Planning and search. Lecture 1: Introduction and Revision of Search. Lecture 1: Introduction and Revision of Search 1

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1 Planning and search Lecture 1: Introduction and Revision of Search Lecture 1: Introduction and Revision of Search 1

2 Lecturer: Natasha lechina ontact and web page web page: nza/g52ps Textbook: Stuart Russell and Peter Norvig. rtificial Intelligence: Modern pproach, 3rd edition Slides: mostly by Stuart Russell (big thanks!) Lecture 1: Introduction and Revision of Search 2

3 Outline What this module is about Where search and planning fit in I Reminder of uninformed search algorithms Definition of planning Plan of the module What to read for next week Lecture 1: Introduction and Revision of Search 3

4 Simple problem-solving agent: Problem-solving agents function Simple-Problem-Solving-gent( percept) returns an action static: 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 Lecture 1: Introduction and Revision of Search 4

5 Example of a search problem: Romania On holiday in Romania; currently in rad. Flight leaves tomorrow from ucharest Formulate goal: be in ucharest Formulate problem: states: various cities actions: drive between cities Find solution: sequence of cities, e.g., rad, Sibiu, Fagaras, ucharest Lecture 1: Introduction and Revision of Search 5

6 71 Oradea Example: Romania Neamt Zerind 75 rad Timisoara Dobreta 151 Sibiu 99 Fagaras 80 Rimnicu Vilcea Lugoj Mehadia 120 Pitesti ucharest raiova 90 Giurgiu 87 Iasi Urziceni Vaslui Hirsova 86 Eforie Lecture 1: Introduction and Revision of Search 6

7 Single-state problem formulation problem is defined by four items: initial state e.g., at rad successor function S(x) = set of action state pairs e.g., S(rad) = { Drive(rad,Zerind),Zerind,...} goal test, can be explicit, e.g., x = at ucharest implicit, e.g., Hasirport(x) path cost (additive) e.g., sum of distances, number of actions executed, etc. c(x,a,y) is the step cost, assumed to be 0 solution is a sequence of actions leading from the initial state to a goal state Lecture 1: Introduction and Revision of Search 7

8 Selecting a state space Real world is absurdly complex state space must be abstracted for problem solving (bstract) state = set of real states (bstract) action = complex combination of real actions e.g., Drive(rad, Zerind) represents a complex set of possible routes, detours, rest stops, etc. For guaranteed realizability, any real state in rad must get to some real state in Zerind (bstract) solution = set of real paths that are solutions in the real world Each abstract action should be easier than the original problem! Lecture 1: Introduction and Revision of Search 8

9 Example: The 8-puzzle Start State Goal State states?? actions?? goal test?? path cost?? Lecture 1: Introduction and Revision of Search 9

10 Example: The 8-puzzle Start State Goal State states??: integer locations of tiles (ignore intermediate positions) actions?? goal test?? path cost?? Lecture 1: Introduction and Revision of Search 10

11 Example: The 8-puzzle Start State Goal State states??: integer locations of tiles (ignore intermediate positions) actions??: move blank left, right, up, down (ignore unjamming etc.) goal test?? path cost?? Lecture 1: Introduction and Revision of Search 11

12 Example: The 8-puzzle Start State Goal State states??: integer locations of tiles (ignore intermediate positions) actions??: move blank left, right, up, down (ignore unjamming etc.) goal test??: = goal state (given) path cost?? Lecture 1: Introduction and Revision of Search 12

13 Example: The 8-puzzle Start State Goal State states??: integer locations of tiles (ignore intermediate positions) actions??: move blank left, right, up, down (ignore unjamming etc.) goal test??: = goal state (given) path cost??: 1 per move Lecture 1: Introduction and Revision of Search 13

