Heuristic Search之Greedy Best First Search

本篇文章介绍Greedy Best Fisrt Search算法。实现GBFS算法时使用了上篇文章介绍的优先队列。下篇文章将尝试介绍著名的A star算法。

Greedy Best-First Search

• use heuristic function as evaluation function: f(n) = h(n)
• always expands the node that is closest to the goal node
• eats the largest chunk out of the remaining distance, hence, “greedy”

The following example is “Touring in Romania”, which is an actual problem for making a plan travelling from Arad to Bucharest, the aim that we use the lowest cost.

example

Touring in Romania: Heuristic

• HSLD(n) = straight-line distance to Bucharest straight-line distance: Euclidean distance
• distance to Bucharest because our goal is to be in Bucharest

[table]

• HSLD(Bucharest) = 0
• HSLD(Fagaras) = 176 < 211 driving distance
• HSLD(n) cannot be computed from the problem description, it represents
  additional information

What’s wrong with GBFS?

for this problem: search proceeds straight to the goal node:

• minimal search cost
• but not the optimal path

Compare to Uniform-Cost Search

• UCS: numbers start from 0 and increase – tendency to expand earlier nodes –
  breadth-first tendency
• UCS的介绍
• GBFS: number start from high and decreases – tendency to expand later nodes
  – depth-first tendency

参考资料

1. 数据结构与算法分析
2. 大话数据结构
3. AI planning 课程资料
4. AI planning Vedio

Code(GBFS)

Path Found:

Arad(366)–>Sibiu(253)–>Fagaras(176)–>Bucharest(0).

package cn.edu.gdut.java.test;import java.util.HashMap;import java.util.Map;import java.util.PriorityQueue;/** * Created by HuGuodong on 2017/10/26. */public class Graph {    private Map<String, AdjList> graph;    /**     * test main     *     * @param args     */    public static void main(String[] args) {        GBFS("Arad", "Bucharest");    }    /**     * algorithm: Greedy Best First Search     * Greedy Best-First Search     * use heuristic function as evaluation function: f(n) = h(n)     * always expands the node that is closest to the goal node     * eats the largest chunk out of the remaining distance, hence, “greedy”     * @param start start node     * @param end   end node     */    public static void GBFS(String start, String end) {        Graph roads = new Graph();        roads.init();        AdjList adjList = roads.graph.get(start);        System.out.println("Greedy Best First Search Starts!");        AdjNode startNode = findNode(adjList, start);        System.out.print("start from node: \n" + start + "(" + startNode.cost + ")" + "-->");        int totalCost = 0;        while (adjList.size() > 0) {            AdjNode nextNode = adjList.poll();            int nodeCost = nextNode.cost;            totalCost += nodeCost;            System.out.print(nextNode.name + "(" + nodeCost + ")-->");            adjList = roads.graph.get(nextNode.name);            if (isExist(adjList, end)) {                int lastNodeCost = adjList.poll().cost;                totalCost += lastNodeCost;                System.out.println(end + "(" + lastNodeCost + ").");                System.out.println("find path! \ntotal cost is : " + totalCost);                return;            }        }    }    /**     * init Touring in Romania road map     */    public void init() {        graph = new HashMap<>();        String name = "Arad";        int cost = 366;        AdjList adjList = new AdjList();        adjList.add(new AdjNode("Arad", 366));        adjList.add(new AdjNode("Zerind", 374));        adjList.add(new AdjNode("Sibiu", 253));        adjList.add(new AdjNode("Timisoara", 329));        graph.put(name, adjList);        name = "Sibiu";        adjList = new AdjList();        adjList.add(new AdjNode("Fagaras", 176));        adjList.add(new AdjNode("Rimnicu", 193));        adjList.add(new AdjNode("Rimnicu", 380));        graph.put(name, adjList);        name = "Fagaras";        adjList = new AdjList();        adjList.add(new AdjNode("Sibiu", 253));        adjList.add(new AdjNode("Bucharest", 0));        graph.put(name, adjList);    }    /**     * whether the node name is in the adjlist     *     * @param adjList     * @param name     * @return     */    public static boolean isExist(AdjList adjList, String name) {        for (AdjNode n :                adjList) {            if (n.name.equals(name)) {                return true;            }        }        return false;    }    /**     * find a node by name     *     * @param adjList     * @param name     * @return     */    public static AdjNode findNode(AdjList adjList, String name) {        for (AdjNode n :                adjList) {            if (n.name.equals(name)) {                return n;            }        }        return null;    }}/** * adjacent list * priority queue */class AdjList extends PriorityQueue<AdjNode> {}/** * adjacent node */class AdjNode implements Comparable<AdjNode> {    String name;    int cost;    public AdjNode(String name, int cost) {        this.name = name;        this.cost = cost;    }    @Override    public int compareTo(AdjNode o) {        return Integer.compare(cost, o.cost);    }    @Override    public String toString() {        return "AdjNode{" +                "name='" + name + '\'' +                ", cost=" + cost +                '}';    }}