Question:

(a) Assume you are a taxi driver. Your taxi can hold four passengers. Passengers pay a flat fee for a ride to the airport, so your goal is to pick up four passengers and take them to the airport in the smallest number of miles. Your world will be modelled as a graph of locations with distances between them. Some, but not all, of the locations have passengers that you can pick up.

(i) Explain the state space of this search problem.

(ii) What would be a good cost function for this search problem?

(iii) Now, consider a case where passengers have to pay according to how far away they are from the airport when they are picked up (note: they don't pay according to how long a ride they take in your taxi, but according to the length of the shortest path from their pickup point to the airport). Explain the state space for this search problem.

(iv) What would be a good cost function for this version of the problem? You still have desire to save petrol.

(v) Is uniform cost search guaranteed to find the optimal solution in either or both versions of the problem? Justify your answer.

(b)

Give brief definitions of the following terms:
• Constraint satisfaction problem,
• Back-tracking search
• Forward checking
• Arc consistency