It should not be that different of time, even if CSO has higher time complexity than PSO. PSO in general has a simple structure.

There are several reasons, one of them could be the answer for your question. First of all, the code, no one can be sure of why CSO is slower than PSO until check the whole codes for both algorithms. Different programming styles lead to different performance, however, the results in terms of the optimal solutions are the same.

Second, you have to check how many no. of function evaluation are performed, make sure both algorithms have the exact same no. of function evaluation.

Third, try tow types of problems, normal and large scale problems. For example, sphere test function with different no. of dim ( 10 , 30, 100, 500). Maybe you will find that CSO is stable while PSO is getting slower as the no. of dim increased ( I proved this already for PSO in a paper which is still under review). Finally, The execution time dose not matter at all, different H/W lead to different execution time, so usually we do not take it serious unless the contribution of the paper is to enhance it, such as implementing a quantum version or parallel version of the algorithm.

Hope this helps,

Regards ..

Dear Saidu Yahaya ,

As I see,

If you look at the pseudocode of PSO and CSO, you can see that they are nearly the same. Both algorithms have two external loops that are generation(epoch) loops and a loop through the entire population.

However, when you code experimentally, you can see clearly that:

     1) CSO implements more operation than PSO, the operator that change the state between seeking mode and tracing mode (for the entire population)

     2) CSO has one more loop, under the seeking_mode phase of cats.

We can see, if we set up a larger number of clone_cats, CSO costs more time to calculate the third loop.

So, in general, the running time complexity of CSO and PSO is O(epoch * N * N_clone_cats) and O(epoch * N) respectively.

You can see what I said very clearly after viewing the source code (python, numpy) in my git:

https://github.com/thieunguyen5991/metaheuristics/blob/master/models/multiple_solution/swarm_based/CSO.py

https://github.com/thieunguyen5991/metaheuristics/blob/master/models/multiple_solution/swarm_based/PSO.py

As a many metaheuristic methods they maintain several similarities and also several diferences. In general terms, CSO mintains a heavy complexity.

Fear Prof. Yahaya,

If you use simulation to test classify your metadata as a heuristic step by using PSO and then use CSO for problem solving I believe you will see that in real experiments the time complexity will not matter.

S.K.Mallick

for S.K.Mallick, S.Raychaudhury, S.Mallick and others,

The RHMHM School,

USA, Japan, Russia, India

Prof. Thieu Nguyen

Thank u for the clarification.

Sir, is there any literature to back this argument up? I will highly appreciate if provided.

thank you in anticipation of your respond

Dear Saidu Yahaya ,

There are few papers below which comparing PSO and CSO, but they only compare the accuracy of the model when using 2 algorithms for their problem, not mentioning the calculation time. If you still want to compare the complexity of time between two algorithms in your article, I think you can do the following:

+ Write the details of pseudocode for both algorithms

+ Calculate the computational complexity for both algorithms (based on my previous comment)

     _CSO = O (epoch * N * N_clone_cats)

     _PSO = O (epoch * N)

+ Give the runtime of both algorithms when you implement it in your problem.

https://link.springer.com/chapter/10.1007/978-3-642-24043-0_20

https://etda.libraries.psu.edu/files/final_submissions/8534

https://pdfs.semanticscholar.org/3b38/a35638f15cbd7ef7543ec75f1ec810424b8c.pdf