#2. Greedy best first search algorithm Solved Example in Artificial Intelligence by Mahesh Huddar

Introduction

In this article, we will explore the Greedy Best First Search algorithm in the context of artificial intelligence through a simple solved example. This example will help illustrate how the algorithm works and its advantages and disadvantages.

Understanding the Greedy Best First Search Algorithm

The Greedy Best First Search algorithm is designed to find the most promising node that is closest to the goal node. The underlying principle is that by expanding the node that appears to be closest to the goal, the algorithm is likely to find a solution more quickly.

In this approach, the algorithm evaluates each node using a heuristic function, represented as ( f(n) = h(n) ). Here, ( h(n) ) is the estimated cost from the current node ( n ) to the goal state. The algorithm selects the node with the lowest ( h(n) ) value and repeats the evaluation until the goal node is reached.

Solved Example

We will illustrate the Greedy Best First Search algorithm with an example graph where ( P ) is the initial state (or start node) and ( S ) is the goal state. The objective is to find a path from ( P ) to ( S ) and calculate the path cost.

Step 1: Evaluating Initial Nodes

From the initial node ( P ), there are three possible paths to analyze:

To node ( A )
To node ( C )
To node ( R )

We will calculate the ( f ) values for these nodes:

( f(A) = h(A) = 11 )
( f(C) = h(C) = 6 )
( f(R) = h(R) = 8 )

Among these, ( C ) has the minimum value of ( 6 ), so we select the path from ( P ) to ( C ).

Step 2: Continuing from Node C

Next, we evaluate the paths available from node ( C ):

To node ( M )
To node ( U )
To node ( R )

We will calculate the ( f ) values again:

( f(M) = h(M) = 9 )
( f(U) = h(U) = 4 )
( f(R) = h(R) = 8 )

The minimum value among these is ( 4 ) from node ( U ), so we select the path from ( C ) to ( U ).

Step 3: Final Evaluation

From node ( U ), we evaluate the final paths:

To node ( S )
To node ( N )

Calculating their ( f ) values:

( f(N) = h(N) = 6 )
( f(S) = h(S) = 0 )

Here, ( S ) has the minimum value, which is ( 0 ). Since ( S ) is the goal node, we have reached our destination.

Conclusion and Path Cost

The path we took to reach the goal node ( S ) is ( P \rightarrow C \rightarrow U \rightarrow S ). The total costs for each segment were ( 4 ), ( 3 ), and ( 4 ) respectively, resulting in a total path cost of ( 11 ).

However, it's important to note the inefficiency of the Greedy Best First Search algorithm. There exists an alternative path ( P \rightarrow R \rightarrow E \rightarrow S ) with a total path cost of ( 10 ). As such, this algorithm does not guarantee an optimal solution since it relies solely on heuristic values and does not consider the actual edge costs.

In summary, the Greedy Best First Search algorithm provides effective solutions in certain scenarios but may not always yield the optimal path due to its greedy nature.

Keyword

Greedy Best First Search, algorithm, artificial intelligence, solved example, goal node, initial node, heuristic function, path cost, optimal solution, edge costs.

FAQ

Q1: What is the Greedy Best First Search algorithm?
A1: The Greedy Best First Search algorithm is a pathfinding algorithm that selects paths based on the heuristic function, evaluating nodes that seem closest to the goal to find solutions quickly.

Q2: How does the Greedy Best First Search algorithm evaluate nodes?
A2: The algorithm evaluates nodes using the heuristic function ( f(n) = h(n) ), which estimates the cost from the current node to the goal node.

Q3: Does the Greedy Best First Search guarantee an optimal solution?
A3: No, the Greedy Best First Search algorithm does not guarantee an optimal solution as it prioritizes nodes based on heuristic values rather than the actual path costs.

Q4: Can you provide an example of the Greedy Best First Search algorithm?
A4: An example is finding a path from node ( P ) to node ( S ). The algorithm selects nodes ( C ) and ( U ) based on the lowest heuristic values before finally reaching ( S ), but the path cost might not be optimal.