Problem Solving by searching, Lecture notes of Artificial Intelligence

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SOLVING PROBLEMS

BY SEARCHING

Nguyễn Ngọc Thảo [email protected] CS420 – Artificial Intelligence

Outline

• Problem-Solving Agents
• Example Problems
• Searching for Solutions

A touring holiday in Romania

What makes a good trip at Arad?

• take in the sights, enjoy the foods, etc.
• avoid hangovers
• … However, there will be your friend’s wedding tomorrow at Bucharest!!!

Goal-based agents

• Intelligent agents are supposed to maximize their

performance measure.

• Different factors for performance measure → making decisions involves many tradeoffs
• Goals help organize behavior by limiting the objectives that

the agent is trying to achieve and the actions it considers.

Traveling from Arad to Bucharest

Goal-based agents in Romania

• The agent initially does not know which road to follow

→ unknown environment, try an action randomly

• Suppose the agent has a map of Romania.

An agent with several immediate options of unknown value

can decide what to do by first examining future actions that

eventually lead to states of known value.

• The agent discovers many hypothetical

journey and finds a journey that

eventually gets to Bucharest.

Solving problem by searching

• Search: the process of looking for a sequence of actions

that reaches the goal

• A search algorithm takes a problem as input and returns a

solution in the form of an action sequence.

• Execution phase: once a solution is found, the

recommended actions are carried out.

• While executing the solution, the agent ignores its percepts when choosing an action → open-loop system

Solving problem by searching

function SIMPLE-PROBLEM-SOLVING-AGENT( percept ) returns an action persistent : seq , an action sequence, initially empty state , some description of the current world state goal , a goal, initially null problem , a problem formulation state ← UPDATE-STATE( state, percept ) if seq is empty then goal ← FORMULATE-GOAL( state ) problem ← FORMULATE-PROBLEM( state, goal ) seq ← SEARCH( problem ) if seq = failure then return a null action action ← FIRST( seq ) seq ← REST( seq ) return action

The state space

• The set of all states reachable from the initial state by any

sequence

• Implicitly defined by the initial state, actions, and transition model
• Directed graph – nodes are states and the links between

nodes are actions.

• A path in the state space is a sequence of states connected by a sequence of actions.

Well-define problems and solutions

• Goal test: determine whether a given state is a goal state
  • The goal is specified by either an explicit set of possible goal states or an abstract property.
  • E.g., 𝐼𝑛(𝐵𝑢𝑐ℎ𝑎𝑟𝑒𝑠𝑡), checkmate
• Path cost: a function that assigns a numeric cost to each

path

• Nonnegative, reflecting the agent’s performance measure
• E.g., 𝑐 𝐼𝑛 𝐴𝑟𝑎𝑑 , 𝐺𝑜 𝑍𝑒𝑟𝑖𝑛𝑑 , 𝐼𝑛 𝑍𝑒𝑟𝑖𝑛𝑑 = 75
• An optimal solution has the lowest path cost.

Formulating problems by abstraction

• Abstraction is critical for automated problem solving
  • Real-world is too detailed to model exactly
  • Create an approximate, simplified, model of the world for the computer to deal with
• The choice of a good abstraction thus involves
  • Removing as much detail as possible while
  • Retaining validity and ensuring that the abstract actions are easy to carry out

Example Problems

• Toy Problems
• Real-world Problems

The Vacuum-cleaner world

• States: determined by both the agent location and the dirt

locations

• 2 × 2 2 = 8 possible world states (𝑛 × 2 𝑛 in general)
• Initial state: Any state can be designated as the initial state.
• Actions: Left, Right, and Suck
• Larger model may include Up and Down, etc.
• Transition model: The actions have their expected effects.
• Except that moving Left in the leftmost square, moving Right in the rightmost square, and Sucking in a clean square have no effect.
• Goal test: whether all the squares are clean
• Path cost: each step costs 1

The Vacuum-cleaner world

The state space for the vacuum world Links denote actions: L = Left, R = Right, S = Suck.