Searching for Solutions

1. Introduction

In Artificial Intelligence (AI), most problems can be expressed as a search problem. Searching for solutions means systematically exploring possible states of a problem until we reach the goal state.

• Example:

  • Solving a maze → start point to exit point.

  • Playing chess → finding the best sequence of moves.

  • Route planning in Google Maps → finding the shortest/fastest path.

Thus, searching for solutions is the process of navigating through a problem space to discover the correct path to the goal.

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2. Problem Formulation for Searching

To search for a solution, a problem must be formally defined with the following components:

1. Initial State → The starting point of the problem.

2. State Space → All possible states reachable from the initial state.

3. Actions/Operators → Possible moves from one state to another.

4. Transition Model → Defines how actions change the current state.

5. Goal Test → A check to determine whether the goal state has been reached.

6. Path Cost → A numeric value (cost, distance, time) associated with a solution path.

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3. Searching Process

The general process of searching for solutions involves:

1. Represent the Problem → Convert into a state space representation.

2. Expand Nodes → Generate successors of the current state.

3. Choose Search Strategy → Decide which node to explore next.

4. Apply Goal Test → Stop when the goal state is found.

5. Construct Solution Path → Trace back from the goal to initial state.

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4. Types of Search Strategies

A) Uninformed (Blind) Search

• Does not use additional knowledge beyond the problem definition.

• Examples:

  • Breadth-First Search (BFS): Explores level by level, guarantees shortest path.

  • Depth-First Search (DFS): Explores deeply before backtracking.

  • Uniform Cost Search (UCS): Expands least-cost node first.

B) Informed (Heuristic) Search

• Uses heuristics (extra knowledge) to guide the search more efficiently.

• Examples:

  • Greedy Best-First Search: Chooses node with lowest heuristic value.

  • A* Search: Combines path cost + heuristic (optimal and efficient).

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5. Example: Searching in a Maze

• Initial State: Start point of maze.

• Goal State: Exit point.

• Operators: Move up, down, left, right.

• Solution: Sequence of moves to reach exit.

• Search Method:

  • BFS → Finds shortest path.

  • DFS → May get stuck in dead ends.

  • A* → Fastest + optimal solution using distance heuristic.

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6. Evaluation of Search Strategies

When searching for solutions, algorithms are compared based on:

• Completeness: Will it always find a solution if one exists?

• Optimality: Will it find the best solution?

• Time Complexity: How fast is the search?

• Space Complexity: How much memory is needed?

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7. Summary

• Searching for solutions is the core of AI problem solving.

• It involves state space exploration using systematic search strategies.

• Two major categories: Uninformed search (blind) and Informed search (heuristic-based).

• The choice of search strategy affects efficiency, optimality, and memory usage.

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