## Beam Search Algorithm: A Comprehensive Guide

The beam search algorithm is a powerful tool used in many applications, ranging from natural language processing to game-playing agents. It is a heuristic search strategy that helps to find the shortest or cheapest path to a target state by maintaining a limited number of the best nodes as the search progresses.

### Definition of Beam Search Algorithm:

Beam search algorithm is a heuristic search strategy that relies on maintaining a limited number of the best nodes as the search progresses.

It is primarily used to find the shortest or cheapest path to a target state, given a set of possible transitions. The algorithm uses conditional probability to determine which node to select next, based on its proximity to the target state.

## Functionality of Beam Search Algorithm:

Beam search algorithm is commonly used to find the shortest or cheapest path to a target state in a large search space. It functions by first creating a set of possible transitions from the current state, and evaluating each transition based on its proximity to the target state.

The algorithm then selects the best nodes based on their proximity to the target state, and retains a fixed number of nodes called the “beam width.”

As the search progresses, the algorithm creates successor nodes based on the current set of best nodes, and evaluates each node based on its conditional probability of being the target state. If a node has a high probability of being the target state, it is added to the list of best nodes, and the worst nodes are eliminated.

The process continues until the target state is reached, or the search space is exhausted.

### Applications of Beam Search Algorithm:

Beam search algorithm has numerous applications in various fields.

- Natural language processing: Parsing sentences and generating meaningful responses to queries.
- Game-playing agents: Finding the best move in a large search space.
- Speech recognition: Transcribing spoken words.

## Working of Beam Search Algorithm:

The beam search algorithm is a heuristic search strategy that works by using a breadth-first search approach to generate a set of possible transitions from the current state. It then evaluates each transition based on its proximity to the target state, and selects the best nodes based on their conditional probability of being the target state.

The algorithm then generates successor nodes based on the current set of best nodes and repeats the process.

### The Heuristic Search Strategy:

The heuristic search strategy employed by the beam search algorithm is a way of finding the best solution in a large search space.

It is a technique that involves estimating the cost-to-go from the current state to the target state. This estimate is based on a set of heuristic rules that are based on the problem at hand.

### The Beam Width and Node Selection:

The beam width is a parameter used by the beam search algorithm to limit the number of nodes that are retained at each level of the search. It is used to balance exploration and exploitation in the search process.

The number of nodes retained is determined by the beam width, and the selection of the nodes is based on their distance from the target state.

### The Search Tree Construction:

The search tree construction process is an essential component of the beam search algorithm.

It involves creating a tree structure that represents all the possible transitions from the initial state. At each level of the tree, the algorithm generates successor nodes based on the current set of best nodes, and evaluates each node based on its conditional probability of being the target state.

## Conclusion:

In this article, we have explained the beam search algorithm, how it works, and its applications. Beam search algorithm is a heuristic search strategy used to find the shortest or cheapest path to a target state by maintaining a limited number of the best nodes as the search progresses.

It is a powerful tool with numerous applications in various fields ranging from natural language processing to game-playing agents, and speech recognition. The working of beam search algorithm involves a breadth-first search approach, a heuristic search strategy, beam width, and the construction of a search tree.

## Algorithm Complexity of Beam Search Algorithm:

When we talk about algorithm performance, there are two main factors to consider: time complexity and space complexity. Time complexity refers to the amount of time it takes for the algorithm to complete its task, and space complexity refers to the amount of memory required by the algorithm.

The time complexity of the beam search algorithm depends on several factors, such as the size of the search space, the number of nodes in the beam, and the branching factor of the tree. In general, the time complexity of the beam search algorithm is O(b^d), where b is the branching factor of the tree, and d is the depth of the search.

This means that the time required to search a larger space will increase exponentially. On the other hand, the space complexity of the beam search algorithm depends on the number of nodes in the beam and the depth of the search.

In general, the space complexity of the beam search algorithm is O(kd), where k is the beam width and d is the depth of the search. This means that the algorithm requires a larger amount of memory to store more nodes in the beam.

## Implementation of Beam Search Algorithm in Python:

Now that we have a good understanding of the beam search algorithm, let’s take a look at how we can implement it in Python. We will be using the NumPy module to create arrays and work with numbers more efficiently.

The implementation will take three parameters: start node, target node, and beam width. First, we will create a function called “beamSearch” that takes these three parameters.

We will also initialize an empty list “beam” to hold the best nodes. We will then add the start node to the list “beam” and initialize the current depth “d” to 0.

```
import numpy as np
def beamSearch(start, target, beamWidth):
beam = [start]
d = 0
```

Next, we will create a while loop that will continue to execute until the target node is found or the beam is empty. Inside the while loop, we will create an empty list called “successors” to hold the possible transitions from the nodes in the beam.

