Multi-objective optimization
Hello everyone,
I'm curious about whether it's feasible to tackle a multi-objective optimization problem using D-Wave. I understand that one approach might involve converting the multi-objective problem into a single objective one (like using the weighted sum method). However, I'm wondering if there's a way to define and solve the objectives separately on D-Wave. Any insights or suggestions would be greatly appreciated! Thanks in advance.
Comments
Hello,
Thanks for reaching out with your question.
When you say "to define and solve the objectives separately", can you give a little more detail about what you mean here?
Do you mean that there are several objectives being solved in parallel with no overlap?
Though this is possible, it is not generally the best approach for multi-objective optimization, as the objectives are all being solved independently from one another and miss out on the benefit of optimization between objectives. There are, however, a few scenarios where this might be helpful for informational purposes, in which case you can add all variables of the objectives with unique labels to accomplish independent objectives.
This paper describes a multi-objective approach which returns a set of non-dominated solutions in one run, and may perform better than solvers based on scalarization on a bi-objective problem:
https://arxiv.org/abs/2205.13399
This paper has multiple scalarization methods for problems of two or more objectives:
https://arxiv.org/pdf/2305.11648
I hope this is helpful. Please let us know if you have any follow up questions.
Thank you. That was helpful!
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