14 Tree search algorithms asic idea: offline, simulated exploration of state space by generating successors of already-explored states (a.k.a. expanding states) function Tree-Search( problem, strategy) returns a solution, or failure initialize the search tree using the initial state of problem loop do if there are no candidates for expansion then return failure choose a leaf node for expansion according to strategy if the node contains a goal state then return the corresponding solution else expand the node and add the resulting nodes to the search tree end Lecture 1: Introduction and Revision of Search 14

15 Tree search example rad Sibiu Timisoara Zerind rad Fagaras Oradea Rimnicu Vilcea rad Lugoj rad Oradea Lecture 1: Introduction and Revision of Search 15

16 Tree search example rad Sibiu Timisoara Zerind rad Fagaras Oradea Rimnicu Vilcea rad Lugoj rad Oradea Lecture 1: Introduction and Revision of Search 16

17 Tree search example rad Sibiu Timisoara Zerind rad Fagaras Oradea Rimnicu Vilcea rad Lugoj rad Oradea Lecture 1: Introduction and Revision of Search 17

18 Implementation: states vs. nodes state is a (representation of) a physical configuration 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! parent, action State Node depth = 6 g = state The Expand function creates new nodes, filling in the various fields and using the SuccessorFn of the problem to create the corresponding states. Lecture 1: Introduction and Revision of Search 18

19 Implementation: general tree search Lecture 1: Introduction and Revision of Search 19

20 function Tree-Search( problem, fringe) returns a solution, or failure fringe Insert(Make-Node(Initial-State[problem]), fringe) loop do if fringe is empty then return failure node Remove-Front(fringe) if Goal-Test(problem, State(node)) then return node fringe Insertll(Expand(node, problem), fringe) function Expand( node, problem) returns a set of nodes successors the empty set for each action, result in Successor-Fn(problem, State[node]) do s a new Node Parent-Node[s] node; ction[s] action; State[s] result Path-ost[s] Path-ost[node] + Step-ost(State[node], action, result) Depth[s] Depth[node] + 1 add s to successors return successors Lecture 1: Introduction and Revision of Search 20

21 Search strategies strategy is defined by picking the order of node expansion Strategies are evaluated along the following dimensions: completeness does it always find a solution if one exists? time complexity number of nodes generated/expanded space complexity maximum number of nodes in memory optimality does it always find a least-cost solution? Time and space complexity are measured in terms of b maximum branching factor of the search tree d depth of the least-cost solution m maximum depth of the state space (may be ) Lecture 1: Introduction and Revision of Search 21

22 Uninformed search strategies Uninformed strategies use only the information available in the problem definition readth-first search Uniform-cost search Depth-first search Depth-limited search Iterative deepening search Lecture 1: Introduction and Revision of Search 22

23 Expand shallowest unexpanded node readth-first search Implementation: fringe is a FIFO queue, i.e., new successors go at end Lecture 1: Introduction and Revision of Search 23

24 Expand shallowest unexpanded node readth-first search Implementation: fringe is a FIFO queue, i.e., new successors go at end Lecture 1: Introduction and Revision of Search 24

25 Expand shallowest unexpanded node readth-first search Implementation: fringe is a FIFO queue, i.e., new successors go at end Lecture 1: Introduction and Revision of Search 25

26 Expand shallowest unexpanded node readth-first search Implementation: fringe is a FIFO queue, i.e., new successors go at end Lecture 1: Introduction and Revision of Search 26

27 Expand least-cost unexpanded node Uniform-cost search Implementation: fringe = queue ordered by path cost, lowest first Equivalent to breadth-first if step costs all equal Lecture 1: Introduction and Revision of Search 27

28 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front H I J K L M N O Lecture 1: Introduction and Revision of Search 28

29 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front H I J K L M N O Lecture 1: Introduction and Revision of Search 29

30 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front H I J K L M N O Lecture 1: Introduction and Revision of Search 30

31 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front H I J K L M N O Lecture 1: Introduction and Revision of Search 31

32 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front H I J K L M N O Lecture 1: Introduction and Revision of Search 32

33 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front H I J K L M N O Lecture 1: Introduction and Revision of Search 33

