Comp3710 Artificial Intelligence Thompson Rivers University

Comp3710 Artificial Intelligence Thompson Rivers University
Search Methodologies Comp3710 Artificial Intelligence Computing Science Thompson Rivers University

Course Outline Part I – Introduction to Artificial Intelligence
Part II – Classical Artificial Intelligence, and Searching Knowledge Representation Searching Search Methodologies Advanced Search Knowledge Represenation and Automated Reasoning Propositinoal and Predicate Logic Inference and Resolution for Problem Solving Rules and Expert Systems Part III – Machine Learning Part IV – Some Advanced Topics TRU-COMP3710 Search Methodologies

Chapter Learning Outcomes
Decide if DFS (Depth First Search) and/or BFS (Breadth First Search) is complete and/or admissible on a tree and/or a graph. Define what an admissible heuristic is. Write a pseudo A* algorithm. Given two heuristics, decide which one is better. Given expanded states within a running A* algorithm, decide the next state to visit. Design and implement a JavaScript program for the n-puzzle game, using an A* algorithm. Use of Hill Climbing for the 4-queens game. TRU-COMP3710 Search Methodologies

Chapter Outline Introduction Problem Solving as Search
Data-Driven and Goal-Driven Search Generate and Test Depth-First Search Breadth-First Search Properties of Search Methods Why Humans Use Depth-First Search Implementing Depth-First and Breadth-First Search Example: Web Spidering Depth-First Iterative Deepening Using Heuristics for Search Hill Climing Best-First Search Beam Search Identifying Optimal Paths TRU-COMP3710 Search Methodologies

Two types of search problems
Goal is known. A solution is to find a best path from the start node to a goal node. Type 2 Goal is not known. A solution is to find a goal that satisfies certain conditions. Type 1 Type 2 Is a goal known? Yes No What is a solution? A best path from the start node to a goal node. A goal node Examples 3 missionaries and 3 cannibals, The tower of Hanoi Navigation system n-Queens Graph coloring TRU-COMP3710 Search Methodologies

Brute Force Search Search methods that examine every node (i.e., state) in the search space – also called exhaustive. It does not say the search order. ‘Generate and Test’ is the simplest brute force search method: Generate all the possible solutions to the problem. Test each one in turn to see if it is a valid solution. Stop when a valid solution is found. The method used to generate possible solutions must be carefully chosen. [Q] Can brute force search find any solution? [Q] What if there are too many possible solutions, i.e., states in the search space? [Q] There could be so many states. Any better ideas? Not to create all the possible states in the beginning. Generate states while the search is running. TRU-COMP3710 Search Methodologies

Depth-First Search (DFS)
Another exhaustive search method. Follows each path to its deepest node, before backtracking to try the next path. [Q] Does the algorithm always find an unique solution in a tree? [Q] Does the algorithm always find an optimal solution in a graph? [Q] A search traversal in the next example is ? [Q] How to implement? A C B G F E D A C B G F E D TRU-COMP3710 Search Methodologies

Breadth-First Search (BFS)
Another exhaustive search method. Follows each path to a given depth before moving on to the next depth. [Q] Does the algorithm always find an unique solution in a tree? [Q] How about a graph? Optimal solution? [Q] A search traversal in the next example is ? [Q] How to implement? A C B G F E D A C B G F E D TRU-COMP3710 Search Methodologies

[Q] How about non-uniform graphs?
When a graph includes negative edge values, search methods on the graph might go over a cycle infinitely. (Note that it depends on search algorithms.) Let’s assume that any edge value on a search graph is positive in this course. Let’s assume also that there is maximum one edge between two nodes. Let’s assume a graph has an uniform value, e.g., 1, on all the edges. (Note that DFS and BFS use the strategy that they do not revisit any node.) [Q] Can DFS find a solution? Can DFS find an optimal solution? A solution is ??? Yes, and NOT always. [Q] Why not? [Q] Can BFS find a solution? Can BFS find an optimal solution? Yes, and YES. [Q] How about non-uniform graphs? S A B C G S, A, C, G is not optimal. TRU-COMP3710 Search Methodologies

