AO* algorithm in AI (artificial intelligence) in HINDI | AO* algorithm with example

Summary

This video delves into the AO* algorithm, a problem-solving technique rooted in AND/OR graph theory. It emphasizes problem decomposition, breaking down complex issues into simpler parts. The script contrasts AO* with the A* algorithm, highlighting that while A* guarantees the optimal solution, AO* does not, but can be more efficient by stopping the search once a solution is found. The video uses the example of passing an exam through cheating or hard work to illustrate AND/OR graphs, where hyperedges represent combined conditions. It also explains the importance of re-evaluating heuristic values at each level of the graph, which is crucial for AO*'s operation.

Takeaways

• 🧩 The AO* algorithm is based on AND/OR graphs, which are specialized graphs used for problem decomposition.
• 🔍 Problem decomposition involves breaking down complex problems into smaller, more manageable pieces to find solutions.
• 📚 AND/OR graphs are unique because they use hyperedges to represent complex relationships between nodes, unlike simple edges in traditional graphs.
• 🚀 AO* and A* are both informed search techniques that use heuristic values to guide the search for solutions.
• ⭐ A* guarantees the optimal solution by exploring all possible paths, while AO* does not guarantee optimality but can find solutions more efficiently.
• 🔄 Underestimation and overestimation play a crucial role in how AO* and A* algorithms determine the heuristic values and path costs.
• 🌐 AO* can stop exploring further once a solution is found, unlike A* which continues to explore all paths to ensure the optimal solution.
• 📈 The AO* algorithm updates and propagates heuristic values up the tree from child nodes to the root node, which can change the estimated costs.
• 🔄 The script provides an example of how AO* calculates and updates heuristic values at different levels of the AND/OR graph to find a solution.
• 🏁 The final solution in AO* is represented by a solution graph or tree, which is constructed by iteratively updating and selecting the minimum heuristic values.

Q & A

What is the AO* algorithm?

The AO* algorithm is a search algorithm based on AND/OR graphs, which works by decomposing complex problems into smaller sub-problems and finding solutions through this process.

What is the primary difference between AO* and A* algorithms?

The primary difference is that A* always guarantees an optimal solution, while AO* does not. A* explores all solution paths to ensure optimality, whereas AO* may stop exploring further once a solution is found.

What is an AND/OR graph?

An AND/OR graph is a specialized graph that represents problem-solving scenarios where solutions can be found through either AND (all conditions must be met) or OR (any condition can lead to a solution) relationships.

How does the AO* algorithm handle problem decomposition?

The AO* algorithm handles problem decomposition by breaking down complex problems into smaller sub-problems, evaluating potential solutions at each step, and then recombining these solutions to solve the original problem.

What is the role of heuristic values in the AO* algorithm?

Heuristic values in the AO* algorithm are used to estimate the cost from a given node to the goal state. These values guide the search process by helping to determine the most promising paths to explore.

Why might AO* not always find the optimal solution?

AO* might not always find the optimal solution because it can stop exploring further paths once a solution is found, without ensuring that all possible paths have been evaluated for potential lower costs.

How does the AO* algorithm update heuristic values as it explores the graph?

The AO* algorithm updates heuristic values by recalculating them at each level of the graph based on the costs and heuristics of child nodes, and then propagates these updated values back to the root node.

What is the significance of hyperedges in AND/OR graphs?

Hyperedges in AND/OR graphs represent a relationship where multiple nodes or conditions must be satisfied simultaneously to reach a solution, distinguishing them from simple edges that represent individual paths.

Can you provide an example of how the AO* algorithm might be used to solve a problem?

An example given in the script is passing an exam, where one can either cheat or work hard. The algorithm evaluates the costs and heuristics of these options and their sub-options to determine the best path to achieve the goal of passing the exam.

How does the AO* algorithm handle the exploration of different paths in the graph?

The AO* algorithm explores different paths by evaluating the costs and heuristics at each node and choosing the path with the lowest estimated cost. However, once a solution is found, it may not explore all other paths that could potentially lead to a better solution.

