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# Introduction to the Hill Climbing Algorithm in AI

• Soumalya Bhattacharyya
• Jan 20, 2023

To solve optimization-related problems, the "hill climbing" heuristic search technique is used in the field of artificial intelligence. The algorithm starts in a less-than-ideal state and gradually becomes better until a certain condition is met. The necessary condition is based on the empirical function.

The algorithm's objective is to go from the present state to an improved one known as the optimum state. The name "Hill Climbing Algorithm" relates to the initial location, which is the suboptimal state, and describes the algorithm's endeavor to iterate (climb) continually until it reaches the peak value.

Local search strategies are used to locate a potential solution that optimizes the criterion on challenging optimization problems. The hill climbing algorithm is a local search algorithm that constantly advances in the direction of increasing height or value to find the top of the mountain or the best solution to the issue.  It comes to an end when it achieves a peak value at which none of its neighbors have a higher value.

A technique for resolving problems using mathematical optimization is the hill climbing algorithm. One of the most popular examples of a hill-climbing algorithm is the traveling salesman. Problem: We need to reduce the travel distance of the salesman.

It is also referred to as greedy local search since it just looks inside its pleasant close neighbor state and does not look farther away. The two parts of a hill climbing algorithm node are state and value.

Also Read: Top 10 AI Algorithms/Models

## What is a Hill Climbing Algorithm?

A local search method known as a "hill-climbing algorithm" keeps moving uphill (growing) until the optimal answer is found. Once the peak is achieved, the algorithm is complete.

A node in this algorithm has two components: status and value. The hill's base is the starting point, which is not optimum and is improved until a certain need is satisfied. The foundation for this prerequisite is the heuristic function.

Climbing is a concept that may be used to describe the process of continuously improving the iteration's present condition. It makes sense now why the method is known as a "hill-climbing algorithm."

The goal of a hill-climbing algorithm is to reach an upgraded version of the current state that is optimum. The method will make additional incremental modifications to the better state once the present state has been improved. This procedure will keep going until the best possible option is found. Further advancements are not possible in peak conditions.

The hill climbing algorithm can be used to efficiently address large computing tasks. It takes into account both the local state and the state that is currently in effect. The hill climbing issue in artificial intelligence is very beneficial when we want to improve or reduce a certain function depending on the input it is getting.

The most well-known AI example of a hill climbing algorithm is the "Traveling Salesman" Problem, in which we must minimize the salesman's travel distance. Although the Hill Climbing Algorithm is skilled at quickly discovering local minima/maxima, it might not find the global optimum (best feasible) solution.

Hill climbing, to put it another way, is a heuristic tactic. It is a search strategy or informed search approach that gives different nodes, branches, and destinations along a path different weights depending on real numbers. These statistics and the heuristic developed for the hill climbing search in the AI model may now be used to enhance the search. The excellent input efficiency and improved heuristic assignment of the hill-climbing algorithm are its distinguishing features.

Hill climbing results from depth-first search quality evaluation (a variant of generating and test strategy). It is an optimization tactic that belongs to the family of local search engines.

It is a reasonably simple implementation method as a well-liked initial choice is investigated. Hill climbing can be useful in some situations, even if more sophisticated algorithms might offer better results.

There are several answers to issues that can be solved, yet some methods are preferable to others. Hill climbing can be used to solve the dilemma of the traveling salesperson. Finding a service that travels to every city is straightforward, but this service is probably not as good as the ideal one.

If there were a way to organize the choices so that the most promising node was investigated first, search efficiency may rise. Hill Climbing advances over a network of pathways in depth-first order, but the possibilities are ordered according to some heuristic value (ie, a measure of remaining cost from current to goal state).

## Importance of Hill Climbing Algorithm in AI:

For optimization issues, the hill climbing algorithm serves as a local search method. It functions by starting at a random location, shifting to the next optimal setting, and repeating this process until it reaches either a local or global optimum, whichever occurs first.

Consider the situation where we need to locate the highest point on a steep area. The hill climbing algorithm might be applied as follows: Choose any random position on the map as your starting point; determine which direction goes to an uphill slope; proceed in that direction; and continue from step two until you reach the highest point on the map (i.e., the top of a nearby mountain).

The hill climbing method can be used to solve issues where an ideal solution must be discovered but when the starting position is unknown. For instance, a scenario involving a traveling employee requests the quickest route that stops in each location precisely once before heading back to the starting point. There is no established optimum path, however, the hill climbing algorithm can be used to identify an ideal path.

Finding the quickest route between two sites and maximizing profit in a commercial situation by deciding on the most lucrative mix of goods or services are two more optimization issues that may be resolved via hill climbing.

