临近节点
*/
private void updateNeighborPoints(Point currentPoint) {
int current_x = currentPoint.getX();
int current_y = currentPoint.getY();
System.out.println("当前节点:[" + current_x + "," + current_y + "]");
// 上
if (checkPosValid(current_x - 1, current_y)) {
System.out.print("上");
updatePoint(mazePoint[current_x][current_y],
mazePoint[current_x - 1][current_y]);
}
// 下
if (checkPosValid(current_x + 1, current_y)) {
System.out.print("下");
updatePoint(mazePoint[current_x][current_y],
mazePoint[current_x + 1][current_y]);
}
// 左
if (checkPosValid(current_x, current_y - 1)) {
System.out.print("左");
updatePoint(mazePoint[current_x][current_y],
mazePoint[current_x][current_y - 1]);
}
// 右
if (checkPosValid(current_x, current_y + 1)) {
System.out.print("右");
updatePoint(mazePoint[current_x][current_y],
mazePoint[current_x][current_y + 1]);
}
System.out.println("---------------");
}
/**
* 检查该节点是否有效
*
*/
private boolean checkPosValid(int x, int y) {
// 检查x,y是否越界， 并且当前节点不是墙
if ((x >= 0 && x < mazePoint.length)
&& (y >= 0 && y < mazePoint[0].length)
&& (mazePoint[x][y].getValue() != 1)) {
// 检查当前节点是否已在关闭队列中，若存在，则返回 "false"
Iterator it = closedQueue.iterator();
Point point = null;
while (it.hasNext()) {
if ((point = it.next()) != null) {
if (point.getX() == x && point.getY() == y)
return false;
}
}
return true;
}
return false;
}
/**
* 更新当前节点
*/
private void updatePoint(Point lastPoint, Point currentPoint) {
int last_x = lastPoint.getX();
int last_y = lastPoint.getY();
int current_x = currentPoint.getX();
int current_y = currentPoint.getY();
// 起始节点到当前节点的距离
int temp_g = GList[last_x][last_y] + 1;
// 当前节点到目的位置的距离
System.out.print(" [" + current_x + "," + current_y + "]"
+ mazePoint[current_x][current_y].getValue());
int temp_h = getPointDistance(current_x, current_y, endPoint.getX(),
endPoint.getY());
System.out.println("到目的位置的距离 :" + temp_h);
// f(x) = g(x) + h(x)
int temp_f = temp_g + temp_h;
System.out.println("f(x) = g(x) + h(x) :" + temp_f + "=" + temp_g + "+"
+ temp_h);
// 如果当前节点在开启列表中不存在，则:置入开启列表，并且“设置”
// 1) 起始节点到当前节点距离
// 2) 当前节点到目的节点的距离
// 3) 起始节点到目的节点距离
if (!openQueue.contains(currentPoint)) {
openQueue.offer(currentPoint);
currentPoint.setFather(lastPoint);
System.out.println("添加到开启列表:" + currentPoint.getValue() + "["
+ currentPoint.getX() + "," + currentPoint.getY() + "]");
// 起始节点到当前节点的距离
GList[current_x][current_y] = temp_g;
// 当前节点到目的节点的距离
HList[current_x][current_y] = temp_h;
// f(x) = g(x) + h(x)
FList[current_x][current_y] = temp_f;
} else {
// 如果当前节点在开启列表中存在，并且，
// 从起始节点、经过上一节点到当前节点、至目的地的距离 < 上一次记录的
从起始节点、到当前节点、至目的地的距离，
// 则:“更新”
// 1) 起始节点到当前节点距离
// 2) 当前节点到目的节点的距离
// 3) 起始节点到目的节点距离
if (temp_f < FList[current_x][current_y]) {
// 起始节点到当前节点的距离
GList[current_x][current_y] = temp_g;
// 当前节点到目的位置的距离
HList[current_x][current_y] = temp_h;
// f(x) = g(x) + h(x)
FList[current_x][current_y] = temp_f;
// 更新当前节点的父节点
currentPoint.setFather(lastPoint);
}
System.out.println("currentPoint:" + currentPoint.getValue() + "["
+ currentPoint.getX() + "," + currentPoint.getY() + "]");
System.out.println("currentPoint.father:"
+ currentPoint.getFather().getValue() + "["
+ currentPoint.getFather().getX() + ","
+ currentPoint.getFather().getY() + "]");
}
}
/**
* 打印行走路径
*
*/
public void printPath() {
System.out.println("================ 开始打印行走路径【用 8 表示】
================");
Point father_point = null;
int[][] result = new int[mazeArray.length][mazeArray[0].length];
for (int i = 0; i < mazeArray.length; i++) {
for (int j = 0; j < mazeArray[0].length; j++) {
result[i][j] = 0;
}
}
int step = 0;
father_point = mazePoint[endPoint.getX()][endPoint.getY()];
while (father_point != null) {
System.out.println("【father_point】" + father_point.getValue() + "["
+ father_point.getX() + "," + father_point.getY() + "]");
if (father_point.equals(startPoint))
result[father_point.getX()][father_point.getY()] = 2;
else if (father_point.equals(endPoint)) {
result[father_point.getX()][father_point.getY()] = 3;
step++;
} else {
result[father_point.getX()][father_point.getY()] = 8;
step++;
}
father_point = father_point.getFather();
}
// 打印行走步数
System.out.println("step is : " + step);
for (int i = 0; i < mazeArray.length; i++) {
for (int j = 0; j < mazeArray[0].length; j++) {
System.out.print(result[i][j] + " ");
}
System.out.println();
}
}
}
,3,实验结果及分析。
实验结果:
很好的完成了实验目的～并且成功给出了最短路径::A*算法作为解决最优路径的一种高效算法～自从1968年诞生以来～得到了广泛的应用～而其的多种改进算法也在许多领域发挥着作用。可以预见～在更优的算法发现以前～A*算法将会得到更广泛的应用～并会由于图论、人工智能、机器人技术、自动控制等多学科的融合而得到更大的发展。
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