The size of the population remains fixed in any metaheuristic optimization approach including PSO. Each element of the population is a candidate solution, so its represents the values of all the variables. So, if the size of the population is 100 and number of variables are 28 then the population matrix is of 100*28 and it remains fixed throughout the generation. However, the final solution is one among the population, so, the optimum solution is of 1*28 which represents the values of all the variables.

The size of the population in GAs usually remains constant from one generation to the next. As a consequence, there is no chance of the chromosome population become either overgrown or extinct during the many iterations of the GA cycle.

(Source: Berry, M. L. A.; Linoff, G., Eds. Data Mining Techniques: for Marketing,

Sales and Customer Support. J. Wiley Computer Publishing, 1997)

As explained in previous answers, the size of the population usually remains constant throghout the execution of the algorithm. Since this size influences performance, there's quite a bit of literature on population sizing. This said, there have been many proposals to dynamically resize populations in response to the evolutiom of the search. Check for example

https://www.researchgate.net/publication/220702069_Evolutionary_Algorithms_with_On-the-Fly_Population_Size_Adjustment

https://www.researchgate.net/publication/220999115_Dynamic_Populations_in_Genetic_Algorithms

The use of dynamically-sized populations is actually quite natural if you move to the area of distributed computing, in situations where you can have faulty computing nodes. Check:

https://www.researchgate.net/publication/221006369_Analyzing_fault_tolerance_on_parallel_genetic_programming_by_means_of_dynamic-size_Populations

https://www.researchgate.net/publication/276100996_Studying_self-balancing_strategies_in_island-based_multimemetic_algorithms

Conference Paper Evolutionary Algorithms with On-the-Fly Population Size Adjustment

Conference Paper Dynamic Populations in Genetic Algorithms

Conference Paper Analyzing fault tolerance on parallel genetic programming by...

Article Studying self-balancing strategies in island-based multimeme...

Because there are 100 chromosomes in the population and each chromosome consists of 28 variables, it indicates 100X28 as a matrix dimension. Each row of the matrix is a chromosome of the population and each column indicates a variable.

Thank you everyone for your answers.

As I mentioned the size of population in the 100th generation as can be seen after program termination is 100x28. Also, each row of this matrix represents the same 28 values that has been chosen as optimized solution by the GA tool. i.e. if the optimized values of 28 variables obtained at the end  [10 29 30 15 16 28 94 15 67 85  ......&so on upto 28 values] then each row in 100x28 population matrix at end shows these values only. Is it correct? Can anyone explain? 

Yes, it is correct. ideally it is expected that all chromosomes are identical in the last iteration of GA. So it is not possible to further improve the chromosomes of the population. Of course, in a highly complex problem, it may not be possible. In that case, the GA terminates because of other criteria such as maximum number of generations, or improvement in x values or fitness function values is negligible, etc.

Thank you sir.

But i have noticed that some values in some rows of 100x28 matrix are different. E.g. for 12th variable (that will be 12th column in 100x28 matrix), out of 100 rows its value is different in 2 or 3 rows (rest all values are same say equal to 116.13 but for that 2 or 3 rows its values are say 50.56, 112.3, 200.89). But since almost all values in the last generation or iteration are same so can we consider that GA has found the optimum value for 12th variable?

Similarly for some variables, all values in each row for that respective variable are same except at one place out of 100 rows. 

If the algorithm terminates because of maximum generations reached then may be the solution is not optimum but if it terminates by its own before maximum number of generations reached then can the above obtained values in the last generation be considered as optimum solution? Please Explain .

In general, GA gives "near optimum" values. For simple problems, it may give the true optimum solution, but in complex problems, it may not give the correct optimum solution. In fact, all Artificial Intelligence techniques should be applied when it is difficult if not impossible to solve the problem by other analytic or numerical methods.

So, people run the algorithm several times by changing parameters and the best result obtained among them is declared as the optimum solution. Because if the problem is difficult to solve by other methods and it is not possible to find solution at all, then an approximate solution is also acceptable.

Thank you sir

size in a standard implementation of GA remains constant throughout, nonetheless there are good number of examples in literature where models for population resizing have been suggested. 

As for the number 28 in your case, the reason may be the alphabet size in the gene pool. The alphabet set is the number of different alleles possible for each locus of the chromosome.

Thank you

 Hi Sunita

it is a custom to keep the population size constant across iterations/generations in GA studies however, the rules in here are not written on stone per say. 

You are welcome to play around with ideas about having varying selection mechanism across generations resulting in expansion and contraction of the population across generation but you might need to do all the coding by yourself since most conventional tools are loyal to basic and conventional designs.

If having dynamic population size is what you have in mind, you need to have a clear and automated mechanism for this to make sure you only extend the population size when better chances of finding the optimum exist or it might be that you should only expand when the population is not performing well.

Basic PSO has a simplistic mechanism for its exploration and exploitation coming from linearly decreasing inertia weight (LDIW) which is based on the assumption that the best strategy to have a large level of exploration in early generations and slowly switch to exploitation forcing the particles to converge toward an optimum. Although I this has no effect on population size but essentially it does what you want to do with your dynamic population size, I think :D

There are several designs of PSO that contradict this idea. for example, AEPSO works under the assumption that having a balance between exploration and exploitation or having a fixed strategy like LDIW is not necessarily the best way. AEPOS tends to switch between exploration and exploitation based on the search requirements and in addition it treats each member of the population separately. which means that at the same generation, one particle might be doing exploration while another is doing exploitation and they all share information with each other.

I hope this help.

You should also be mindful that if "all values in the rows" of the final population are the same, you may have created a cloned population. This does not guarantee that the optimal solution was located. It may suggest that not enough diversity was interjected into the creation of child solutions through mutation, or possibly that the selection of parents did not allow the population to diversify.

Thank you all for the reply

What is the total no. of chromosomes in the population in each generation? Is it fixed or varied?

hello please how i can solve my problem with the AG method if i have a variable size population