ARA* java实现

ARA*（Anytime Repairing A*）是A*算法的一种扩展形式，可以在有限的时间内找到一个近似最优的解。与传统的A*算法不同，ARA*算法允许在搜索过程中随时停止，返回已经找到的最优解，并且返回的解会随着时间的增加而逐渐接近最优解。

以下是一个简单的Java实现：

import java.util.*;

public class ARAStar {
    private PriorityQueue<Node> openList;
    private HashSet<Node> closedList;
    private double epsilon;
    private double lowerBound;

    public ARAStar(double epsilon) {
        this.epsilon = epsilon;
        this.openList = new PriorityQueue<>();
        this.closedList = new HashSet<>();
        this.lowerBound = Double.MAX_VALUE;
    }

    public List<Node> search(Node start, Node goal, double timeLimit) {
        start.setHeuristic(goal);
        start.setG(0);
        start.setF(start.getHeuristic());
        openList.add(start);

        long startTime = System.currentTimeMillis();
        long elapsedTime = 0;
        while (!openList.isEmpty() && elapsedTime < timeLimit) {
            Node current = openList.poll();
            if (current.equals(goal)) {
                return reconstructPath(current);
            }
            closedList.add(current);

            for (Node neighbor : current.getNeighbors()) {
                if (closedList.contains(neighbor)) {
                    continue;
                }

                double tentative_g = current.getG() + current.distanceTo(neighbor);
                if (!openList.contains(neighbor) || tentative_g < neighbor.getG()) {
                    neighbor.setG(tentative_g);
                    neighbor.setHeuristic(goal);
                    neighbor.setF(neighbor.getG() + epsilon * neighbor.getHeuristic());

                    if (!openList.contains(neighbor)) {
                        openList.add(neighbor);
                    }
                }
            }

            double currentCost = current.getG() + current.getHeuristic();
            if (currentCost < lowerBound) {
                lowerBound = currentCost;
            }

            elapsedTime = System.currentTimeMillis() - startTime;
            if (elapsedTime >= timeLimit && openList.isEmpty()) {
                return null;
            }
        }

        return null;
    }

    private List<Node> reconstructPath(Node goal) {
        List<Node> path = new ArrayList<>();
        Node current = goal;
        while (current != null) {
            path.add(current);
            current = current.getParent();
        }
        Collections.reverse(path);
        return path;
    }
}

其中，Node类表示搜索中的一个节点，包含位置、代价g值、启发式h值、估价函数f值、父节点等属性：

public class Node implements Comparable<Node> {
    private int x;
    private int y;
    private double g;
    private double h;
    private double f;
    private Node parent;

    public Node(int x, int y) {
        this.x = x;
        this.y = y;
        this.g = Double.POSITIVE_INFINITY;
        this.h = 0;
        this.f = Double.POSITIVE_INFINITY;
        this.parent = null;
    }

    public int getX() {
        return x;
    }

    public int getY() {
        return y;
    }

    public double getG() {
        return g;
    }

    public void setG(double g) {
        this.g = g;
    }

    public double getHeuristic() {
        return h;
    }

    public void setHeuristic(Node goal) {
        this.h = distanceTo(goal);
    }

    public double getF() {
        return f;
    }

    public void setF(double f) {
        this.f = f;
    }

    public Node getParent() {
        return parent;
    }

    public void setParent(Node parent) {
        this.parent = parent;
    }

    public double distanceTo(Node other) {
        int dx = Math.abs(this.x - other.x);
        int dy = Math.abs(this.y - other.y);
        return Math.sqrt(dx * dx + dy * dy);
    }

    @Override
    public int compareTo(Node other) {
        return Double.compare(this.getF(), other.getF());
    }

    @Override
    public boolean equals(Object other) {
        if (this == other) return true;
        if (other == null || getClass() != other.getClass()) return false;
        Node node = (Node) other;
        return x == node.x && y == node.y;
    }

    @Override
    public int hashCode() {
        return Objects.hash(x, y);
    }
}

在使用ARA*算法进行搜索时，需要给定起点和终点，并设置一个时间限制。epsilon表示误差因子，值越大，搜索速度越快，但找到的解可能越差。lowerBound表示当前已经找到的最优解的代价值下界，随着搜索的进行而逐渐减小。

在search方法中，首先将起点加入openList中，然后不断从openList中取出f值最小的节点进行扩展，直到找到终点或者搜索时间超过限制为止。在扩展一个节点时，如果当前节点的代价值加上到相邻节点的距离小于相邻节点的代价值，则更新相邻节点的代价值，并将其加入openList中。同时，如果当前节点的代价值加上启发式值小于lowerBound，则更新lowerBound的值。最后，如果搜索时间超过限制并且openList为空，则说明没有找到可行解，返回null；否则，返回找到的最优解的路径。