Artificial Intelligence Chapter 3: Problem Solving and Searching - The Agent's Roadmap
Hello and welcome back, everyone! Professor Zeeshan Bhatti here from Zeeshan Academy. In our last chapter, we deconstructed the different architectures of intelligent agents. We learned about goal-based agents—the ones that don't just react, but plan for a desired future.
Now, we're going to put that theory into practice. Welcome to Chapter 3: Problem Solving and Searching. This is where the rubber meets the road. This chapter is dedicated to one specific kind of goal-based agent, called a problem-solving agent.
We'll explore how these agents take a goal and systematically figure out how to achieve it. Furthermore, we'll see that at the heart of this process lies one of the most fundamental concepts in all of AI: search.
The "Why": From Complex Desires to Simple Goals
Let's start with a fundamental question. Intelligent agents are supposed to maximize their performance measure, which can be incredibly complex. So, why would they adopt a single, simple goal?
Let me illustrate this with a story. Imagine an agent on a touring holiday in the beautiful city of Arad, Romania. Its performance measure is multifaceted: it wants to improve its suntan, practice its Romanian, see the sights, and enjoy the nightlife, all while avoiding hangovers. The decision problem is a mess of trade-offs!
But now, imagine this agent has a non-refundable ticket to fly out of Bucharest tomorrow. Suddenly, the decision is dramatically simplified. The agent can adopt a clear, singular goal: Get to Bucharest on time.
Consequently, any action that doesn't contribute to this goal can be instantly rejected. This is the power of a goal: it organizes behavior and drastically narrows down the vast universe of possible actions the agent needs to consider. Therefore, goal formulation is the very first step in problem solving.
What is a Problem-Solving Agent?
A problem-solving agent is a goal-based agent that uses atomic representations. This is a key term. It means the agent views the states of the world as whole, indivisible units, with no internal structure visible to its algorithms.
Think of it like this: in a navigation problem, a city is just "Arad" or "Bucharest." The agent doesn't yet care about the streets within Arad; it just cares about Arad as a single point on the map. In contrast, more advanced agents (called planning agents) use factored or structured representations, where they understand that a state (like a city) is made up of components (streets, traffic lights, etc.). We'll save that for a later chapter!
The Building Blocks: Formulating a Problem
To solve a problem, an agent must first define it precisely. Essentially, formulating a problem means defining its five core components:
The Initial State: Where does the agent start? (e.g., In Arad).
The Goal State(s): What is the desired situation? This can be a single state (e.g., In Bucharest) or a test to check if a state meets the goal (e.g., Checkmate the opponent's king).
Actions: What can the agent do? For each state
s, there is a set of possible actions,ACTIONS(s). (e.g., Drive to Zerind, Drive to Sibiu, Drive to Timisoara).Transition Model: What happens when you take an action? This describes the state that results from taking a given action in a given state. It's often described by a
RESULT(s, a)function. (e.g.,RESULT(In Arad, Drive to Sibiu) = In Sibiu).Path Cost: A numerical cost associated with a path of actions. This reflects the performance measure. (e.g., the total distance in kilometers, or the time taken).
Together, these components define the state space—the set of all states reachable from the initial state by any sequence of actions. We can visualize this as a state space graph, where nodes are states and edges are actions.
The "How": Search Algorithms - The Engine of Problem Solving
Once the problem is formulated, the agent needs to find a solution. A solution is a sequence of actions that leads from the initial state to a goal state. The optimal solution is the one with the lowest path cost.
This is where search algorithms come in. They are the methods for exploring the state space to find a solution. We can broadly classify them into two categories.
Part 1: Uninformed Search (Blind Search)
Uninformed search strategies are given no information about the problem other than its definition. They have no way to know if one non-goal state is more promising than another. They are, in a sense, searching in the dark. Let's look at two fundamental ones.
1. Breadth-First Search (BFS): The Cautious Explorer
How it works: BFS explores the state space in layers. It expands the root node (initial state) first, then all of its children, then their children, and so on. It uses a First-In, First-Out (FIFO) queue.
