I have a problem where the objective function takes a considerable amount of time to evaluate. The problem has continuous search space. However, most of the variables don't need the level of accuracy provided with this continuous search space.
I was thinking of discretizing the search space where the optimizer would pick from a specific set of values for each parameter. This would give a near optimal solution that I am satisfied with if the optimization time is reduced.
I want your opinion or personal experience with similar problems.
Thanks in advance.
Dear Amr,
I faced with the same optimisation problem and applied the discretization of search space. The results showed that the convergence rate has increased. However, to have high quality solutions at the end of optimisation process, that would be great to let the algorithm exploit the search space continuously. Our team's paper received the best paper award from GECCO conference (A rank).
Conference Paper Optimisation of large wave farms using a multi-strategy evol...
Conference Paper BEST PAPER AWARD (GECCO2020)
Yes. It should improve, Because metaheuristic algorithms designed for continuous data.
Hi Amr,
In general, I think it's safe to say that the answer to your question is yes. Discretization generally leads to a reduced search space which implies that the algorithm has less intermediate values to work with and that subsequently translates to less computational effort. I should point out, however, that there are a few cases where this generalization is untrue. During my research in the field, I have noticed how algorithms that work with discrete variables show significantly reduced performance when tackling problems with higher dimensions. Basically, it requires more effort from the algorithm to escape a local optimum when you have so many decision variables to change. That can be remedied with increased exploration from the algorithm, but continuous optimization, I have found, is the best alternative in that case.
Furthermore, if algorithmic stability is a concern for you in your present study, then having discrete variables will most surely reduce that. Higher mean, worst, and standard deviation values from the multiple runs you perform will become immediately manifest. This is true whether the dimensionality of the problem is large or small.
My advice is to try discretization if the number of decision variables is less than 10. Anything greater than that, will only lead to slower performance. But every problem is different, so I guess give it a try and see what you get. You may need to perform another parameter sensitivity analysis for acceptable results. Good luck.
Convergence speed is different from time taken by the algorithm in performing complex calculations. Better convergence means that a better solution is found in limited number of iterations without pre-mature convergence. Meta-heuristics are obviously applied when search space is huge. Discretizing may not be helpful as it can affect the exploitation in a continuous problem. One possible way to improve the convergence speed is to balance exploration and exploitation. In initial few iterations you can focus more on exploration and later exploit to terminate and converge to a better solution.
In fact, if you discretize the algorithm optimally, the convergence speed will be increase, and the execution time will also decrease.
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