Let’s assume a graph has non-uniform values on edges
Let’s assume a graph has non-uniform values on edges. (Note that DFS and BFS use the strategy that they do not revisit any node.) [Q] Can DFS find a solution? Can DFS find an optimal solution? Yes, and NOT always. [Q] Can you give an example? [Q] Can BFS find a solution? Can BFS find an optimal solution? [Q] Why not? We need search methods that traverse in the manner of acyclic directed graph over the given search space (graph). (Note that a solution is a path to a goal node and we need to construct the path.) S A B C G 1 5 D 3 TRU-COMP3710 Search Methodologies

It is important to choose the correct search method for a given problem.
In some situations, for example, depth first search will never find a solution, even though one exists. [Q] Can you give an example of this case? TRU-COMP3710 Search Methodologies

Properties of Search Methods
Complexity How much time and memory the method uses. Completeness A complete method is the one that is guaranteed to find a goal if one exists. Optimality & Admissibility A method is called optimal (or admissible) if it is guaranteed to find a best path to a goal. [Q] Is an admissible method complete? [Q] Is a complete method admissible? Irrevocability A method is irrevocable if, like hill climbing, it does not ever back-track. [Q] Assuming a tree with uniform edge values, Is DFS complete? Is DFS admissible? Is BFS complete? Is BFS admissible? [Q] Assuming a tree with non-uniform edge values, [Q] Assuming a graph with uniform edge values, TRU-COMP3710 Search Methodologies

Implementations Generic search algorithm:
The start node; // expansion While Select a non-visited node; // using an evaluation function Visit the node; Test if the node is a goal, then stop; // using a goal test function Otherwise, expand the neighbors; // What if a neighbor was expanded before? Implementation: Two lists of nodes are used. Visited nodes Expanded nodes that are not visited. [Q] BTW, how to implement depth-first search? Stack [Q] How to implement breadth-first search? Queue [Q] Data structure for graphs? TRU-COMP3710 Search Methodologies

DFS – Expanded[] is a stack
B C G 1 5 D 3 DFS – Expanded[] is a stack Expanded: [S]; Visited: [] Visiting S, and expanding A, B Expanded: [A, B]; Visited: [S] Visiting B, and expanding S Expanded: [A]; Visited: [S, B] Visiting A, and expanding D, G, C, S Expanded: [D, G, C]; Visited: [S, B, A] [Q] What about S? Visiting C, and expanding A, D Expanded: [D, G, D]; Visited: [S, B, A, C] Visiting D, and expanding A, C, G Expanded: [D, G, G]; Visited: [S, B, A, C, D] Visiting G, and found the goal. [Q] What is the solution? How to obtain the solution? [Q] Can you trace BFS too? TRU-COMP371 Introduction

DFS – Expanded[] is a stack
Can you try BFS instead? S A B C G 1 5 D 3 DFS – Expanded[] is a stack Expanded: [S]; Visited: [] Visiting S, and expanding A, B Expanded: [(A,S), (B,S)]; Visited: [S] Visiting (B,S) and expanding S Expanded: [(A,S)]; Visited: [S, (B,S)] Visiting (A,S), and expanding D, G, C, S Expanded: [(D,A), (G,A), (C,A)]; Visited: [S, (B,S), (A,S)] Visiting (C,A), and expanding A, D Expanded: [(D,A), (G,A), (D,C)]; Visited: [S, (B,S), (A,S), (C,A)] Visiting (D,C), and expanding A, C, G Expanded: [(D,A), (G,A), (G,D)]; Visited: [S, (B,S), (A,S), (C,A), (D,C)] Visiting (G,D), and found the goal. Visited: [S, (B,S), (A,S), (C,A), (D,C), (G,D)] [Q] What is the solution? (G,D), (D,C), (C,A), (A,S), S => S –> A –> C -> D -> G What about the cost of the path? TRU-COMP371 Introduction

Depth-First Iterative Deepening
An exhaustive search method based on both depth-first and breadth-first search. Carries out depth-first search to depth of 1, then to depth of 2, 3, and so on until a goal node is found. Efficient in memory use, and can cope with infinitely long branches. Not as inefficient in time as it might appear, particularly for very large trees, in which it only needs to examine the largest row (the last one) once. [Q] The search path in the next example is ? S A B C G 1 5 D 3 TRU-COMP3710 Search Methodologies

