Introduction to Artificial Intelligence CS 438 Spring 2008 Today –AIMA, Ch. 3 –Problem Solving Agents State space search –Programming Assignment Thursday –AIMA, Ch. 3 –Uniformed Search Can your IA make you money as a gold farmer?

Goal-based Problem Solving To develop an IA there two major concerns –KR –Search Method Assume for right now that knowledge is encoded in some form that it can be easily retrieved and applied

Goal Formulation Goal –A state of the environment that meets some desirable property or properties –Examples Chess: checkmate (opponents king cannot avoid capture) Path finding: being in a specific geographic location Robot Vacuum: Clear floor Goals may include factors that determine which solutions are more desirable than others –Speed, shortest path, safety

Goal Formulation Before you can decide what to do you must determine what it is you are trying to do –Take an “intentional stance” D. Dennett –“Goals help organize the behavior by limiting the objectives that the agent is trying to achieve” p. 60 –Given all possible actions to take, some can be rejected outright because they are not relevant of the agent reaching its goals.

State-space Search Search –The activity of looking for a sequence of actions that solves (achieves) the goal (goal state) State-space –Defined by the initial state, the actions the agent can take to go from one state to the other, and goal state

State-space search Path –Any sequence of action that leads from one state to another Solution –A path starting at the initial state and leading to the goal state Path cost –Sum of the cost of each action –g(n) cost of path from initial state to state n –Note that path cost differs from “search cost”, which refers to the computational complexity of the search algorithm

Problem Formation Initial State –State the agent starts in Actions available to the agent –Defines actions that allow IA to transform one state into another –Successor function: S(x) given state x returns set of new states given each applicable action (action-state pairs) Goal test –Determines if a state meets the specific properties of the goal Path cost –Function assigns a cost to a solution path

Example: Romania

Single-state problem formulation 1.initial state: "at Arad" 2.actions or successor function S(x) = set of action–state pairs –S(Arad) = {, … } 3.goal test – x = "at Bucharest" 4.path cost (additive) –sum of distances, number of actions executed, etc.

Example: The 8-puzzle states? actions? goal test? path cost?

Example: The 8-puzzle states? locations of tiles actions? move blank left, right, up, down goal test? = goal state (given) path cost? 1 per move

Example: robotic assembly states?: real-valued coordinates of robot joint angles parts of the object to be assembled actions?: continuous motions of robot joints goal test?: complete assembly path cost?: time to execute

Example: Water Jug Problem Goal formulation: measure precisely 2 gallons of water Problem formulation –Two jugs 4 gallon jug with x amount of water 3 gallon jug with y amount of water –Initial state (0,0) : both jugs empty –Goal (2, y) or (x, 2) –Path cost: 1 unit for each pouring action

Water Jug Problem Actions:

Search Expanding a state –Generating new states by applying possible (valid) actions to current state using the successor function S(x) Search Tree –Root is the initial state –Each expanded state is a search node Search Node –Encodes the state, parent node, action applied, depth, and path cost

Example: Water Jug Problem