Hello, Amirhosein.

I want to note that each task is specific and there is no optimal optimizer that equally effectively solves all problems with a certain number of variables (see 'No free lunch theorem'). Test problems in a sense serve as an example of how an algorithm behaves with functions of different types (smooth / not smooth / with a large number of resonances / monotonically changing, ...), and here it is also important to understand whether a local or global search is needed. You can find works on your chosen topic and see what methods were used there.

For a global search for the optimum of a complex function with a large number of variables and without an approximate initial solution, I usually use stochastic optimization (JADE or CMA-ES algorithms).

Roman Gaponenko

Hi dear bro

Thanks for your reply!!

I already knew abt it but I'm gonna write and essay and I have to implement my innovative evolutionary method to a real world engineering problem.

for instance the design of an aircraft is a large scale optimization problem which also have usually more than 6 objectives and can be categorized in the field of many objective optimization but the equations of such a huge problem doesn't exist in the published article.

But I need one of them for my master thesis!!!

With All Respect

All sciences are integrated to each other but the real world managing objective for existing problems must be based on especilist and experience to reach for your aim.

Best regards

Hi Amirhosein,

I published a paper on a real-world problem a few years ago that had 9 objectives. For the paper, I 'encapsulated' the problem so that it could be used as a test function too. The paper is:

E. J. Hughes, “Radar waveform optimisation as a many-objective application benchmark”,EMO 2007. Lecture Notes in Computer Science Vol.4403, 2007, p 700-714, Springer

Newer versions of the same problem can have up to 15 objectives (I have not published those however). For lots of problems with many objectives, often a 'partial epsilon-constraint' approach can be taken where some low-priority objectives are turned into constraints, which reduces the overall number of objectives to solve for. Visualising what is going on with 4 or more objectives is very difficult, in particular analysing where there may be discontinuities or holes in the estimated Pareto front set of results. With the radar design problem, I can often apply constraints to get the search down to 5 objectives, and possibly 4 at a push, which makes visualisation and analysis simpler, with the exception that it is only on a projected fragment of the Pareto surface due to applying the 'partial epsilon constraint' process.

Best regards, Evan

Hi Evan

Thanks for your immediate and complete answer to my Q.

I've read your paper before and I thinks that it can be a good real world engineering problem for my master thesis.

and also I appreciate you for giving me some useful information abt the many objective optimization.

Do I have a permission to use your functions in my paper ????

Hi Amirhosein,

Yes the code for the test function version is available to download (the link in the paper still works) and is available to the community for free use for the investigation of many-objective problems and in developing new algorithms, so you have permission to use the functions. There is also code for assorted optimisation algorithms on the site; they are all a bit old now and there are many better ones have been developed over the years, although a number of the algorithms were developed specifically for many objective optimisation and they aim to estimate the Objective Front, of which, the Pareto Front is a subset. By estimating the Objective Front, it becomes easier to identify which regions of the Pareto set has discontinuities due to concavities that are too deep to be non-dominated, compared to search directions where the objective surface is undefined (for example if there are multiple disconnected feasible regions).

Best regards,

Evan