It’s like seeing tomorrow, not past, not future.
Best-First Search It’s like seeing tomorrow, not past, not future. Picks the most likely path (based on heuristic value) from the partially expanded tree at each stage; No revisiting strategy. Tends to find a shorter path than depth-first or breadth-first search, but does not guarantee to find the best path in a graph. [Q] What is the search path in the next example? Is the result the best path? [Q] What if the costs are all the same? [Q] Complete? Admissible? A solution? [Q] Is this idea useful or useless? S A B C G 1 3 D 2 TRU-COMP3710 Search Methodologies

Best First Search [Q] What is the solution?
G 1 5 D 3 Best First Search Expanded: [(S,0)]; Visited: [] Visiting S, and expanding A, B Expanded: [(A,1,S), (B,1,S)]; Visited: [(S,0)] Visiting (B,1,S), and expanding S Expanded: [(A,1,S)]; Visited: [(S,0), (B,1,S)] Visiting (A,1,S), and expanding D, C, G, S Expanded: [(D,3,A), (C,1,A), (G,5,A)]; Visited: [(S,0), (B,1,S), (A,1,S)] Visiting (C,1,A), and expanding A, D Expanded: [(D,3,A), (G,5,A), (D,1,C)]; Visited: [(S,0), (B,1,S), (A,1,S), (C,1,A)] Visiting (D,1,C), and expanding A, C, G Expanded: [(D,3,A), (G,5,A), (G,1,D)]; Visited: [(S,0), (B,1,S), (A,1,S), (C,1,A), (D,1,C)] Visiting (G,1,D), and found the goal. [Q] What is the solution? (G,1,D), (D,1,C), (C,1,A), (A,1,S), (S,0) => S –> A –> C -> D -> G Length = = 4 TRU-COMP371 Introduction

Beam Search Breadth-first method.
Only expands the best few paths at each level. Thus has the memory advantages of depth-first search. Not exhaustive, and so may not find the best solution. May not find a solution at all. [Q] Complete? Admissible? [Q] What’s the point of using Beam Search? All the search methods so far have too large time complexity. [Q] What do we have to do? We need some better ideas. TRU-COMP3710 Search Methodologies

Dijkstra’s shortest path algorithm
Past information S A B C G 1 5 D 3 Selection strategy: The distances from the start node are used instead. Minimum priority queue Expanded: [(S,0)]; Visited: [] Visiting S, and expanding A, B Expanded: [(A,1,S), (B,1,S)]; Visited: [(S,0)] Visiting (B,1,S), and expanding S Expanded: [(A,1,S)]; Visited: [(S,0), (B,1,S)] Visiting (A,1,S), and expanding C, D, G, S Expanded: [(D,4,A), (C,2,A), (G,6,A)]; Visited: [(S,0), (B,1,S), (A,1,S)] Visiting (C,2,A), and expanding A, D; c(C,D) is = 3 Expanded: [(D,3,C), (G,6,A)]; Visited: [(S,0), (B,1,S), (A,1,S), (C,2,A)] Visiting (D,3,C), and expanding A, C, G; c(D,G) is = 4 Expanded: [(G,4,D)]; Visited: [(S,0), (B,1,S), (A,1,S), (C,2,A), (D,3,C)] Visiting (G,4,D), and found the goal. [Q] What is the solution? (G,4,D), (D,3,C), (C,2,A), (A,1,S), (S,0) => S –> A –> C -> D -> G Length = 4 D is updated with (D,3,C)

Entire future information
Heuristics Heuristic: a rule or other piece of information that is used to make methods, such as search, more efficient or effective. In search, often use a heuristic evaluation function, h(n): h(n) tells you the approximate distance (or cost) from a node, n, to a goal node. h(n) may not be 100% accurate, but it should give better results than pure guesswork. Entire future information TRU-COMP3710 Search Methodologies

Heuristics – How Informed?
In general, the more informed a heuristic is, the better it will perform. Heuristic h1 is called more informed than h2, if: h1 (n)  h2(n) for all nodes n. In general, a search method using h1 will search more efficiently than one using h2. A heuristic should reduce the number of nodes that need to be examined. [Q] Can you solve the 8-puzzle game? [Q] Can you find any good heuristic for the 8-puzzle game? [Q] Can you decide which heuristic is better? The more informed, the better. Goal [Q] Which one do you want to move first? h1: the sum of Manhatan distances h1(left) = 5 h2: the number of miss tiles h2(left) = 4 [Q] Which one is more informed? TRU-COMP3710 Search Methodologies

