# A Comprehensive Overview of Cuckoo Search Algorithm with Examples

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## Introduction

The Cuckoo Search Algorithm is a powerful optimization technique inspired by the brood parasitism of some cuckoo species. In this comprehensive overview, we will explore the core principles of the Cuckoo Search Algorithm through detailed examples, covering essential topics like how to calculate values using Levy's flight, the transition between cuckoos' positions, and answering common questions arising from initial implementations.

## Understanding Cuckoo Search Algorithm

### What is Cuckoo Search?

Cuckoo Search is an algorithm based on the behavior of cuckoo birds, which lay their eggs in the nests of other bird species. The algorithm utilizes a few primary parameters:

- Total population of nests
- Probability of discovering cuckoo eggs (typically set at 0.25)
- Maximum number of iterations, often set to 300

These parameters work effectively together to resolve maximum optimization problems by replacing poorer solutions with superior ones in the population.

### Key Features

- Simple Implementation: The algorithm requires only two primary parameters (population size and the probability of discovery).
- Iterative Process: It operates in multiple iterations, refining solutions at each step.

## Calculating Levy's Flight

### What Is Levy's Flight?

Levy's flight is a critical component in determining the new position of a cuckoo within the search space. It allows for a random walk characterized by a series of small and large jumps, enhancing the exploration capabilities of the algorithm.

### Step-by-Step Calculation

**Select a Cuckoo (i):**Choose a random cuckoo from the population.**Levy's Distribution Parameters:**Establish parameters for creating random steps from Levy's distribution.**Step size equation:**$$ s = ext{current position} + ext{Levy flight step size} $$

- For optimization, if the calculated value of 's' is too small, the generated new solution will be too close to the previous one. Adjust the step size accordingly to ensure effective exploration.

## Updating Cuckoo Positions

Once the cuckoo's new position is calculated using Levy's flight, the next step is to update the host nests. The primary aim here is to ensure that bad solutions are replaced with better alternatives. This process involves:

**Choosing a Random Nest:**For the currently selected cuckoo, randomly select one of the host nests.**Condition Checking:**If the cuckoo solution is better than the host nest, replace the nest's solution with the cuckoo's solution and discard the least favorable egg (nest).**Iteration Process:**This process is repeated across populations iteratively until the specified maximum number of iterations is reached.

### Example Illustration of the Process

Let’s illustrate the algorithm's workings:

**Initialization:**Start with a fixed population of host nests, e.g., five.**Generate Initial Positions:**Assign initial positions to each cuckoo in the nests, tracking their solution values.**Calculate New Solutions:**Using Levy's flight, calculate new positions iteratively for each cuckoo based on the growth of the population.**Rank and Select Best Solutions:**As iterations progress, maintain the best solutions and update as necessary, ensuring no distinction is made between cuckoo eggs and nests during calculations.

## Addressing Common Questions

As users engage with the Cuckoo Search Algorithm, several questions often arise, including:

### 1. Is each cuckoo egg equivalent to a nest?

Yes, within this algorithm, cuckoo eggs and host nests are treated as comparable, emphasizing that all are points within a search space undergoing positional changes.

### 2. How do we calculate Levy's distribution?

Levy's distribution is characterized by a sequence of smaller steps, which can be effectively calculated using previous examples within the algorithm's framework.

### 3. Does entry-wise multiplication mean element-by-element?

Absolutely, in the context of the algorithm, entry-wise multiplication is performed, ensuring that every point in the solution vector is multiplied element-wise.

## Conclusion

The Cuckoo Search Algorithm offers a fascinating insight into optimization techniques inspired by nature. By leveraging simple mathematical parameters and iterative processes, it showcases remarkable capabilities in enhancing solution populations through calculated randomness. The understanding of Levy's flight is central to the algorithm, providing a foundation for effective exploration in optimization problems. We encourage you to engage with any remaining questions or clarifications, and appreciate your interest in this remarkable algorithm.

Hello in this video i will try to explain cuckoo search algorithm using an example. Before this i tried to explain what is cuckoo search all about that is explained in the cuckoo search part 1.. so everything is explained step by step. In this video i will try to explain what is coco search

using example. Topics that are covered in this video: how we can calculate the values for levy's flight? how we can calculate the value for cuckoo's each step? and how we can update the cuckoo's new position? then we have certain question asked by user in

cuckoo search part 1 before starting this video i want to mention one thing whatever calculation done in this video it's my own calculation and if you found any error please comment below. Simplicity of this algorithm is we use here only two parameter

that is the total population of the nest and then we have the probability of discovery of cuckoo egg for that value is 0.25 and these parameters are sufficient for maximum optimization problems third step is set the maximum number of iteration that is here 300 and one thing is here we cannot

make any difference between cuckoo egg and a nest so the aim of this algorithm is we will replace the new and the butter solution with bad solution that are in the current population so it is important to remember that we cannot make any difference between Egg, nest and cuckoo

so what is the aim of this algorithm? we are updating or we will replace the bad solution with new and better one so initialize the population of the host nest that is five in the research paper that is cuckoo search by levy's flight...