34 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front H I J K L M N O Lecture 1: Introduction and Revision of Search 34

35 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front H I J K L M N O Lecture 1: Introduction and Revision of Search 35

36 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front H I J K L M N O Lecture 1: Introduction and Revision of Search 36

37 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front H I J K L M N O Lecture 1: Introduction and Revision of Search 37

38 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front H I J K L M N O Lecture 1: Introduction and Revision of Search 38

39 Expand deepest unexpanded node Depth-first search Implementation: fringe = LIFO queue, i.e., put successors at front H I J K L M N O Lecture 1: Introduction and Revision of Search 39

40 Depth-limited search Sometimes DFS does not terminate (infinite branch) Fix: introduce a depth limit l acktrack when reach l (as if found a leaf node) Lecture 1: Introduction and Revision of Search 40

41 Iterative deepening search Do depth-limited search with l = 1, 2, 3,... Lecture 1: Introduction and Revision of Search 41

42 Iterative deepening search l = 0 Limit = 0 Lecture 1: Introduction and Revision of Search 42

43 Iterative deepening search l = 1 Limit = 1 Lecture 1: Introduction and Revision of Search 43

44 Iterative deepening search l = 2 Limit = 2 Lecture 1: Introduction and Revision of Search 44

45 Iterative deepening search l = 3 Limit = 3 H I J K L M N O H I J K L M N O H I J K L M N O H I J K L M N O H I J K L M N O H I J K L M N O H I J K L M N O H I J K L M N O H I J K L M N O H I J K L M N O H I J K L M N O H I J K L M N O Lecture 1: Introduction and Revision of Search 45

46 Summary of basic search algorithms riterion readth- Uniform- Depth- Depth- Iterative First ost First Limited Deepening omplete? Yes a Yes a,b No No (Yes, if l d) Yes a Time O(b d ) O(b /ǫ ) O(b m ) O(b l ) O(b d ) Space O(b d ) O(b /ǫ ) O(bm) O(bl) O(bd) Optimal? Yes c Yes No No Yes c is the cost of the optimal solution, ǫ is the minimal cost of a step, b the branching factor, d the depth of the shallowest solution, m the maximum depth of the search tree, l the depth limit. a complete if b is finite; b complete if step costs ǫ, c optimal if step costs are identical Lecture 1: Introduction and Revision of Search 46

47 Planning Planning: devising a plan of action to achieve the goal (for example: buy milk, bananas, and a cordless drill) lso talking about states of the world and actions, but more sophisticated representation States have structure (properties); actions have pre- and post-conditions. ction: uy(x) Precondition: t(p), Sells(p, x) Effect: Have(x) t(p) Sells(p,x) uy(x) Have(x) Lecture 1: Introduction and Revision of Search 47

48 Search vs. planning contd. Planning systems do the following: 1) open up action and goal representation to allow selection 2) divide-and-conquer by subgoaling 3) relax requirement for sequential construction of solutions Search Planning States Data structures Logical sentences ctions ode Preconditions/outcomes Goal ode Logical sentence (conjunction) Plan Sequence from S 0 onstraints on actions Lecture 1: Introduction and Revision of Search 48

49 Plan of the module: search topics nother revision lecture on properties of uninformed search algorithms, heuristic search ( ) Graph search, direction of search Local search (annealing, tabu,...) Population-based methods (genetic algorithms...) Reducing search to ST Search with non-determinism and partial observability Logical agents; first-order logic Lecture 1: Introduction and Revision of Search 49

50 Plan of the module: planning topics Situation calculus What is classical planning. Forward planning. lassical planning continued. Regression Planning lassical planning continued. Partial-Order Planning lassical planning continued. GraphPlan. lassical planning continued. SatPlan. Planning with time and resources HTN planning. Planning and acting in non-deterministic domains. Lecture 1: Introduction and Revision of Search 50

51 What to read for the next lecture hapter 3 in Russell and Norvig (this is revision) Lecture 1: Introduction and Revision of Search 51