Problem Formulation in AI

✅ Problem Formulation in AI

Problem formulation is the process of defining a search problem in terms of:

Initial State – The starting point.
Goal Test – The condition that defines a successful outcome.
Successor Function – All possible actions and resulting states.
Cost Function – The cost associated with each step or path.

Below are the formulations for the given problems:

i. 🚕 Autonomous Taxi Driver

Initial State: Taxi is at a certain location, passenger(s) at pickup location(s), destination(s) known.
Goal Test: All passengers are dropped off at their respective destinations.
Successor Function: Move to adjacent location, pick up a passenger, drop off a passenger.
Cost Function: Distance travelled (e.g., number of blocks), fuel consumption, or time taken.

ii. 🕳️ Wumpus World Problem

Initial State: Agent in the start square (usually [1,1]), with no knowledge of Wumpus/pit locations.
Goal Test: Agent has found the gold and returned safely to the start square.
Successor Function: Move forward, turn left/right, grab gold, shoot arrow, climb out.
Cost Function: Each action has a cost (e.g., -1 per move, -10 for using arrow, +1000 for gold), minimizing danger and maximizing score.

iii. 🐒 Monkey and Bananas Problem

Initial State: Monkey at location A, crates at different locations, bananas hanging from the ceiling.
Goal Test: Monkey has bananas in hand.
Successor Function: Move monkey, move crates, stack crates, climb crate, grab bananas.
Cost Function: Number of actions or time steps taken to obtain bananas.

iv. 🔢 8-Puzzle Problem

Initial State: Any random configuration of 8 numbered tiles and 1 blank on a 3x3 grid.
Goal Test: Tiles arranged in order:
```
1 2 3  
4 5 6  
7 8 _
```
Successor Function: Move the blank tile (up, down, left, right) to swap with adjacent tile.
Cost Function: Each move costs 1; total path cost is the number of moves.

These formulations are designed to be precise and implementable for designing intelligent agents or search algorithms.