Informed Search and Exploration - Air Universityportals.au.edu.pk/imc/Content/course/lecs/Lecture-4...

Informed Search and Exploration

Uninformed vs Informed

Search Strategies,

Best-First Search Algorithm,

Uniform Cost Search

Algorithm (UCS),

Greedy best-first search

algorithm,

- Complete?,

- Time?,

- Space?,

- Optimal?.

A* search algorithm,

Iterative Deepening Search

Algorithm,

- QueuingFn,

- Expand(state),

Explore: Topics based

Research Areas:

@Copyrights: Advanced Artificial Intelligence Organized by Dr. Ahmad Jalal (http://portals.au.edu.pk/imc/)

1. Uninformed Vs Informed Search Strategies

Uninformed Search Strategies:

Uninformed search strategies look for solutions by systematically

generating new states and checking each of them against the goal.

This approach is very inefficient in most cases.

Most successor states are “obviously” a bad choice.

Such strategies do not know because they have minimal problem-

specific knowledge.

Strategies are;

- Breadth-first search,

- depth-first search.

1. Uninformed Vs Informed Search Strategies (Cont…)

Informed Search Strategies:

Informed search strategies exploit problem-specific knowledge as

much as possible to drive the search.

They are almost always more efficient than uninformed searches

Also, more consistent and optimal.

Main Idea:-

①Use the knowledge of the problem domain to build an evaluation function f.

②For every node n in the search space, f ( n ) quantifies the desirability of expanding

n in order to reach the goal.

③Then, use the desirability value of the nodes in the fringe (destination) to decide

which node to expand next.

1. Uninformed Vs Informed Search Strategies (Cont…)

Informed Search Strategies:

Informed search strategies deal as best-first search.

Idea: use an evaluation function for each node to estimate of

“desirability”.

Strategy: Always expand most desirable unexpanded node.

Implementation: fringe is a priority queue sorted in decreasing order

of desirability.

Special cases:

Best-first search

Uniform-cost search

Greedy search

A* search

2. Best-First Search Algorithm

Efficient selection of the current best candidate for extension is

typically implemented using a priority queue.

Best-first search only as good as heuristic.

– Example heuristic for 8 puzzle:

– Manhattan Distance

Example:- Step -1:-

2. Best-First Search Algorithm (Cont…)

Example:- Step -2:-

Example:- Step -3:-

Example:- Step -4:-

Example:- Step -5:-

Example:- Step -6:-

Example:- Step -7:-

Example:- Step -8:-

Example:- Step -9:-

Is there any other “GOAL” is possible at specific “Estimated

distance” ????

Example:- Class Evaluation:-

Estimated distance = 24, 37, 49

e u i a ai o

a r g g m t s z w tt

19 6 11 9 14 2317

16 12 826

315 13 14

31 0 27

Example:- Generate “English dictionary” by using best-first search

algorithm.

2. Best-First Search Algorithm (Class Participation)

Parent Node Total level (max) Total Estimated distance Total number of nodes

S 4 34 18

D 3 46 16

R 2 23 12

A 5 69 27

I 2 18 9

P 3 25 14

3. Uniform Cost Search Algorithm (UCS)

QueueingFn is SortByCostSoFar.

Cost from root to current node n is g(n).

– Add operator costs along path

First goal found is least-cost solution.

Space & time can be exponential because large subtrees with

inexpensive steps may be explored before useful paths with costly

steps.

If costs are equal, time and space are O(bd).

– Otherwise, complexity related to cost of optimal solution.