Analogy: It's like exploring a house room by room, checking all rooms on the first floor before going up to the second.
Properties:
Completeness: Yes, it will always find a solution if one exists.
Optimality: Yes, it always finds the shallowest solution (the one with the fewest steps). However, this may not be the lowest-cost solution if step cost varies.
Time & Space Complexity: O(b^d), where
bis the branching factor anddis the solution depth. This is a huge memory cost, as it must store all the nodes in each layer.
2. Depth-First Search (DFS): The Determined Adventurer
How it works: DFS explores the state space by going as deep as possible down one branch before backtracking. It uses a Last-In, First-Out (LIFO) stack.
Analogy: It's like exploring a maze by always taking the leftmost turn until you hit a dead end, then backtracking to the last junction.
Properties:
Completeness: Not guaranteed in infinite state spaces or with cycles (unless cycle-checking is done). It can get stuck going down an infinite path.
Optimality: No, it often finds a solution, but not necessarily the optimal one.
Time & Space Complexity: The space complexity is O(b*m), where
mis the maximum depth, which is much better than BFS. However, time complexity can be very poor if it chooses a bad path.
Part 2: Informed Search (Heuristic Search)
Uninformed search can solve any solvable problem, but as you've seen, it's often terribly inefficient. Informed search algorithms are the solution to this. They use problem-specific knowledge beyond the problem definition to guide the search. This knowledge is encapsulated in a heuristic function.
What is a Heuristic Function?
A heuristic function, h(n), provides an estimate of the cost from a state n to the nearest goal state. It's an educated guess, not a guaranteed value.
Example: In our Romania problem, a good heuristic for "distance to Bucharest" is the straight-line distance on a map. It's not the actual road distance, but it's a great estimate.
1. Best-First Search: The Ambitious Dreamer
How it works: This algorithm expands the node that seems to be closest to the goal, based only on the heuristic function h(n). It uses a priority queue ordered by h(n).
The Pitfall: It's greedy. It can be misled by an optimistic heuristic and often fails to find the optimal solution, much like DFS.
2. A Search: The Perfect Balance*
This is the superstar of informed search algorithms. A search* combines the best of both worlds.
How it works: It evaluates nodes using a cost function: f(n) = g(n) + h(n)
g(n) is the actual cost from the initial state to node
n.h(n) is the estimated cost from
nto the goal.f(n) is, therefore, the estimated total cost of the path through node
n.
The Magic: A* expands the node with the lowest f(n). It's like saying, "Let's choose the path that has the best combination of what it has cost me so far and what I expect it to cost me in the future."
Properties:
Completeness: Yes.
Optimality: Yes, provided the heuristic is admissible. An admissible heuristic never overestimates the true cost to the goal. Our straight-line distance heuristic is admissible because the shortest road will never be shorter than a straight line.
Efficiency: A* is optimally efficient for a given heuristic. No other optimal algorithm is guaranteed to expand fewer nodes.
Conclusion: From Formulation to Solution
We've now covered the complete pipeline for a problem-solving agent:
Formulate the Goal.
Define the Problem (Initial State, Actions, etc.).
Choose a Search Algorithm to find a solution sequence.
Execute the Solution.
We've seen that while uninformed search methods like BFS and DFS are fundamental, they are often too computationally expensive for real-world problems. Therefore, informed search methods like A*, powered by intelligent heuristic functions, are the key to building efficient and powerful AI systems.
This framework of problem solving and search is universal. It applies not just to navigation, but to puzzle solving (like the 8-puzzle), scheduling, logistics, and even video game AI. It is one of the most powerful tools in your AI arsenal.
In our next chapter, we'll see what happens when we move beyond atomic representations and into the world of planning, where agents can reason about the structured, internal details of their world.
Instructor: Prof. Dr. Zeeshan Bhatti
YouTube Channel: "Zeeshan Academy" (https://www.youtube.com/@ZeeshanAcademy)
Think of a simple problem in your daily life, like packing a suitcase or planning a route to run errands. Can you formulate it using the five components (Initial State, Goal, Actions, etc.)? What would a good heuristic be? Share your example below!
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