What is the importance of terminal nodes in the AO* algorithm?

Terminal nodes in the AO* algorithm represent goal states or end conditions. The algorithm evaluates the costs to reach these nodes and uses their heuristic values to guide the search process towards a solution.

Outlines

00:00

🧠 Introduction to AO* Algorithm and AND/OR Graph

The video begins with an introduction to the AO* algorithm, which is based on AND/OR graphs. The presenter explains that the AO* algorithm operates through problem decomposition, breaking down complex problems into smaller, more manageable pieces. The AND/OR graph is introduced as a specialized graph that differs from simple or complete graphs due to the presence of hyperedges. An example is given to illustrate the concept: passing an exam can be achieved either by cheating or by hard work. The video emphasizes that the AND/OR graph allows for the representation of choices where one option (AND) or multiple options (OR) must be satisfied to reach a solution. The presenter also hints at the upcoming discussion on the differences between AO* and A* algorithms, setting the stage for a deeper exploration of these algorithms.

05:01

🔍 Comparing AO* and A* Algorithms

This paragraph delves into the differences between AO* and A* algorithms. Both are informed search techniques that use heuristic values to find solutions, but A* is guaranteed to provide the optimal solution. The presenter clarifies that the star in A* signifies admissibility, indicating that A* always delivers an optimal solution. In contrast, AO* does not guarantee optimality but can still find solutions. The discussion then shifts to the concepts of underestimation and overestimation in heuristics and how they contribute to solution finding. The presenter directs viewers to a previous video for more details on these concepts. The key takeaway is that while A* explores all possible paths to ensure an optimal solution, AO* may stop once a solution is found, potentially missing better solutions that could be discovered with further exploration.

10:03

🌐 AO* Algorithm's Problem Solving Process

The final paragraph walks through the AO* algorithm's problem-solving process using an AND/OR graph example. The presenter explains how heuristic values are used to estimate the cost of reaching a goal state from different nodes. The video demonstrates how the algorithm updates these values as it explores different paths. The process involves selecting the path with the lowest estimated cost and updating the heuristic values as new information becomes available. The presenter also discusses the importance of revisiting nodes to potentially find a more optimal solution, as the algorithm may initially miss better paths by stopping at the first solution found. The example provided illustrates how the AO* algorithm iteratively refines its estimates and explores the graph to construct a solution tree, ultimately aiming to find the most efficient path to the goal.

Keywords

💡AO* algorithm

The AO* algorithm is a heuristic search algorithm that is used for problem-solving in AI. It is based on AND/OR graphs, which allow for the representation of complex problems as networks of simpler sub-problems. The AO* algorithm iteratively refines the estimated costs of reaching the goal from different nodes in the graph, aiming to find an optimal path. In the video, it is contrasted with the A* algorithm, highlighting its ability to potentially find solutions more quickly by not exploring all possible paths exhaustively.

💡AND/OR graph

An AND/OR graph is a specialized graph structure used in AI for problem-solving. It consists of AND nodes, which represent goals that require multiple sub-goals to be achieved, and OR nodes, which represent choices between different paths to achieve a goal. The video uses the example of passing an exam, where one can either cheat or study hard, to illustrate the concept of AND/OR graphs. The graph helps in visualizing the problem decomposition and the relationships between different problem components.

💡Problem decomposition

Problem decomposition is a strategy in AI where complex problems are broken down into smaller, more manageable sub-problems. This approach is central to the AO* algorithm, as it allows for a more efficient search by focusing on relevant sub-problems. In the video, the process of breaking down the problem of passing an exam into smaller tasks like cheating or studying is used to demonstrate how problem decomposition simplifies the search for a solution.

💡Heuristic value

A heuristic value in the context of search algorithms like AO* and A* represents an estimate of the cost to reach the goal from a given node. It is used to guide the search towards more promising paths. The video explains how heuristic values are calculated and updated as the algorithm explores the AND/OR graph, with examples showing how these values influence the search process and the selection of paths.