Optimal Paths An optimal path is one that is the shortest possible path from start to goal. In other words, an optimal path has the lowest cost (not necessarily at the shallowest depth, if edges have costs associated with them). How to find an optimal path? Check all the possible paths? There are more efficient ways. We need to use some good heuristics. [Q] Which ones then? TRU-COMP3710 Search Methodologies

Heuristics – admissible
Definition: A heuristic h(n) is admissible if, for every node n, h(n) ≤ h*(n), where h*(n) is the true cost to reach the goal state from n. An admissible heuristic never overestimates the cost to reach the goal, i.e., it is optimistic. Examples: hSLD(n) (never overestimates the actual road distance) on a map h(n) = 0 for all n. Dijkstra’s shortest path algorithm. [Q] Can you give admissible heuristics for the 8-puzzle game? h1: the sum of Manhatan distances h1(left) = 5 h2: the number of miss tiles h2(left) = 4 h3: ZERO function h3(left) = 0 TRU-COMP3710 Search Methodologies

Optimal Path – A* Algorithms
Uses the cost function: f(node) = g(node) + h(node), where g(node) is the cost of the path so far leading to the node from the start node. h(node) is an underestimate of how far the node is from a goal node. (This is the definition of an admissible heuristic.) f is a path-based evaluation function. An A* algorithm expands paths from nodes that have the lowest f value until the algorithm visits, not expands, the goal node. Theorem: If h(n) is admissible, A* using h is optimal. [Q] Which admissible heuristic is better? [Q] When two admissible heuristics satisfy h1(n)  h2(n) for all nodes n, which one is better? Past info Future info TRU-COMP3710 Search Methodologies

Optimal Path – A* Algorithms
A* algorithms are optimal, i.e., they are guaranteed to find the shortest path to a goal node, provided h(node) is always an underestimate. (This is the definition of an admissible heuristic.) A* methods are also optimally efficient – they expand the fewest possible paths to find the right one. If h is not admissible, the method is called A, rather than A*. Algorithm: expand the start node; while (the queue is not empty) select the next node to visit from the expanded node queue; // A non-visited node having the smallest f-value visit the node; test if the node is a goal; if so, break the loop; expand nodes; // Any visited nodes are excluded. // The g-values of some nodes that were already // expanded might be updated. Do you remember Dijkstra’s algorithm? TRU-COMP3710

Extreme example [Q] zero is an admissible heuristic? [Q] How about Dijkstra’s shortest path algorithm? Like A*, but uses: f(node) = g(node). g(node) is the cost of the path leading up to node. I.e., h(node) = 0. Even when a goal node is expanded (at the child node expansion; still not visited yet), the method needs to continue to run in case a preferable solution is found, till a goal node is visited. TRU-COMP3710 Search Methodologies

Let’s use the heuristic of Manhatan distances. \
Let’s expand the current node (283, 164, 705), then 283, 104, 765 g = 0+1; h = 4; f = 5 283, 164, 075 g = 0+1; h = 6; f = 7 283, 164, 750 g = 0+1; h = 6; f = 7 283, 104, 765 (g=1) is selected and visited. Let’s expand this new node. 283, 164, 075 g = 1; h = 6; f = previous ones in the queue 283, 164, 750 g = 1; h = 6; f = 7 203, 184, 765 g = 1+1; h = 3; f = new ones 283, 014, 765 g = 1+1; h = 5; f = 7 283, 140, 765 g = 1+1; h = 5; f = 7 283, 164, visited already The cost to move to the next node is always 1.

283, 104, 765 (g=1) is selected and visited. Let’s expand this new node.
283, 164, 075 g = 1; h = 6; f = previous ones in the queue 283, 164, 750 g = 1; h = 6; f = 7 203, 184, 765 g = 2; h = 3; f = new ones 283, 014, 765 g = 2; h = 5; f = 7 283, 140, 765 g = 2; h = 5; f = 7 203, 184, 765 (g=2) is selected and visited. Let’s expand this new node. 283, 164, 075 g = 1; h = 6; f = 7 023, 184, 765 g = 2+1; h = 2; f = 5 230, 184, 765 g = 2+1; h = 4; f = 7 283, 104, visited already 023, 184, 765 (g=3) is selected and visited. Let’s expand this new node.

