Hello Nicolas.

Thank you for your answer. I forgot to mention that I am looking for continuous problems.

Hi Miha,

the simplest continuous single objective optimisation problems are the ones you could in principle solve by hand, i.e. linear (min c^T x) or quadratic problems (min x^T A x).

Stepping up the complexity, you can try with any convex problem, where there is still only one local optimum and thus that optimum is also the global one.

All these problems are usually trivially solvable by gradient based methods, so if you can invent a convex problem, you can numerically find its solution with a gradient based method and then see how well your evolutionary method works.

After that, you can try with multimodal and nonconvex problems, where the story changes significantly

as far i understand you aim at solving numerical (continuous) problems.

you should look at BBOB benchmark. there is 24 test functions with increasing difficulties ( different properties) and with different dimensions.

Than you Nacim, I have heard of BBOB benchmark. I'll check the problems.

Don't hesitate to contact by mail, if you need some help on using BBOB or to discuss on benchmarking numerical optimization algorithms.

Also, if you are interested i built a small library collecting several problems. So I have several problem that are ready to be used.

cheers!

You can use simple benchmarks such as Mc Cormick, Booth, Rastrigin, Ackley and etc. they will be appropriate to your aims.

For more info

https://en.wikipedia.org/wiki/Test_functions_for_optimization

Just minimize f(x)= x^2 is easy to solve with several optimization methods.

You can get multiple mathematical benchmark problems from the below link https://en.wikipedia.org/wiki/Test_functions_for_optimization

I have implemented evolutionary and few swarm based algorithms on all such functions and it achieved global minimum for all of them.

Cheers!

You may try CEC2005 benchmark functions.

Those that have only one optimum (uni-modal functions)

Following