Dear Boris,

I suggest you to see links and attached files in topics.

- A review of simheuristics: Extending metaheuristics to deal with ...

https://www.sciencedirect.com/science/.../pii/S221471601500007X

- Trends in Developing Metaheuristics, Algorithms, and Optimization ...

https://books.google.dz/books?isbn=146662146X

- Handbook of Research on Modeling, Analysis, and Application of ...

https://books.google.dz/books?isbn=152252858X-

- Modeling, Analysis, and Applications in Metaheuristic Computing: ...

https://books.google.dz/books?isbn=1466602716 -

Best regards

It depends on what you mean by the term "convergence" - in general you know nothing at all, unless you have an additional scheme that produces lower bounds on the optimal value. (This has bugged me for a long time - how can you spend so much time coming up.with yet another cool-sounding name for a heuristic when in reality you have - typically - no clue whatsoever how good it is going to be for a sufficiently rich test bed of problems.) Further, I know of no metaheuristic that has any guarantees, unless it is somehow linked to an approximate branch-and-bound process - and if so then I for one would not call it a meta-heuristic. This thread of papers borders on being unscientific.

I do not cease to wonder why so much attention is paid to meta-heuristic algorithms, which have nothing to do with science in general. I tried to express my more detailed opinion on this in the discussions:

https://www.researchgate.net/post/Why_people_from_Mathematics_dont_like_Evolutionary_Algorithms_like_GA_or_PSO

https://www.researchgate.net/post/What_is_the_time_complexity_of_meta-heuristic_algorithms

https://www.researchgate.net/post/Should_be_revised_todays_Complexity_Theory

https://www.researchgate.net/post/Who_will_achieve_success_in_life_more_a_clever_which_does_not_know_that_he_is_clever_or_a_fool_which_knows_that_he_is_fool

We are all fools. :-) But some of us occasionally are bigger fools than others.

Dear Michael Patriksson,

Your phrase "We are all fools. :-) But some of us occasionally are bigger fools than others" reminded me of one remarkable episode when the ingenious physicist Niels Bohr came to Moscow in May 1961. At the Institute of Physical Problems of Pyotr Kapitsa there was a solemn reception at which Bohr pronounced his speech, and translated from English into Russian Evgeny Livshits. A question was asked to Bohr: "How did you manage to create such a wonderful school of theoretical physicists?" Bohr answered and Livshits translated this: "Because I never stopped telling my students that they are fools". However, the full hall of the people was very surprised and there was a strong laugh. It turned out that Livshits translated (apparently consciously) incorrectly Bohr's original phrase: "Because I never stopped telling my students that I'm a fool". Kapitsa, who sat in the study, stood up and loudly declared: "This is not an accidental reservation, and it expresses a fundamental difference between the schools of theoretical physicists Bohr and Landau, to which Livshits himself belongs".

I am definitely not as big a fool as Niels Bohr.

All the answers are great

If a metaheuristic - under specified problem conditions - were to be shown to be convergent to a stationary point, then I might get slightly interested in it. As it is, caution is needed, as meta-people are getting louder and and louder - with no real excuse.

Dear Michael Patriksson,

"as meta-people are getting louder and and louder - with no real excuse."

It seems that the world elite is doing everything to ensure that humanity has become a "meta-people". However, COVID-19 stood across on the way to this outcome and declared war on humanity. COVID-19 is simply a revenge of nature on humanity for its abuse of nature. However, the total digitalization of all mankind intends to turn people into "meta-people" like managed objects. Why think when you can just click on the device buttons. The goal will be achieved if people cease to doubt, but COVID-19 gives a chance to come to their senses.

Indeed - we can't just fumble in the dark and randomly state that "this point is good enough". What does that mean? Without optimality conditions, estimates, and/or devises to cut off inferior solutions, we are lost. And metaheuristics that we see here are of that type. I'm puzzled indeed why this has gone for so long, and no-one says "stop!", or at least "please combine these things with mathematical optimisation, such that you give the combination a chance. That might be a very good idea, but I don't see people biting.

The trend is that they still do not converge, and we are getting impatient to either see a breakthrough, or that this charade will soon stop. Too many are attached to a theme that seems to not develop. New names, same old story.

Betting on metaheuristics will probably not lead to "Bingo!" The thousands upon thousands of papers yield a trace of mostly failures ...

Genady: I'm laughing. :-) Would be nice to see you laugh. But anyway, the number of meta-people will shrink eventually - as they more and more realise that mathematical optimisation is a better tool.