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Introduction to Artificial Intelligence Problem Solving through Search (Goal-based agents) BFS, DFS, Greedy Search Janyl Jumadinova September 12-16, 2016 Example: Romania On holiday in Romania; currently in Arad. Flight leaves tomorrow from

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Introduction to Artificial Intelligence Problem Solving through Search (Goal-based agents) BFS, DFS, Greedy Search

Janyl Jumadinova September 12-16, 2016

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Example: Romania

On holiday in Romania; currently in Arad. Flight leaves tomorrow from Bucharest Formulate goal: be in Bucharest Formulate problem: states: various cities actions: drive between cities Find solution: sequence of cities, e.g., Arad, Sibiu, Fagaras, Bucharest

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Example: Romania

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Tree search algorithms

Basic idea:

ffline, simulated exploration of state space

by generating successors of already-explored states (a.k.a. expanding states)

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Tree search example

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Tree search example

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Tree search example

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Implementation: states vs. nodes

A state is a (representation of) a physical configuration A node is a data structure constituting part of a search tree includes parent, children, depth, path cost g(x) States do not have parents, children, depth, or path cost!

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Breadth-first search

Expand shallowest unexpanded node

◮ FIFO queue, i.e., new successors go at end

A B C D E F G

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Breadth-first search

Expand shallowest unexpanded node

◮ FIFO queue, i.e., new successors go at end

A B C D E F G

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Breadth-first search

Expand shallowest unexpanded node

◮ FIFO queue, i.e., new successors go at end

A B C D E F G

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Breadth-first search

Expand shallowest unexpanded node

◮ FIFO queue, i.e., new successors go at end

A B C D E F G

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Breadth-first search

Arad

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Breadth-first search

Zerind Sibiu Timisoara Arad

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Breadth-first search

Arad Oradea Zerind Sibiu Timisoara Arad

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Breadth-first search

Arad Oradea Rimnicu Vilcea Fagaras Arad Lugoj Arad Oradea Zerind Sibiu Timisoara Arad

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Breadth-first search

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Depth-first search

Expand deepest unexpanded node

◮ LIFO queue, i.e., put successors at front

Arad

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Depth-first search

Expand deepest unexpanded node

◮ LIFO queue, i.e., put successors at front

Zerind Sibiu Timisoara Arad

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Depth-first search

Expand deepest unexpanded node

◮ LIFO queue, i.e., put successors at front

Arad Oradea Zerind Sibiu Timisoara Arad

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Depth-first search

Expand deepest unexpanded node

◮ LIFO queue, i.e., put successors at front

Zerind Sibiu Timisoara Arad Oradea Zerind Sibiu Timisoara Arad

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Best-first search

Idea: use an evaluation function for each node – estimate of “desirability”

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Best-first search

Idea: use an evaluation function for each node – estimate of “desirability” ⇒ Expand most desirable unexpanded node

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Best-first search

Idea: use an evaluation function for each node – estimate of “desirability” ⇒ Expand most desirable unexpanded node Implementation: a queue sorted in decreasing order of desirability

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Best-first search

Idea: use an evaluation function for each node – estimate of “desirability” ⇒ Expand most desirable unexpanded node Implementation: a queue sorted in decreasing order of desirability Special cases: greedy search, A∗ search

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Romania with step costs in km

Bucharest Giurgiu Urziceni Hirsova Eforie Neamt Oradea Zerind Arad Timisoara Lugoj Mehadia Dobreta Craiova Sibiu Fagaras Pitesti Rimnicu Vilcea Vaslui Iasi Straight−line distance to Bucharest 160 242 161 77 151 241 366 193 178 253 329 80 199 244 380 226 234 374 98

Giurgiu Urziceni Hirsova Eforie Neamt Oradea Zerind Arad Timisoara Lugoj Mehadia Dobreta Craiova Sibiu Fagaras Pitesti Vaslui Iasi Rimnicu Vilcea Bucharest

71 75 118 111 70 75 120 151 140 99 80 97 101 211 138 146 85 90 98 142 92 87 86

A* slide

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Greedy search

Evaluation function h(n) (heuristic) = estimate of cost from n to the closest goal Example: h(n) = straight-line distance from n to Bucharest

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Greedy search

Evaluation function h(n) (heuristic) = estimate of cost from n to the closest goal Example: h(n) = straight-line distance from n to Bucharest

◮ Greedy search expands the node that appears to be closest to

goal

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Greedy Search

Arad 366

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Greedy Search

Zerind Arad Sibiu Timisoara 253 329 374

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Greedy Search

Rimnicu Vilcea

Zerind Arad Sibiu Arad Fagaras Oradea Timisoara 329 374 366 176 380 193

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Greedy Search

Rimnicu Vilcea

Zerind Arad Sibiu Arad Fagaras Oradea Timisoara Sibiu Bucharest 329 374 366 380 193 253

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Greedy search

◮ Can get stuck in loops, e.g.,

Iasi → Neamt → Iasi → Neamt → Complete in finite space with repeated-state checking

◮ A good heuristic can give dramatic improvement in search cost 29/38

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http://aispace.org/search/

Explore Best first search (explanation from AIspace: http://www.aispace.org/deduction/help/tut3.shtml)

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A* search

Idea:

avoid expanding paths that are already expensive

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A* search

Idea:

avoid expanding paths that are already expensive

◮ Evaluation function f (n) = g(n) + h(n) ◮ g(n) = cost so far to reach n ◮ h(n) = estimated cost to goal from n ◮ f (n) = estimated total cost of path through n to goal

Romania with step costs

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Example: Romania

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A* Search

Arad 366=0+366

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A* Search

Zerind Arad Sibiu Timisoara 447=118+329 449=75+374 393=140+253

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A* Search

Zerind Arad Sibiu Arad Timisoara

Rimnicu Vilcea

Fagaras Oradea 447=118+329 449=75+374 646=280+366 413=220+193 415=239+176 671=291+380

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A* Search

Zerind Arad Sibiu Arad Timisoara Fagaras Oradea 447=118+329 449=75+374 646=280+366 415=239+176

Rimnicu Vilcea

Craiova Pitesti Sibiu 526=366+160 553=300+253 417=317+100 671=291+380

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A* Search

Zerind Arad Sibiu Arad Timisoara Sibiu Bucharest

Rimnicu Vilcea

Fagaras Oradea Craiova Pitesti Sibiu 447=118+329 449=75+374 646=280+366 591=338+253 450=450+0 526=366+160 553=300+253 417=317+100 671=291+380

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A* Search

Zerind Arad Sibiu Arad Timisoara Sibiu Bucharest

Rimnicu Vilcea

Fagaras Oradea Craiova Pitesti Sibiu Bucharest Craiova

Rimnicu Vilcea

418=418+0 447=118+329 449=75+374 646=280+366 591=338+253 450=450+0 526=366+160 553=300+253 615=455+160 607=414+193 671=291+380

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