💡Optimal solution

An optimal solution is a solution that has the lowest possible cost or the best performance for a given problem. The video discusses the difference between the A* and AO* algorithms in terms of their guarantees of finding an optimal solution. While A* is guaranteed to find the optimal path, AO* may find a good solution quickly but does not guarantee it is the best possible solution.

💡Underestimation and Overestimation

Underestimation and overestimation refer to the accuracy of heuristic values in search algorithms. An underestimating heuristic always gives a value that is less than or equal to the true cost, which is necessary for algorithms like A* to guarantee an optimal solution. Overestimation, where the heuristic value is greater than the true cost, can still be used but does not provide the same guarantees. The video touches on these concepts in the context of how they affect the performance and guarantees of the AO* algorithm.

💡Root node

In the context of the AND/OR graph, the root node is the starting point of the search. The video explains how the AO* algorithm begins at the root node and explores the graph, updating heuristic values as it goes. The root node is crucial for understanding the initial conditions and the structure of the search space.

💡Hyperedge

A hyperedge is a concept used in AND/OR graphs to represent a connection between multiple nodes that must all be satisfied for the goal to be achieved. In the video, the hyperedge is used to illustrate the AND condition, where both cheating and studying hard are necessary to pass the exam. This concept is central to understanding how AND/OR graphs model complex problems.

💡Solution graph

A solution graph is the final representation of the path or paths taken to solve a problem using an algorithm like AO*. The video describes how the AO* algorithm constructs a solution graph by selecting the most promising paths based on heuristic values and explores these paths until a solution is found. The solution graph is the end result of the search process and shows the steps taken to reach the goal.

💡Estimation value

An estimation value in the AO* algorithm is the updated heuristic value for a node after considering the costs of reaching it from its children nodes. The video explains how these values are calculated and used to guide the search process. Estimation values are crucial for the AO* algorithm's ability to find solutions efficiently by focusing on the most promising paths.

💡Exploration and Expansion

Exploration and expansion are key steps in the search process of algorithms like AO*. Exploration refers to the process of evaluating nodes and their paths to find potential solutions, while expansion is the act of adding new nodes to the search space. The video contrasts the exploration strategies of A* and AO*, highlighting how A* explores all paths exhaustively while AO* may stop exploring once a solution is found.

Highlights

Introduction to AO* algorithm and its basis on AND/OR graphs.

Explanation of problem decomposition in AO* algorithm.

Definition and speciality of AND/OR graphs.

Example of passing an exam using AND/OR graph to illustrate the concept.

Difference between simple edges and hyperedges in AND/OR graphs.

Comparison between AO* and A* algorithms in terms of search techniques.

Guarantee of solution by AO* algorithm versus the optimality of A*.

Explanation of underestimation and overestimation in heuristic values.

Behavior of A* algorithm in exploring all solution paths.

Example of AO* algorithm using an AND/OR graph to demonstrate the process.

Calculation of total cost for different paths in the AND/OR graph.

Concept of choosing the path with the least cost in AO* algorithm.

Discussion on the possibility of missing optimal solutions by not exploring all paths.

Explanation of how heuristic values change as the algorithm progresses.

Process of updating and propagating new heuristic values in AO*.

Final solution graph or tree construction in AO* algorithm.

Summary of how AO* algorithm works by finding and updating heuristic values at each level.

Transcripts

Hello friends, welcome to gate smashers.

In this video we will discuss

about AO* algorithm.

AO* algorithm is actually based on

AND/OR graph.

It works on the basis of problem decomposition.

What we do in problem decomposition?

Complex problems are breaked down

in smaller pieces or problems.

After that we find out the solution.

So firstly here i would like to tell

AND/OR graph

is a specalised graph

You have seen so many graph simple multiple

complete graph and all but

here special graph is AND/OR.

Its speciality is

we will understand with a example.

We want to pass in exam.

Means we have to find this.

