Introduction
The Cuckoo Search Algorithm is a novel optimization technique inspired by the brood parasitism of some cuckoo species, where these birds lay their eggs in the nests of other bird species. This algorithm is particularly effective for solving complex optimization problems due to its unique approach to exploring potential solutions. In this article, we'll dive deep into the workings of the Cuckoo Search Algorithm, using a practical example to illustrate its key principles and calculations.
What is the Cuckoo Search Algorithm?
The Cuckoo Search Algorithm employs the concept of levy flights and uses a simple mechanism based on the following parameters:
- Total population of nests
- Probability of discovering a cuckoo egg (set to 0.25)
- Maximum number of iterations (set at 300)
Main Objectives:
The algorithm's primary goal is to replace inferior solutions (bad solutions) in the current population with better ones, ensuring that it can efficiently converge towards optimal solutions.
Since the algorithm operates without differentiating between a nest, a cuckoo egg, and a cuckoo, it has certain unique characteristics compared to traditional optimization approaches.
The Step-by-Step Process of Cuckoo Search
Initialization of Hosts and Cuckoes
- Initialize the population of host nests: For our example, we consider five host nests (or cuckoos).
- Representation of initial positions: Each host nest has a specific position, as illustrated in the example.
- Assumption of uniformity: There is no differentiation among cuckoo eggs, nests, and solutions, simplifying calculations.
Levy’s Flight Calculations
The next crucial step involves calculating the values for Levy's flight. Levy's flight refers to random walks where larger steps are frequently replaced by series of smaller steps. A mathematical approach is used for calculating these values efficiently:
- The standard deviation of the flight can be calculated, guiding how far each cuckoo might move based on their current position.
- Random Walk Mechanism:
- Cuckoos choose a random nest to generate their new position via Levy's distribution, a vital component that determines their next movement.
- Step size is critical; it influences how far a cuckoo can travel from its current location. A small step size leads to minimal change, while a larger step size may cause extensive exploration of the search space.
Iteration and Updating Positions
-
Updating cuckoo positions:
At every iteration, cuckoo positions are updated based on their most recent calculations:- If a newly calculated cuckoo solution is better than the existing nest solution, the nest is replaced.
- Overall, the algorithm attempts to converge towards an optimal solution by iteratively updating nests based on their values and positions in the search space.
-
Comparison Check Between Cuckoo and Nest:
- Each cuckoo's solution is compared with a randomly selected nest. If a cuckoo finds a nest similar to its egg, that nest's solution will be replaced by the cuckoo's better solution. If not, the worst-performing nest is destroyed and replaced with a new one nearby.
Convergence towards Optimal Solutions
With each iteration, cuckoos update their positions while maintaining a counter that tracks their progress. The current best solution is consistently evaluated as new solutions are generated.
- Ranking the Solutions: After each iteration, solutions are ranked, and the current best is identified, allowing the algorithm to track progress towards optimization.
Conclusion
The Cuckoo Search Algorithm is a powerful tool for solving optimization problems, characterized by its randomized search process and clever use of biological phenomena. By logically deducing new potential solutions and iteratively updating them, it can efficiently navigate through complex search spaces. With this step-by-step guide and practical example, you'll better understand how to implement and utilize the Cuckoo Search Algorithm for your optimization challenges. If you have any questions or feedback regarding this tutorial, feel free to leave a comment below. Happy optimizing!
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 :)
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