you can see here this is the final location of the nest and you can see the search path of nest using cuckoo search so this example that is given in this video i use the algorithm that is given in this research paper you can see a

number of research paper over the internet and according to that there is a little bit difference in their algorithm so this example is based on this algorithm initialize the population we have only five host nest you can see the position of each host nest here you can see

the initial population of host nest that is five and the position of each host nest here one thing i mentioned before that we cannot make any difference between host nest, egg and a solution so you can see here each position of the cuckoo that is that we have only five cuckoo and the

position of each cuckoo here and this is the optimal point that is hundred and the position of cuckoo you can see their position so next step is now we will obtain the new position for i(th) cuckoo we will select the cuckoo randomly for that we will obtain a new position using levy's flight

suppose in this first of all i will choose first cuckoo that is the value of i is one and the value of i is one to n so i'm selecting here first cuckoo this one and we will perform lab slide using this equation here this is the current

this is a new solution this is the current location this is the step size this is the anti-vice multiplication and this is the lavish exponent so in order to calculate the levy's flight that is the random walk done by bird that is cuckoo here cuckoo search algorithm is a random

searching process here a bird that is cuckoo searching for a suitable host nest by laying egg so we will calculate lavish flight using this and random steps can be drawn from levy's distribution levy's distribution means series of smaller steps and we can express step size using this equation

here one thing that is important if the value you calculated for s is too small that mean the new solution generated will be far away from the older one if the value of s is smaller then it means changing position will be too small so it is important to use proper step size

for the search space put the values here here u is this we you can see all the value value of beta is 3 by 2 and we got the value for standard deviation is 0.6966 next put the values here and we got the step size is 0.33802 here that is the step size

that determines how far a random walker can go for a fixed number of iteration in general render walk means it is a chain whose next location depends on the current location current location is the first term in the above equation that we will see in the example

you can see in the lab slide we are using x best that is the global best position right now this is the initial stage so we don't have any best position for any cuckoo or you can say host so we will consider this value zero put the value of x best for the this situation zero

and we will calculate new solution using this this is the old position plus levy slide next select a cuckoo randomly that i selected here first cuckoo fuji is now first cuckoo is 4 put the values here set the counter 0 put the value of t 0 you can see here now position of first cuckoo at iteration 0

that is 4 put the values here global best is 0 right now we don't have any global best position for any cuckoo this is the initial stage so we got the new solution for the first cuckoo that is 5.35 next step is choose a nest randomly then we will compare the value of cuckoo with the randomly

selected nest here i selected a nest randomly that is nice number two that is this one and the value is here now six now check this condition condition is false it means google is not similar to host tag so we will destroy the lowest rank ag and then we will generate a new egg near the older one so

the aim of this algorithm again i'm repeating this point replace the bad solution with the new and better one this is the value that we calculated now for first cuckoo at first iteration keep the bat solution and we will increment the counter until we met the condition

now we will select another cuckoo that is hoku number two and the value for this cuckoo is 6. put the value in the levy's flight and we got this one now we will select again any nest randomly put the value here condition is true it means that cuckoo egg is similar to host bird egg now

we will replace the randomly selected nest with new solution and we will destroy the lower rank nest then we will calculate the value that is the new solution for the cuckoo for the second cuckoo that is here update the position then we will select another cuckoo that is cuckoo number

three you can see here this is the recently updated position for this cuckoo put the values here and in the levy's flight and we got the solution here again check randomly select any you can select any nest randomly then put the value here check the condition if it is true then

replace the solution by new solution and then calculate the new nest near the older one update it like that we will update this for all and this one is for the fifth cuckoo done so these are the value we updated and then according on the basis of these two

we got this one this is at iteration one now we will increment the counter one you can see here now we are here keep the batch solution that is here now we will rank the solution and we will find the current best according to this you can see the current best is now

this cuckoo number five this is the nearest one so this is the front best so for iteration one first value of counter is zero that is the initial stage now value of counter is one so it is two and now we have global best position that is cuckoo number here you can see 5 this is

the global best position now in the next iteration put the value of global best 28.844 and you can see when you will try to calculate this now the value of counter is 2 so this is the new solution we are calculating for the first cuckoo here we will put the value position off first cuckoo at

iteration one that we recently calculated 7.16 put the value here and global vast is here 28.884 we are updating the bad solution with the new and the battery one so we have now random questions that are asked in the part one so first question is in cuckoo search is each egg is equivalent to a nest?

and the solution yeah ... in this algorithm they assumed that the cuckoo egg and host they are similar we cannot make any difference between any cuckoo egg and host nest so all of them are point in the space that are changing their position done. second question is how we can

calculate levy's distribution? levy's distribution means series of smaller steps that you can see in this slide how we are calculating these smaller steps using levy's flight done next question is does entry wise multiplication means element by element and

multiplication? Yes this in this example they are using vector form so in the cuckoo search.. we are doing entry wise multiplication and you can see here that we have different parameters that are used for maximum optimization problem and these parameters are

sufficient i provided all the important link in the description box and still if you have any question you can comment below and thanks for watching this video :)