How to pass in exam?

In that we have one option do cheating.

Second option is do hard work and pass it.

But if we see here carefully

There is a hyperedge this is a simple edge.

Simple arc

but this is a hyper edge or hyper arc.

So what does it mean

We have one solution that is do cheating.

Means we do cheating and pass in exam.

We find out our solution.

Solution is we have to pass in exam

This is the question. Do cheating

want to pass in exam yes i will pass exam.

Second option we have

Do hard work and pass it.

Means what it denotes here?

Whenever it moves these both condition will move.

Do hard work and pass it.

This is second choice we have.

This is the first choice this is second one

Obviously we say choice or.

That's why it is known as AND/OR graph.

Either choose this option in it or this.

But this is just for example.

You have to choose these option always.

In these option there are chances you will pass

but you cannot come first.

Obviously choose for this option

but from this you will clear

What is AND/OR graph?

How it works?>

Next we are going to discuss here

difference between AO* and A*.

If we talk about AO* and A*.

Then both works on best for search.

Both are informed search techniques

In which heuristic value is given.

On the basis of heuristic value we find out solution.

But A* always gives the optimal solution.

Means it always give optimal solution.

Firstly i want to tell

What does this star means?

Star means admissible.

Means A* will give solution this is a guarantee.

But AO* will give solution this is a guarantee.

But A* always give optimal solution.

If we works on underestimation.

What is this underestimation or overestimation?

How it gives solution?

I have made already on this.

Please check that.

Link is in the description.

But AO* will always give optimal solution

there is no guarantee.

But the major difference between A* and AO*

It goes in depth

but if it gets solution one time

Means A* does not explore all the

solution paths once it got a solution.

If it gets solution one time.

It will not explore for further solution.

It will not expand.

But A* will definitely do.

It will go to full depth

It will troverse.

Finally it will give it optimal solution.

We can understand this with simple example

In AO* i have given a example

In which i have taken AND/OR graph.

From this AND/OR graph we will see

we will try to prove it.

If we talk firstly

A is root node

Here we have AND/OR

between B and C there is hyperedge and D.

These values

6, 10 and 12 are heuristic values

estimation values.

B is estimating i will take A to goal state at cost of 6.

Such way we have estimation.

Further after B we have G, H, E, F nodes.

Firstly if we talk

From A to B, C and D.

Three options we have here.

If we talk about B and C.

Then what is the concept of B and C.

The value of B here it is given six.

If we talk about this edge cost

Every edge cost is one.

Means every edge

If we want to go from A to B, C, D

Here every cost is one.

So first thing we talk here

If we go towards B and C.

If we go towards B and C.

Then what will be this total cost

Six plus twelve

Six plus twelve is eighteen.

Total cost is eightteen.

Plus two because whenever you go to end

then this six plus twelve eighteen plus two

That is what eighteen plus two is twenty.

Next if we go towards D

If we go towards D then

D is taking at cost of ten.

Heuristic value of D is ten.

Ten plus one here is eleven.

Means first of all we finded

If we go to BC from it

Then it will be six plus twelve

Six plus twelve that is eighteen

plus two twenty.

Or if we go towards D

Then ten plus one that is eleven.

Next we have

From these both which one we will choose

We will choose eleven.

If we choose eleven

because this value is less.

Next we go to D

From D we can move further toward E

or towards F.

In these both ends are normal

It goes towards E and F.

In E and F here if we make end

Means in these both you have to go.

So obvious cost of E and F here is 4 plus 4

Eight plus one and one two

See four plus four plus one one that is two

because in between there is end

you have to go both sides.

Obviously how much cost here is?

Ten

Revised cost comes 10.

So obviously

On A total cost comes

If we go to this way then total cost is 11.

It will stop here.

Means it get solution tree it will stop.

But here i would like to tell

it does not explored this side.

It is possible if it expplored this side

the the chances of less cost will occur.

Lets say if it explore after C

then it is possible the cost becomes less.

