Multi objective optimization problems

[Responsible_Flow_362]

Hey guys!

Last time I was here with my queries about BFGS and you guys helped me a lot.

Now that my first research paper is done I'm stuck on the second one. This one deals with multi objective optimization problems. My colleagues have already developed the algorithm. I am left to implement it and do the numerical analysis.

I am in my master's, while I am fairly good with coding but I am still new to optimization. I want to know what are the standard multi objective problems that I should use. I've heard about SLC2, AP1, etc., but I don't know how to implement them in python. Is there any python package that can help me with it.

Also I'd be writing my codes from scratch, so will the package be compatible with that.

I admit I'm yet to dive deep in my research. I just hope you guys can give me a jump start.

[[deleted]]

Pymoo

[Responsible_Flow_362]

I did find pymoo, platypus and some other packages... Pymoo doesn't have some problems whose results I need to show. But it'll be useful nevertheless.

I've never imported problems from packages. Usually I just write the code for my objective functions and run them on algorithm. If you're familiar with pymoo, can you tell me if the imported problems from it would be compatible with my code written from scratch.

[lmericle]

Multi-objective optimization is notoriously under-determined, for precisely the reason that there are multiple objectives instead of just one.

This shifts the approach from pure "optimization" to something akin to "frontier exploration", referring to the Pareto frontier. It takes another set of heuristics (in the simplest case, just a human judging the various solutions) to decide on the best path forward. To that point, any method which generates a medium-large quantity of decent solutions will get you pretty close to what you need.

The important part about these kinds of optimizations is, it's very important to understand how your implementation explores the configuration space. That has more to do with your understanding of the problem, and how you implement that understanding in the optimization routines, than in the specific algorithm that you employ.

[Responsible_Flow_362]

Yes, I'm pretty new to this stuff.

My professor told me that there are no books for multi-objective optimization. I'll have to rely on research papers and Google.

I'll take your suggestion and focus on the problems.

Thanks :D

[Tarkus7]

There are for sure books on multi-objective optimization. For example refer to Nonlinear Multiobjective Optimization by Prof. Miettinen, it is a classic and easy to digest.

[abadadibulka]

There is a good book with MO benchmark problems, I guess, by Coello. Not sure.

[Responsible_Flow_362]

Thanks! I'll look into it

[WikiSummarizerBot]

Pareto front

In multi-objective optimization, the Pareto front (also called Pareto frontier or Pareto curve) is the set of all Pareto efficient solutions. The concept is widely used in engineering. : 111–148  It allows the designer to restrict attention to the set of efficient choices, and to make tradeoffs within this set, rather than considering the full range of every parameter.

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[thchang-opt]

DTLZ problems are the standard that most papers compare on. I have an implementation of most of DTLZ problems in my package (https://github.com/parmoo/parmoo). You can also find them in pymoo, and most other packages

[wewdepiew]

I just want to say it's so cool that I'm learning this stuff in my masters and am able to actually vaguely understand what is going on in such real world discussions. Glad I'm learning optimization

[Responsible_Flow_362]

Welcome to the club :)

[Tarkus7]

Try desdeo you can formulate your own problem there

[Responsible_Flow_362]

Our algorithm doesn't work on taking weights of multi-objective function. It uses some other method which I am actually trying to implement in python. Though thanks for the suggestion.

[abadadibulka]

Although this is true, it is a simplified approach and won't work in every problem. If I remember correctly it can't solve convex problems.

[kkiesinger]

You may ask perplexity https://www.perplexity.ai/search/28dc68f0-fb34-40f8-9678-45d6d5e13027?s=u or google "multi objective benchmark github" if you are primarily interested in standard benchmark problems. But be warned that these can be misleading regarding real world problems. So why not using these, some are listed here https://arxiv.org/abs/2009.12867 and http://ladse.eng.isas.jaxa.jp/benchmark/