You can use hill climbing to accomplish activities like puzzle-solving or competitive games of chess or checkers. In these circumstances, the method is used to determine the next best move by evaluating all of the potential movements and selecting the one that maximizes the score or minimizes the number of pieces left after the move.

Finding a route that optimizes both travel time and fuel usage is an example of how to use the hill climbing technique for issues with multiple goals.

Artificial intelligence uses "hill climbing" to improve the mathematical interpretation of the issues that are provided. Thus, an algorithm tries to find a potential solution to the given issue in a fair amount of time given the large collection of mandated inputs and heuristic functions. Hill climbing works well when there isn't enough time allocated and the issue could or might not have definite solutions. According to this concept, picking values from the input allows hill-climbing to resolve problems where it is necessary to reduce or maximize the real function (that is also given).

A traveling salesman's issue, where we may need to either reduce or maximize the distance traveled by the salesman, can be an example of a hill-climbing algorithm.

Hill climbing only discovers local optima (solutions that cannot be improved upon by any nearby configurations) for non-convex problems, which are not always the best possible solution (the global optimum) out of all potential solutions (the search space). Binary search and the simplex algorithm for linear programming are two examples of algorithms that solve convex problems by climbing hills.

Restarts (i.e. repeated local search) or more complicated iterative or memory-based methods (i.e. reactive search optimization and tabu search) might be used to try to prevent being trapped in local optima. Memory-less stochastic modifications could also be used (like simulated annealing).

The method is a common initial pick among optimizing algorithms due to its relative simplicity. It is frequently used in artificial intelligence to transition from a beginning node to the desired state. In related algorithms, many options for beginning nodes and next nodes are employed.

Hill climbing is sometimes equally as effective as more sophisticated algorithms like simulated annealing or tabu search, even if they may provide superior results. When there is a limited amount of time available to execute a search, such as with real-time systems, hill climbing can frequently yield a better result than other algorithms, provided that a small number of increments generally converges on a suitable answer (the optimal solution or a close approximation).

At the opposite extreme, bubble sort may be thought of as a hill-climbing algorithm (each nearby element exchange reduces the number of disordered element pairs), but even for a low N, this strategy is inefficient since the number of exchanges needed increases quadratically.

Also Read: 5 Types of Intelligent Agents in Artificial Intelligence

## Problems with Hill Climbing Algorithm:

Hill Climbing comes with several drawbacks. There may be no answer found after much searching, but nothing further can be done to make things better. The local maximum, a plateau, or a crest will have been attained if this has occurred.

• ### Local maximum:

It's a state that performs better than all of its neighbors but not as well as certain states that are farther away (there might be a better solution ahead and this solution is referred to as the global maximum.) All actions seem worse from this position. If this happens, go back to a previous state and try to solve the problem from a different angle.

• ### Plateau:

A region of the search space that is level and where all nearby states have the same value. The best course cannot be chosen in advance. In this case, perform a sharp turn and try to reach a different area of the search area. Flat maximum is another name for it.

• ### Ridge:

This is a region of the search space that is higher than the nearby terrain but cannot be reached by making a single movement in a single direction. This particular local maximum is unique. Here, you should use two or more guidelines before taking the exam, which entails traveling in many directions at once.

## Types of Hill Climbing Algorithm:

Types of Hill Climbing Algorithm

The different types of hill-climbing algorithms are as follows:

1. ### Simple Hill Climbing:

Simple hill climbing is the most straightforward way to ascend a hill. Ascending to the mountain's highest summit is the objective. In this situation, how the climber climbs depends on his steps and movements. If he believes his subsequent step will be better than the one before it, he will continue to progress; otherwise, he will remain where he is. The only activities he took before and after are the subject of this search.

1. ### Steepest-ascent Hill Climbing:

Rather than just ascending a hill, it compares all of the consecutive nodes and chooses the one that is closest to the solution. The steepest hill-climbing search is analogous to the best-first search since it focuses on all nodes rather than just one.

1. ### Stochastic hill climbing:

In stochastic hill climbing, the nodes are not all focused on one point. It randomly selects one node and then decides whether to expand it or find a better one.

1. ### Random-restart Hill Climbing:

The random-restart algorithm is built on a try-and-try methodology. It iteratively searches the node and selects the best candidate at each level up until the target is not reached. The shape of the slope is typically what determines success. If there aren't many hills, plateaus, or nearby maxima, getting there is easier.

## Conclusion:

A variety of issues, including Network-Flow, the Traveling Salesman Problem, the 8-Queens Problem, Integrated Circuit design, etc., can be resolved using the hill climbing approach. The inductive learning approaches also include hill climbing. Coordination between several robots working as a team is achieved using this approach in robotics. This method may be used for a wide variety of different issues.

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