Class Overview. Introduction to Artificial Intelligence COMP 3501 / COMP Lecture 2. Problem Solving Agents. Problem Solving Agents: Assumptions

Transcription

1 Class Overview COMP 3501 / COMP Lecture 2 Prof. JGH 318 Problem Solving Agents Problem Solving Agents: Assumptions Requires a goal Assume world is: Requires actions Observable What actions? Discrete Requires state representation Known How should state be represented? Deterministic

2 Problem Solving Agents: Approach General approach is called search Input: environment, start state, goal state Env.: states, actions, transitions, costs, goal test Output: sequence of actions Sample Domains Vacuum world Sliding-tile puzzle 8-queen puzzle Path planning Actions are executed after planning Percepts are ignored when executing plan Vacuum world Vacuum world States: Initial state: Actions: Transitions: Goal test: Action Cost: States: All combinations of agent & dirt locations [8] Initial state: Any state Actions: Left / Right / Suck Transitions: Left / Right put you in Left / Right cell Suck removes dirt Goal test: No dirt Action Cost: 1 for all actions

3 ld #5. Solution?? Sliding Tile Puzzle States: Initial state: Actions: Transitions: Goal test: Action Cost: Path planning Path planning variations States: Initial state: Actions: Transitions: Chapter 3 8 Chapter 3 8 Traveling sales problem Rectangle packing Robot navigation Multi-agent planning Goal test: Action Cost:

4 Search Terminology Search tree: implicit/explicit set of searched states Node: single state in tree Multiple nodes may represent the same state Expansion: generating the neighbors of a state Children: new neighbors of a state Parent: state from which neighbors were generated General Best-First Search Open list: set of states considered next for expansion Also called search frontier States are ordered by some priority of best Closed list: set of states which have been expanded Not all algorithms maintain a closed list Algorithm Performance Measures Completeness: Will we always find a solution when one exists? Optimality: Will we find the shortest possible solution? Time complexity: How long will it take to find a solution? Space complexity: How much storage is required? Uninformed search strategies

5 Breadth-first search Special case of best-first search Best is by minimum depth Can be implemented by a FIFO queue Breadth-first search Complete? Optimal? Time complexity? Space complexity? Depth-first search Special case of best-first search Best is by maximum depth Can be implemented by a LIFO queue Implications of space complexity?

6 Depth-first search Complete? Optimal? Time complexity? Space complexity? Implications for infinite graphs? Depth-first iterative deepening Iterated depth-first search Iteratively perform depth-first search Each iteration has a depth bound Gradually increase depth bound until a solution is found

7 Depth-first search Complete? Optimal? Time complexity? Space complexity? Uniform-cost (Dijkstra) search Special case of best-first search Best is by minimum cost Priority queue needed to sort nodes by cost g-cost is the cost from the start to current state Uniform-cost search 2 2 Complete? Optimal? Time complexity? Space complexity? 2

8 Uninformed vs. informed search Previous approaches were goal agnostic Given the same start state the search is identical Incorporate information about the goal into the search Heuristic function A heuristic estimates the cost to the goal from a state h(s) or h(s, g) We are interested in admissible heuristics Where h*(s) is a perfect heuristic For an admissible heuristic h(s)! h*(s) for all s. Heuristic function Sometimes assume a heuristic is consistent Obeys the triangle inequality h(a) - h(b)! c(a, b) For undirected graphs g Informed search strategies 1 3 7

9 Greedy best-first search (Pure heuristic search) Special case of best-first search Best is by minimum heuristic value Priority queue needed to sort nodes by cost h-cost is the cost from the start to current state Assume heuristic is distance from leaves S G Greedy best-first search Complete? Optimal? Time complexity? Space complexity?

10 A* Search Special case of best-first search Best is by f-cost, where f(s) = g(s)+h(s) Estimates total path cost through a node to the goal S If heuristic is consistent, f-costs will be monotonically non-decreasing G A* search Complete? Optimal? Time complexity? Space complexity? Iterative-Deepening A* Perform depth-first iterative deepening on f-costs instead of g-costs How do we update the bounds? How do we get our initial bound? Can we do better than A*?

11 S G Assume heuristic is distance from leaves IDA* Uniform Cost Search Complete? Optimal? Time complexity? Space complexity?

12 Greedy Best-First Search Regular A* Weighted A* [f = g+10 h] A* with better heuristic

13 Where do heuristics come from? Exact solution to relaxed version of original problem Relax the constraints in the original problem to make it easier to solve Use solution as heuristic in original problem Heuristics for pathfinding & tsp Pathfinding Normally constrained to move on grid/graph Cannot move through obstacles Relax by allowing straight-line movement Traveling Salesman Problem Must visit all cities in a tour Relax by visiting all cities in minimum spanning tree Heuristics for sliding-tile puzzle Optimized A* What heuristic would you use for the sliding-tile puzzle? Manhattan distance Domain abstraction for pattern databases See Figure 3.30

14 A*: Break ties towards lower g-costs A*: Straight-line heuristic Homework: Problem 3.14