3. Uniform Cost Search Algorithm (UCS Example) (Cont…)

Step 1:- Open list: C

Step 2:- Open list: B(2) T(1) O(3) E(2) P(5)

Step 3(ordering):- Open list: T(1) B(2) E(2) O(3) P(5)

Step 4:- Open list: B(2) E(2) O(3) P(5)

{T(1) is excluded}

Step 5:- Open list: E(2) O(3) P(5)

{B(2) at stack}

Step 6:- Open list: E(2) O(3) A(3) S(5) P(5) R(6)

Step 7:- Open list: O(3) A(3) S(5) P(5) R(6)

{E(2) at stack}

Step 8:- Open list: O(3) A(3) S(5) P(5) R(6) G(7)

Step 9:- Open list: A(3) S(5) P(5) R(6) G(7)

{O(3) at stack}

Step 10:- Open list: A(3) I(4) S(5) N(5) P(5) R(6) G(7)

Step 11:- Open list: I(4) P(5) S(5) N(5) R(6) G(7)

{A(3) is excluded}

Step 12:- Open list: P(5) S(5) N(5) R(6) Z(6) G(7)

{I(4) at stack}

Step 13:- Open list: S(5) N(5) R(6) Z(6) F(6) G(7) D(8) L(10)

{P(5) at stack}

Step 14:- Open list: N(5) R(6) Z(6) F(6) G(7) D(8) L(10)

{S(5) is excluded}

Step 15:- Open list: R(6) Z(6) F(6) G(7) D(8) L(10)

{N(5) is excluded}

Step 16:- Open list: Z(6) F(6) G(7)D(8) L(10)

{R(6) is excluded}

Step 17:- Open list: F(6) G(7)D(8) L(10)

3. Uniform Cost Search Algorithm (Class Participation)

2 3 41

9 10 11 12 Goal

Comparison of Search Techniques

Complete N Y Y

Optimal N N Y

Heuristic N N N

Time bm bd+1 bm

Space bm bd+1 bm

4. Greedy best-first search algorithm

Greedy best-first search expands the node that appears to be

closest to goal.- Less number of nodes,

- shortest time in between compared nodes.

Evaluation function f(n) = h(n) (heuristic) = estimate of cost from

n to goal.

Example; hSLD(n) = straight-line distance from n to Bucharest.

4. Greedy best-first search algorithm (Example) (Cont…)

Complete? No – can get stuck in loops, e.g., Iasi Neamt

Iasi Neamt

Time? O(bm), but a good heuristic can give dramatic

improvement

Space? O(bm) -- keeps all nodes in memory

Optimal? No

4. Greedy best-first search algorithm (Cont…)

5. A* search algorithm

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 from n to goal

f(n) = estimated total cost of path through n to goal

5. A* search algorithm (Example) (Cont…)

Sibiu = cost + estimated cost

Sibiu = 140+253

Arad = (140+140)+366

Arad = 280+366

Fagaras= (140+99)+176

Fagaras= 239+176

Oradea= (140+151)+380

Oradea = 291+380

Rimnicu Vilcea= (140+80)+193

Rimnicu Vilcea = 220+193

6. Iterative Deepening Search Algorithm

DFS with depth bound.

QueuingFn is enqueue at front as with DFS

- Expand(state) only returns children such that

depth(child) <= threshold

- This prevents search from going down infinite

First threshold is 1

- If do not find solution, increment threshold and

repeat.

Problem:-

What about the repeated work?

Time complexity (number of generated nodes)

[b] + [b + b2] + .. + [b + b2 + .. + bd]@Copyrights: Advanced Artificial Intelligence Organized by Dr. Ahmad Jalal (http://portals.au.edu.pk/imc/)

6. Iterative Deepening Search Algorithm (Cont…)

Figure: Example of iterative deepening search

7. Explore: Topics based Research Areas

(1) Dynamic Walking over Uneven Terrain :-

Proposed architecture of Model

Implemented results

Assignment # 2(Searching Algorithms)

1. Adversarial Search

2. Bidirectional Search

3. Beam Search

4. Local & International

applications of;

a) Best-First Search

Algorithm,

b) Uniform Cost Search

Algorithm (UCS),

c) Greedy best-first

search algorithm,

d) A* search algorithm.

Informed Search and Exploration - Air Universityportals.au.edu.pk/imc/Content/course/lecs/Lecture-4...

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