Introduction
Artificial Intelligence (AI) is getting
machines to think and behave smartly, and much of this smartness is all about
problem-solving. From finding one’s way around a city to defeating an opponent
at chess to solving the Rubik’s Cube, a smart system needs to make choices
given a list of options and limitations. Search algorithms enter the picture
here.
Search in AI is navigating a problem space
to reach a goal state. It can be imagined as moving from one node to another
within a tree or graph in which the nodes are states and the actions are edges.
Selecting the right path is crucial for effective problem-solving, particularly
when navigating complex environments, limited resources, or time constraints.
Search procedures are generally classed
into two categories:
- Uninformed search: These searches the search space without using
any knowledge of the domain regarding how close a node is to the goal.
They are straightforward and systematic but usually inefficient.
- Heuristic search: These utilize heuristics – rules of thumb or
approximations – to more intelligently direct the search to the solution.
These search algorithms are the basis for
disciplines like robotics, video games, navigation, puzzle solving, and
planning. In this blog, we will guide you through some of the most popular
search methods used in AI, such as Breadth-First Search, Depth-First Search,
A*, and Greedy Search, and show you real-life examples and diagrams of how they
operate.
1.
Uninformed
(Blind) Search
Uninformed search strategies work without
any domain knowledge. They search systematically from nodes until a solution is
reached, though they can be ineffective for larger spaces.
Types of Uninformed Search
The following are the types of Uninformed
Search
a.
Breadth-First
Search (BFS)
BFS visits all the nodes at a particular
depth before moving to the next depth level to ensure the shortest path (in
terms of the number of edges) in unweighted graphs.
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Breadth-First Search (BFS) |
Complexity
The time and space complexity of the BFS is
O (bm), where m is the maximum depth and b is the branching factor.
Use Case
BFS is used in tree searching.
b.
Depth-First
Search (DFS)
DFS goes as deep as possible along a single
branch before backtracking. It uses little memory but isn’t optimal, and can get
into infinite loops in circular spaces.
![]() |
Depth-First Search |
Complexity
The time complexity of the DFS is O(bm),
where m is the maximum depth.
The space complexity of the DFS is O(b.m),
keeping one path in memory at a time.
Use Case
DFS is used for solving puzzles when there
are deep solutions but not enough memory.
c.
Iterative
Deepening (IDDFS)
IDDFS unites Breadth-First Search’s
completeness/ optimality with Depth-First Search’s space efficiency. It does
DFS to depth 0, 1, 2,... incrementally until a goal is reached.
Complexity
The time complexity of the IDDFS is still
O(bd), but with the additional overhead of repeated execution of
shallower searches.
Whereas the space complexity of IDFFS is
O(b.d)
Use Case
IDDFS is useful in scenarios where the
depth of the solution is now known or potentially infinite, and memory is a
constraint.
Comparison of Uninformed Methods
Uninformed searches are easy but unsuitable
for large-scale problems, which encourages the use of heuristic methods.
2.
Heuristic
(Informed) Search
Heuristic search applies problem-specific
knowledge (heuristic) to direct the search toward the goal more effectively.
Types of Heuristic Search The following are the types of Heuristic search:
a.
Greedy
Best-First Search
Greedy search chooses the node nearest to
the goal using the heuristic value h(n) (estimated distance to goal).
The advantage of this search is that it is very
Quick.
This type of search is not optimal and can
be trapped in cycles or dead ends if the heuristic is poor.
Complexity
The space and time complexity of the greedy
best-first search is O(bm), where b represents the branching factor
(the maximum number of children a node has) and m is the maximum depth of the
search space.
Use Case
Greedy Best-First Search is usually used in
pathfinding in video
games.
b.
A* Search
A* integrates path cost g(n) (cost to date)
and heuristic h(n) (estimated cost to goal) into evaluation function f(n)=g(n)
+ h(n)
This type of search never overestimates the
true cost to reach the goal; the algorithm is guaranteed to find the optimal
solution.
Complexity
The complexity of the A* search algorithm
depends on heuristic accuracy and branching factor. The space complexity
of the algorithm is O(bd).
Use Case
This type of search algorithm is used in
navigation, game AI, and network routing.
c.
Route
Planning with A*
A* is crucial in navigation, such as maps or
games. Example:
- Heuristic: Straight-line distance
(Euclidean)
- Cost: Weights on road nodes
connected by edges.
- Goal: To determine the shortest
path between two cities.
The application is widespread in GPS,
robotics, and game AI.
d.
IDA *
(Iterative Deepening A*)
IDA* uses A* evaluation in ascending cost
limits, marrying the benefit of A*’s optimality with IDDFS’s better space
efficiency.
- Advantages: Utilizes Linear memory
only.
- Disadvantages: Visits the same node
multiple times.
Use Case
It is used in finding puzzles such as the
15-puzzle, where the storage of the full path is impractical.
Real-World Applications in Games and Problem Solving:
These search methods drive much AI
functionality:
- Maize Navigation: A* computes the shortest path.
- Board Games: IDDFS applies to deep game trees.
- Robot Planning: Greedy search computes near-optimal paths fast.
- Puzzle Solvers: A* and IDA* generate fast optimal solutions.
Conclusion
Search algorithms from the core of
intelligent problem-solving in AI. From finding routes through mazes and
puzzles to playing intricate games of strategy and mapping out optimum journeys, these methods grant machines the power to think several steps ahead, weigh up
alternatives, and make rational decisions.
Naive search algorithms like Breadth-First
Search and Depth-First Search provide a systematic means of visiting all
possible paths, although they tend not to be efficient in big or infinite search
spaces. Improvements like Iterative Deepening assist in merging the strengths
of both breadth and depth approaches. Conversely, heuristic search algorithms
such as Greedy Search and A* add a level of intelligence by approximating the
cost of reaching the goal, leading to much better performance in most real-world
applications.
Sophisticated algorithms such as IDA*
improve memory efficiency further without losing informed search properties,
holding them well-suited for environments with limited resources.
As it continues to advance, search-based
problem-solving is still relevant – not just as a starting point for
constructing intelligent systems but as an applied technique in areas like
robotics, logistics, and game design. Learning these algorithms paves the way
to developing smarter, more flexible, and goal-driven systems that can traverse
the complexities of our real and virtual worlds.
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