GA are stochastic optimization technic, so it is normal to have a different result from the different running of the experiment. They also can reach local minima and stay there depending on the mutation rate of your GA.

On other hands, you change the parameter space in which the GA will search for the optimum. In your case, the parameter space is much bigger (~9 times bigger in each dimension so it's roughly speaking 700 times bigger in volume).

I would try to increase the number of generations to give enough time to te algorithm to reach the optimum.

Let seid: popSize = 2000

Erick Olivares,

Sir,

Thanks for answering. I tried the experiment by increasing the number of iterations and setting popSize=2000, and the result I got is:

Iterations = 446

Fitness function value = -19288.59

Solution =

a b c

[1,] 2876.211 0.02320801 4.145813

These are obviously not the optimal values as estimated in the paper.

In general, I see that in the case of my function that I am estimating the parameters estimated by ga() settle close to my initial values even if I take more no. of iterations and population size. Is this to be expected and is there any way to get improved estimates?

GA solutions are heavily dependent on their parameters. I can suggest two different approaches.

- Try to find the best parameter value with repeatedly testing which would be time consuming.

- Use self-adaptive parameters based on convergence rates.

If you run the experiment several times you will have different results each time. In my case I ran it 3 times with your ranges [min = c(1000, 0, 0.5), max = c(10000, 10, 10)] and I got fitness of -22204, -3296 and -7624.

The algorithm is converging to local minima and not reaching the global minima. You can try to avoid fall into local minima increasing the mutation rate (e.g.: pmutation = 0.2, see example in 4.3), but it doesn't guaranty anything.

As a general idea, GA are less likely than gradient methods in order to get stuck in local minima, but they are not infallible.

On another hand, you are not changing the initial values, but the range of the parameter space in which the GA will search for the optima.

As I said, you are increasing the volume of the parameter space in about 700 times, so it's much harder for the GA to get in to the optimal position.

@ Osman Pala

Sir, thanks for responding. You write

- "Use self-adaptive parameters based on convergence rates." Please tell how this can be achieved in R programming language using the ga() function.

@ Erick Olivares

Sir, thanks. In such a case would the fitness function be an indicator of the global optimum? If one cannot really have a fairly accurate idea of the global optimum, should one try out various guesses?

I do not use R programming but the general concept of using self-adaptive parameter is defining some input variables like number of iterations that the global best is unchanged or current best performance evaluation and so on. Then based on these inputs change the GA parameters through the iterations

There is no guarantee to obtain a global optimal solution with any metaheuristic, unless you make near infinite iterations. Also, because GAs are random, the solution obtained may be different in any moment. If you can use another method to obtain a good approximation to the optimal solution, GA will improve it.

Respected all,

Thank you all for the answers. I have tried the non-linear method (implemented using various algorithms) and they are probably not adequate as they do not yield statistically significant results. I also tried the Simulated Annealing package in R and used the same seed values for the problem that I cited, and I got quite different results. In view of this, even if I use hybrid global optimization methods, is there any possibility of reaching the global optima? In any case, how do I know that a particular combination of parameters represents the global optima?

Practically speaking, if I use the SA and out of many seeds if I reach the best solution based on the value of the fitness function and then use GA using seeds from SA would that suffice? Any help is welcome.

Hello,

As far as I understand your question, your purpose is to fit a function on a time-series data.

First : Can you tell us what is your objective function ? I mean : minimising the sum of residual squares ? maximise the likelihood ?

Second : Be aware that the ga() function always attempt to maximise (not to minimize, this is in relation with the first point when using the sum of residual squares)...

Patrick Coquillard ,

Sir,

The function is a sum of residual squares. In relation to that I am using the negative of the function.

The simplest approach is to try with Random Search: https://en.wikipedia.org/wiki/Random_search

In many cases Random Search is efficient enough.

Todor Balabanov

Sir, Please suggest a package in R that implements random search.

It is better you to do your own implementation, but you can try something like this one: http://mlampros.github.io/2016/03/14/random_search_R/

In the context of the problem, I am trying to leverage the power of global search algorithm with a localized technique as suggested in Section 3.3 of the paper available here : https://arxiv.org/pdf/1605.01931.pdf

I am using optim=TRUE as an argument of the ga() function. However, the error that I get is: Error in fitness(Pop[i, ], ...) : unused argument (optim = TRUE).

fitness is the fitness function. I am using the latest version of R and the latest version of GA package (binary:2.2, source: 3.0.2). Please suggest what can be done.