Dear Jayshree Jayshree,

A study in comparison of the three evolutionary algorithms namely : genetic algorithm (GA), particle swarm optimization (PSO), and differential evolution (DE). While GA is more suitable for discrete optimization, PSO and DE are more natural for continuous optimization. Finally the results indicate the overall advantage of differential evolution (DE) and are closely followed by the optimization of particle swarms (PSO), then comes the genetic algorithm (GA) and other approaches.

For more information about this subject i suggest you to see links and attached files on topic.

Article Improving the performance of differential evolution algorith...

Article Coupled eagle strategy and differential evolution for uncons...

Article Evolutionary algorithms and their applications to engineering problems

Article Differential Evolution: A Survey and Analysis

Best regards

Dear Jayshree Jayshree,

I would add to the previous answer that DE may be easier to use because it has less parameter to configure : PSO has more parameters and might be very sensible to neighborhood size and topology in the speed equation. I might also converge too early if your objective function is very complex.

But you should check different kind of mutation schemes that could provide better results than the default one.

Best regards.

Before asking this question I recommend asking yourself “why should I use a metaheuristic or evolutionary algorithm?!!”

If you ask it from yourself and study the theory of optimality, you will find that a metaheuristic is inferior in comparison with mathematical programming. The heuristics are inefficient and unreliable in large scale problems. This is while mathematical programming has many years of strong theoretical background which makes it robust, reliable, and efficient. I recommend the following books for more information:

“Andreasson, N., Patriksson, M., & Evgrafov, A. (2020). An introduction to continuous optimization: foundations and fundamental algorithms. Courier Dover Publications.”

Indeed: take the advise from a senior scientist, with more than 30 years of work on mathematical optimisation (that is ME!) that you should NOT be content to use inferior tools like any metaheuristic to "solve" the problem. We have much better and more reliable tools than any meta stuff could ever come up with. Scrap meta.

In with mathematical optimisation! I have observed what it can do, through decades of work - alone, with PhD students, with gifted master students, and with gifted industry partners, and it is definitely the way to go. Listen to those of us who have done a lot of work together with industry, too, and be amazed how much better you can do. Yes, heuristics let you easily to get together something, but do you know how good it is??? How does it compare with mathematical optimisation? IT DOES NOT. And don't you want to know how good it can be?

Listen to me. Follow me. I have spoken.

Sure, mathematical optimisation is exellent for continous optimization. Metaheuristics are great for hard combinatorial optimization problems.

Patriksson, Rostami, what are the good mathematical optimisatin methods for combinatorial optimisation problems?

DE and PSO can be used for multi-objective problems. I am not sure, but I would like to find out, are there any good mathematical optimisation methods for multi-objective and many-objective continous optimization problems?

According to the No Free Lunch theorem, all optimisers perform equally when compared across all possible problems, so you do have to be careful when discussing which optimiser is better. It is, however, the case that certain optimisers tend to do better on certain classes of problem, though identifying this pairing is difficult. There are all sorts of potential pitfalls when doing experimental comparisons of optimisers, and there are many examples of poorly-executed comparisons, so you shouldn't necessarily believe it when a paper says that one optimiser is better than another. However, there are some good comparative papers out there; for example the following, which compared a group of metaheuristics on the BBOB continuous optimisation benchmarks: Article Analyzing the BBOB Results by Means of Benchmarking Concepts

Dear Nikola Ivkovic :

I have not much experience in combinatorial and multi-objective optimization using mathematical programming. We should request from Michael Patriksson for answering this question who is an expert. I can find some of such papers in his resume.

But generally, I would like to recommend Jayshree Jayshree to use the method of moving asymptotes (MMA) which is a very good mathematical technique in continuous optimization. We have used it in many structural optimization problems. The related reference is as follows:

“Svanberg, K. (1987). The method of moving asymptotes—a new method for structural optimization. International journal for numerical methods in engineering, 24(2), 359-373.”

Professor Svanberg supports for the Matlab sub-routine for his solvers (MMA/GCMMA) by writing an Email which is available on his page:

https://people.kth.se/~krille/

I agree with Michael Patriksson and Pooya Rostami , you should consider exact optimization methods first, before embarking on using metaheuristics. Many problems can easily be solved by exact methods. You may publish your article, but are you prepared for the criticism that may follow? Consider the following:

Article An optimal solution to a three echelon supply chain network ...

Hi,

I do not want to start a war, and I am fully aware of my scientific position regarding all the people who are responding here BUT why on earth when someone is asking advices on turntables, you are responding "you should buy a CD player" ;)

Everyone should agree to the fact that exact methods should be prefered, but it is not responding to the question, this is evangelism :D

The answers provided by Mohamed-Mourad Lafifi and Peio Loubiere pretty much summarize everything, but I would like to say that you can never ascertain, based on perceived advantages alone, whether one algorithm will work better than another for a given problem on account of the NFL theorem. You have no choice but to apply the three algorithms to the problem you're studying and from there quantify their differences. Performance reigns over any list of advantages that can be provided.