123, 804, 765 (g=5) is selected and visited. This is the goal node.
023, 184, 765 (g=3) is selected and visited. Let’s expand this new node. 283, 164, 075 g = 1; h = 6; f = 7 283, 164, 750 g = 1; h = 6; f = 7 283, 014, 765 g = 2; h = 5; f = 7 283, 140, 765 g = 2; h = 5; f = 7 230, 184, 765 g = 3; h = 4; f = 7 123, 084, 765 g = 3+1; h = 1; f = 5 283, 104, visited already 123, 084, 765 (g=4) is selected and visited. Let’s expand this new node. 023, 184, visited already 123, 804, 765 g = 4+1; h = 0; f = 5 123, 784, 065 g = 4+1; h = 2; f = 7 123, 804, 765 (g=5) is selected and visited. This is the goal node.

123, 804, 765 (g=5) is selected and visited. This is the goal node.
[Q] How to construct the path from the start node to the goal node? Back tracking We need to keep the track of the parent node at the expansion step. When a node is newly expanded, or When an expanded node is updated with a smaller g-value. What data structure can be used? Stack

[Q] Can you try the Dijkstra’s shortest path algorithm with the next graph?
B C G 1 5 D 3

Optimal Path – with no heuristic
From Arad to Bucharest Using the heuristic hZERO TRU-COMP3710 Search Methodologies

[Q] How many nodes are visited?
Arad(0): Zerind(75:Ar); Sibiu (140:Ar); Timisoara(118:Ar) Zerind(75:Ar): Oradea(75+71:Ze); Sibiu(140:Ar); Timisoara(118:Ar) Timisoara(118:Ar): Lugoj( :Ti); Oradea(146:Ze); Sibiu(140:Ar) Sibiu(140:Ar): Oradea( :Si); Rimnicu(140+80:Si); Fagaras(140+99:Si); Lugoj(229:Ti); Oradea(146:Ze) Oradea(146): Rimnicu(220:Si); Fagaras(239:Si); Lugoj(229:Ti) Rimnicu(220:Si): Craiova( :Ri); Pitesti(220+97:Ri); Fagaras(239:Si); Lugoj(229:Ti) Lugoj(229:Ti): Mehadia(229+70:Lu); Craiova(366:Ri); Pitesti(317:Ri); Fagaras(239:Si) Fagaras(239:Si): Bucharest( :Fa); Mehadia(299:Lu); Craiova(366:Ri); Pitesti(317:Ri) Mehadia(299:Lu): Dobreta(299+75:Me); Bucharest(450:Fa); Craiova(366:Ri); Pitesti(317:Ri) Pitesti(317:Ri): Bucharest( :Pi); Bucharest(450:Fa); Dobreta(374:Me); Craiova(366:Ri) Craiova(366:Ri): Dobreta( :Cr); Dobreta(374:Me); Bucharest(418:Pi) Dobreta(374:Me): Bucharest(418:Pi) Bucharest(418:Pi) [Q] The solution? [Q] How many nodes are visited? TRU-COMP3710 Search Methodologies

Optimal Path – more informed heuristic
Your project for BC? From Arad to Bucharest Using the heuristic hSLD Additional information TRU-COMP3710 Search Methodologies

[Q] How many nodes are visited?
Arad(0): Zerind(75+374:Ar); Sibiu ( :Ar); Timisoara( :Ar) Sibiu(140:Ar): Oradea(( )+380:Si); Fagaras((140+99)+176:Si); Rimnicu((140+80)+193:Si); Zerind(75+374:Ar); Timisoara( :Ar) Rimnicu(220:Si): Craiova( :Ri); Pitesti( :Ri); Oradea( :Si); Fagaras( :Si); Zerind(75+374:Ar); Timisoara( :Ar) Fagaras(239:Si): Bucharest( :Fa); Craiova( :Ri); Pitesti( :Ri); Oradea( :Si); Zerind(75+374:Ar); Timisoara( :Ar) Pitesti(317:Ri): Craiova( :Pi); Bucharest( :Pi); Bucharest(450+0:Fa); Craiova( :Ri); Oradea( :Si); Zerind(75+374:Ar); Timisoara( :Ar) Bucharest(418:Pi) [Q] How many nodes are visited? TRU-COMP3710 Search Methodologies

h1: the sum of Manhatan distances h1(left) = 5
(0+5): (1+4); (1+6); (1+6) (1+4): (2+3); (2+5); (2+5); (1+6); (1+6) (2+3): (3+2); (3+4); (2+5); (2+5); (1+6); (1+6) (3+2): (4+1); (3+4); (2+5); (2+5); (1+6); (1+6) (4+1); (5+2); (5+0); (3+4); (2+5); (2+5); (1+6); (1+6) (5+0) [Q] How many times do you need to move? h1: the sum of Manhatan distances h1(left) = 5 TRU-COMP3710 Search Methodologies