This is possible.

but he does not explore these possibilities

then due to this there can be a problem.

Lets say if we talk here B and C

If i go towards B

What is the cost of B here? Six.

Cost of B is six.

If i go to G from B.

Then if i go to G from B.

Lets say G take us to I

Heuristic value of I is one.

Just for solution

We take heuristic value of I one.

See here the cost comes

If we go from A to B

Cost is one, one plus one two

Two plus one three because

its cost is one.

If we see from G to I

Heuristic value of I is one.

Heuristic value of G will change because

here we have to go from G to I.

I is taking us upto which value

It is taking to one

Means one plus one becomes two.

So here the heuristic value of G changes 2.

Similarly if we talk about B

Then see B

is taking us to G at one cost

G is further taking us at cost of two.

So the cost of B will also change here.

New estimation value that is 2+1=3.

Next if we talk here

See here

Lets say C

From C if we go to

Let's say towards F

The value of F is also one.

So obviously here

heuristic value of C will change

Heuristic value of C will become 1 plus 1

That is two.

See here finally

New heuristic value of B is three.

New heuristic value of C is two.

Total is three plus two five

plus two that is seven

Means its cost is less but this cost

will come only when it explores this side.

But if it does not explored this side

Then obviously it will not cover this value

This point i want to explain.

If AO* does not explore all the solution paths

once it got a solution.

As it gets solution from this side

It does not explored this side

It might be possible after G I and C F

it gives optimal solution.

So this is how AO* algorithm works

You have to find out new estimation value at every level.

Then this new estimation value

we take it to root node.

Here i tell you a small point.

F is already used so F

Instead of F you take a new node lets say.

Take name J because F is already used.

You will not confuse why F is taken 2 times

We go this way.

See where B is taking us to E and F.

Cost of E is six.

Its cost is 8 so how much here

Six plus one seven

Means firstly heuristic value was four

New estimated value comes seven

and according to this it comes 9.

Obviously which one is less seven

Which one we will consider? Seven

New heuristic value comes seven.

Now this value also we have to take to root level.

Here we take the values to top.

So here seven plus one becomes eight.

New heuristic value of A comes eight

but here it will see less value is seven.

As 7 is less value then it will explore it.

If we explore it then see here carefully.

C and D

C is taking us to G, H, I.

D is taking to J.

So from C if we go to G

Heuristic value of G is two.

So two plus one becomes three.

New heuristic value of C according to G

So two plus one becomes three.

If we go to H and I.

Heuristic value of H and I are zero.

Zero zero means these are terminal nodes.

Zero means zero plus zero equal to zero.

Plus one plus one that is two.

Heuristic value of C comes two.

According to this it comes 3 if we move to G

and if we go to H and I then it comes two.

Other than this I and J are terminals.

Terminal means these are sold.

Sold means here solution tree is becoming.

See here carefully.

What new value comes here?

Two which is minimum

Between 2 and 3 which one is less? Two.

If we talk about D

Then where D is taking us.

Towards J it is taking.

Heuristic value of J is zero.

Zero again here is terminal

Terminal heuristic value will be zero.

Means new heuristic value of D comes 1.

One plus zero becomes one.

New heuristic value of D comes 1.

Together with it J is solved here.

If J is solved then obvious my D is solved.

See here from 2 and 3, 2 is minimum.

New heuristic value of C becomes two

and of D it is one.

Here C is also solved.

We have finded the minimum value

Means optimal answer is coming here.

See two plus one

We are taking new heuristic value to A.

Two plus one becomes three.

Plus two see two

2+1=3, 3+1=4, 4+1=5

Here finally

New heuristic value of A comes 5.

New estimation is 5.

We can say it one of the solved graph.

Means you can say it solution graph.

Final solution graph or tree is made here.

By this way AO* works

You have to find out heuristic value at a level.

Then you have to find out new heuristic value at second level.

New estimated value.

Again we update that value

and take it to root level.

This is all about

How to solve the AO* algorithm?