The increase of the population leads to (at least initially) increased diversity of the population, but if one increases the population size too much, there may be slow convergence of the population to the global optimum. But if the population is too small, it will lead to entrapment to local optima. It is widely suggested to increase the population in order to avoid local optima, especially if the objective function has many parameters. As for the number of iterations, an increased number will increase the possibility for convergence to global optimum, but you may start doing useless computations. In this case, you might need a good termination criterion that prevents useless computations after reaching global optimum.

For the latter, read the following paper.

Spanakis, C., Mathioudakis, E., Kampanis, N., Tsiknakis, M., & Marias, K. (2016). A Proposed Method for Improving Rigid Registration Robustness. International Journal of Computer Science and Information Security, 14(5), 1.

You need to be advised that no matter the population size, the method will most likely not lead you to an optimum - and if you are at one, how would you know?

The research article in the following link may help you

Article A Comprehensive Review of Swarm Optimization Algorithms

Dear Hassen,

I suggest you to see links and attached file on topic.

https://arxiv.org/ftp/arxiv/papers/1804/1804.05319.pdf

https://www.inderscience.com/info/ingeneral/forthcoming.php?jcode=ijbic

Article A Solution Quality Assessment Method for Swarm Intelligence ...

Article Evolutionary algorithms, swarm intelligence methods, and the...

Best regards

Aren't you interested in learning the actual optimum/optima? With these methods you're doomed to NOT know.

Increasing the population size would increase the cost of calling the objective function with no (or very few) impact on the solution quality (because of the convergence of the method, many particles would be close to each other and will not increase the solution quality).

And decreasing too much will lead to a poor exploration of the search space.

The objective of a correct population size is to find a compromise between the cost of the computation and a correct convegence.

The population size should depend on the size of the search space, to get a correct exploration rate. A common value for poulation size is E(10 + 2 * sqrt(dimension)).

Good luck !

Hello Hassan Almazini

In general, in swarm algorithms, the parameters setting are problem dependent and there is no optimal parameter setting that will work with every problem.

Usually, in discrete problem (large scale problem) the population size and the number of iterations needs to set a high number to give good results with a high quality of solutions. While a small problem needs to set a small number to give good results with a high quality of solutions. Plz, check the attached articles.

Regards,

How do you know that the output is good/good enough? Answer: You do not. Learn discrete optimisation - promptly!!

You can try meta optimization techniques such as meta PSO to optimize the parameters first with respect to the cost function. It will help you to find the optimum parameter settings and reduce the time for fine-tuning.

Hello dear Michael Patriksson

I answered based on related work about the parameters tuning for swarm Intelligence algorithms when dealing with a discrete problem such as Routing (TSB and VRP), Scheduling (Job shop and Total weighted tardiness), Assignment (Quadratic assignment and University course timetabling)........Etc.

https://web2.qatar.cmu.edu/~gdicaro/15382/additional/aco-book.pdf

For the output, we can see that previous studies used large values for population size and the number of iterations to explore and exploit the search space to get good results..... after that should compare the current results with previous studies that have used the same dataset for a specified problem.

Article Parameter Selection of Discrete Particle Swarm Optimization ...

Regards,

And I say that you should implement the model also in python, gurobi and cplex:

https://medium.com/opex-analytics/optimization-modeling-in-python-pulp-gurobi-and-cplex-83a62129807a

Otherwise you will never know what the ideal (i.e., the optimum) is!! Perhaps you will find that your problem instances processes very well through your method, so that you can say that

"these instances are favourable when comparing CPU time against the mathematical optimisation software, and was surprisingly close to the actual optimal value of the problem," but you will never be able to say that the method you are now using will always provide near-optimal solutions: that guarantee you will never be given, and that is why you should always compare your output with the optimal one. To not try to compare is a disservice to the reader, in fact.

Well done Michael Patriksson

Dear Hassan:

your question has no single (nor simple) answer.

Your are not saying anything regarding the problem you are trying to solve, nor the instances under study. Moreover, what you may learn for one instance may not be true for another one.

My suggestion is to focus in the problem being solved and try differente solvers.

And... there are hundreds of papers exploring the effects of several features in population based techniques (just take a look at papers using genetic algorithms and forget all of these "new" animal and insects inspired techniques)