Best-First Search (BFS) is an informed search algorithm that explores a search space by selecting nodes estimated to be closer to the goal. Unlike uninformed search algorithms such as Breadth-First Search or Depth-First Search, BFS uses a heuristic function to guide the search efficiently, making it suitable for large search spaces.

Key Concepts:

1. Heuristic Function (h(n)):

   • Estimates the distance or cost from the current node to the goal.
   • Guides the algorithm to select the most promising node first.
   • Example: Euclidean distance or Manhattan distance between nodes.

2. Priority Queue (Open List):

   • Stores nodes yet to be explored.
   • Nodes with lower heuristic values (closer to goal) are given higher priority.
   • Ensures efficient selection of nodes during search.

3. Node Expansion:

   • The algorithm expands the current node to explore its neighbors.
   • For each neighbor, the heuristic value is calculated.
   • Neighboring nodes are added to the priority queue according to their heuristic values.

4. Node Selection:

   • The next node to expand is selected from the priority queue based on the lowest heuristic value.
   • This node is considered the most promising path toward the goal.

5. Goal Test:

   • The search stops when the selected node is the goal.
   • If the goal is found, the path from start to goal is returned as the solution.

6. Iteration:

   • If the selected node is not the goal:
     • Expand its neighboring nodes.
     • Calculate heuristic values for neighbors.
     • Add neighbors to the priority queue.
   • Repeat until the goal is reached or the priority queue is empty.

7. Termination:

   • If the priority queue becomes empty and the goal is not found, the search terminates without a solution.
   • BFS may not always find the shortest path unless the heuristic is admissible.

Advantages:

• Faster than uninformed search algorithms.
• Focuses on promising paths toward the goal.

Drawbacks:

• Not guaranteed to find the optimal path with a non-admissible heuristic.
• Can get stuck in local minima if heuristic is misleading.