[Q] How to implement the 8-puzzle game?
[Q] Is the n-puzzle game always solvable from any start node? No, only half Algorithm again? expand the start node; while (the queue is not empty) select the next node to visit from the expanded node queue; // A non-visited node having the smallest f-value visit the node; test if the node is a goal; if so, break the loop; expand nodes; // Any visited nodes are excluded. // The g-values of some nodes // that were already expanded might be updated. TRU-COMP3710 Search Methodologies

Project idea A* algorithm with hSLD for BC map (not whole BC)
Rubik’s cube n-Puzzle game is still slow even if A* algorithm is used. Can you develop better heuristics? TRU-COMP3710 Search Methodologies

Optimal Path – Greedy Search
Similar to A*, but uses: f(node) = h(node). Hence, always expands the node that appears to be closest to a goal, regardless of what has gone before. We humans often use this approach. Not optimal, and not guaranteed to find a solution. Can easily be fooled into taking poor paths. [Q] Can you give an example? The previous example of map search problem. TRU-COMP3710 Search Methodologies

Two types of search problems
Goal is known. A solution is to find a best path from the start node to a goal node. Type 2 Goal is not known. A solution is to find a goal. Type 1 Type 2 Is a goal known? Yes No What is a solution? A best path from the start node to a goal node. A goal node Examples 3 missionaries and 3 cannibals, The tower of Hanoi Algorithm A* TRU-COMP3710 Search Methodologies

Local Search Algorithms
In the previous problems, we know what a goal state is. However, in many optimization problems, the path to the goal is irrelevant; the goal state itself is the solution. E.g., How to find the highest mountain in BC? [Q] Can we make any good heuristic? [Q] Can we use A* algorithms? Why? State space = set of "complete" configurations Find configuration satisfying constraints, e.g., n-queens. (We do not have to consider of the order of move.) In such cases, we can use local search algorithms. Keep a single "current" state, and try to improve it. [Q] Isn’t it a greedy approach? TRU-COMP3710 Heuristic Search

Example: n-queens Problem: Put n queens on an n × n board with no two queens on the same row, column, or diagonal. [Q] What is a goal state? How do we solve? [Q] Can we use a local search algorithm with a start state that can be made randomly? Which one do you want to move first? TRU-COMP3710 Heuristic Search

Cannot know if it is the highest.
Hill Climbing A local search algorithm An informed, irrevocable (i.e., no back-tracking) local search method. Just a question. [Q] Why do you need irrevocable methods? Easiest to understand when considered as a method for finding the highest point in a three dimensional search space: Check the height one foot away from your current location in each direction; North, South, East and West. As soon as you find a position whose height is higher than your current position, move to that location, and restart the algorithm. How to find the highest mountain in BC? As a term project? Cannot know if it is the highest. TRU-COMP3710 Search Methodologies

Hill Climbing – Foothills
Difficulties for hill-climbing methods. A foothill is a local maximum. TRU-COMP3710 Search Methodologies

Hill Climbing – Plateaus
Difficulties for hill-climbing methods. Flat areas that make it hard to find where to go next. TRU-COMP3710 Search Methodologies

Hill Climbing – Ridges Difficulties for hill-climbing methods
B is higher than A. At C, the hill-climber can’t find a higher point North, South, East or West, so it stops. TRU-COMP3710 Search Methodologies

Local search algorithms use
Cumulative improvement. But they are prone to local maxima. [Q] How to improve? One idea is to use multiple initial starting points. It is called diversity. We will discuss genetic algorithms later. They look like advanced hill climbing that uses some interesting ideas to solve the previous problems. TRU-COMP3710 Search Methodologies

Summary A* algorithms with heuristics Greedy search
Searching for a path to a goal Greedy search [Q] When a goal is known? Local search [Q] How to improve? TRU-COMP3710 Search Methodologies

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