We will then loop through each node in the beam and generate its successors by calling a function that returns a list of successor nodes. We will then append these successor nodes to the list “successors”.

```
while beam != [] and target not in beam:
successors = []
for node in beam:
successors += getSuccessors(node)
```

After generating all the successors, we will sort them based on their conditional probability of being the target node. We will then select the best “beamWidth” nodes and update the list “beam” with these best nodes.

We will also increment the current depth “d” by 1.

```
successors = sorted(successors, key=lambda x: conditionalProbability(x, target))
beam = successors[:beamWidth]
d += 1
```

Finally, we will check if the target node is in the last beam.

If the target is found, we will return the path to the target by selecting the node that has the highest conditional probability of being the target node and then recursively selecting its parent until we reach the start node. If the target is not found, we will return “None” to indicate that no path was found.

```
if target in beam:
path = [beam[0]]
while path[-1] != start:
parent = getParent(path[-1])
path.append(parent)
return path[::-1]
else:
return None
```

## Output and Path Selection:

Once we have implemented the beam search algorithm in Python, we can execute it on a given search space and see the output. The output will either be the path from the start node to the target node or “None” if no path was found.

The path selection depends on the specific problem being solved. In some cases, we may only need to find the shortest path, while in others, we may need to find the path that satisfies certain constraints.

Once we have found the target node, we can select the path that meets the specific requirements using a simple iterative process that traverses the nodes from the target to the start node.

In conclusion, the beam search algorithm is a powerful search strategy used to find the shortest or cheapest path to a target state.

It is commonly used in various fields, ranging from natural language processing to game-playing agents and speech recognition. The implementation of the algorithm in Python can be achieved using the NumPy module, and the output and path selection depend on the specific problem being solved.

## Comparison with Best First Search Algorithm:

The best-first search algorithm is another search strategy that uses heuristics to guide the search towards the target state. In this section, we will compare the beam search algorithm with the best-first search algorithm and highlight their advantages, shortcomings, and applications.

### Advantages of Beam Search Algorithm:

The beam search algorithm has several advantages over the best-first search algorithm. One of its key benefits is scalability.

The beam search algorithm can handle large search spaces and still provide an efficient solution. This is because the algorithm maintains a limited number of nodes in the beam, reducing the amount of memory required and the time taken to search the space.

Another advantage of the beam search algorithm is its ability to work with limited resources. In situations where there are memory or time constraints, the beam search algorithm can be used to provide an optimised solution while still taking into account the available resources.

### Shortcomings of Beam Search Algorithm:

One of the shortcomings of the beam search algorithm is its incompleteness. The algorithm may fail to find the target state even if it exists in the search space.

This can happen when the beam is too narrow or the depth of the search is limited. In some cases, the beam search algorithm may not reach the optimal solution as it only considers a limited number of nodes at each level.

Another shortcoming of the beam search algorithm is its subpar performance on certain search spaces. In some situations, the search space may not be well defined, making it difficult for the algorithm to find the optimal solution.

Additionally, if the best nodes are not selected during the search, the algorithm may not find the target state, which is a risk associated with any heuristic search method.

### Applications of Beam Search Algorithm:

The beam search algorithm has several applications in various fields.

- Machine translation: Generating possible translations from one language to another.
- Problem solving with multiple solutions: Generating possible solutions and selecting the best one based on specific requirements.

## Summary of Beam Search Algorithm:

In summary, the beam search algorithm is a heuristic search strategy used to find the shortest or cheapest path to a target state. It maintains a limited number of nodes in the beam, reducing the amount of memory required and the time taken to search the space.

The algorithm has several applications in various fields, including natural language processing, game playing, and speech recognition. While the algorithm has some shortcomings, it remains a powerful tool for solving large-scale search problems.

In conclusion, the beam search algorithm is an efficient way to find the cheapest or shortest path to a target state while maintaining limited resource usage. It is a heuristic search strategy used in various applications, including natural language processing and game-playing agents.

Its main advantages include scalability and the ability to handle limited resources, while its shortcomings include incomplete results and subpar performance on some search spaces. Nonetheless, it remains a powerful tool for solving large-scale search problems, particularly in situations where the search space is well-defined.

Its implementation in Python is straightforward with the NumPy module and can provide optimised solutions to complex problems. Overall, the beam search algorithm is significant in solving large-scale search problems, and its applications continue to grow in various fields.