“This is the 15th day of my participation in the First Challenge 2022. For details: First Challenge 2022”

preface

This is mainly based on my current views to briefly talk about a problem of multi-objective optimization, which can be done no matter in the process of mathematical modeling competition in school, or in actual production and life, or in several papers. Of course, I am currently learning according to MOEA. In the later stage, we will propose optimization and build a platform based on Flink (open your eyes, in case of paper issue, it will be wonderful).

Multi-objective problem has always been a way to solve practical problems that we pay close attention to and use widely. In our traditional approach, we are committed to transforming multi-objective optimization into single-objective optimization, such as the classic case of investment. Suppose that through modeling, we get the investment function F (x) and the return function G(x), how can we design them so that they can be unified to maximize the benefits of our system?

Is the Max (F (x), G (x))

There are conflicts between them, but there is also a certain relationship between them, so in the traditional solution, we can realize the idea of transforming multiple goals into single goals.

Traditional multi-objective

This is also the easiest idea to consider in mathematical modeling, or the easiest to think of in the actual modeling process, and the most stable idea. Of course, these practices also face many problems, among which the most difficult is how to reasonably transform into a single objective problem.

There are several common ways to convert multiple goals into single goals.

The constraint method

This is the simplest, that is, limit G(x) and F(x), select a range for constraint, and then optimize for the main function, for example, I don’t need money, maximize G(x) and F(x)don’t care

As for the effect, it’s a little subjective.

Hierarchical sequence method

The multiple objectives are sorted according to their importance, the optimal solution of the first objective is obtained, and then the optimal solution of the second objective is obtained under the condition of achieving this objective, and so on until the end of the last solution is the optimal solution.

In human language, you optimize F(x) and then G(x), using the optimal solution set of F(x) as a constraint. This will be familiar to those of you who have played linear programming and Lingo.

But the problem is that if the conditions for your optimal solution are unique, it doesn’t make much sense for all the solutions that follow to consider this particular case, but of course you can put a weight on it, although I don’t use that much.

Linear coefficient method

I don’t know how to say this, but there’s a lot of ways to turn F of x and G of x into a function where H of x is equal to aF of x plus bG of x plus a weight, but before we do that, we have to do the same dimension. Of course you don’t have to be linear here, you can think about nonlinear coefficients, it doesn’t matter, it depends. But the problem is that the coefficient, at the same time, this method also is a kind of method, one of my favorite into single objective, the neural network weight + + single objective optimization, but there is a premise that need plenty of data, or fitting, based on the neural network to determine weights, and then optimization, this should also be tiger balm.

Multiple goals now

We’ve gone through a lot of ways to convert a multiple goal into a single goal, so how can we really achieve our multiple goals? Apparently there is. I don’t know what I’m doing.

Yes, with the development of our computer, we derive a new discipline, called the intelligent optimization algorithm, evolutionary algorithm, the first explain the evolutionary algorithm is what, the comrades of the university of we should know that in addition to the data structure back and introduction to algorithms, optimization, followed by intelligent algorithm part of us, including our evolutionary algorithm, It is my great honor to be in the intelligent optimization algorithm lab of our school and goofing off with the teachers. Ah, it’s a mess.

In fact, evolutionary algorithm is to simulate the natural phenomenon of our animals to optimize a target, so this part is still a single objective optimization problem. Such as particle swarm optimization, genetic algorithm, evolutionary algorithm, annealing algorithm, Wolf algorithm, monkey algorithm and so on, too many. It’s simulating nature, it’s simulating the survival of the fittest, to get the optimal solution, because the bad ones get passed, and then new ones get generated and of course there are a lot of articles on this, and I won’t go into the details, but what this article is really about is broadening the perspective, not thinking about distributed, distributed locks, SpringCloud K8s that are framework virtual CURD changed a scene, of course, deep into the bottom that is also very interesting, SpringBoot various implementation principles ask senseless you, there are what high concurrency JVM tuning, back to the eight-part article got, I will, you dare let me to optimize not?

OK, so now let’s answer what intelligence is, based on neural network optimization EA (evolutionary algorithm), sounds and intelligence has no relationship! Well, it’s actually a little bit of a relationship, but when you play it, it’s actually not difficult, but you know the name is very nice ~ (I just say it is very simple, but there are a lot of points to consider when doing it, it is also quite complicated)

So let’s take G(x), F(x).

If we look at them all as single-objective optimizations we can easily get a bunch of solutions, which are shown here.

So now we have some optimal solutions using evolutionary algorithms, but in fact, what we find is that our G(x) F(x) is constrained, so we need to eliminate some points, and then we have a solution set. It looks something like this

Then this solution set is called Pareto frontier, which is also a set of optimized solutions. There is no doubt that multiple objects will result in a set of solutions.

So our task is how to obtain this frontier in a more rational and optimized way. As for this multi-objective and who collocation problem is not big, we are mainly multi-objective idea.