The problem is that PCB design is hard. Writing a "cost function" for placement is basically impossible when later design steps are going to introduce hard constraints, and earlier design steps are actually extremely flexible.

For example, the general rule-of-thumb is to place one 100nF decoupling capacitor per power pin. But in practice there isn't always space for that. Do you suboptimally route your critical high-speed traces to place one? Do you add additional board layers for it? Do you switch to a smaller (and more expensive to manufacture) capacitor package size? Do you more it further away from the chip - making it significantly less effective? Do you make two power pins share a single capacitor? Do you switch to a different IC package or even a completely different chip with an easier pinout?

What is the impact of your choice on manufacturing requirements, manufacturing cost, part cost, part availability, testability, repairability, EMC/FCC/whatever certification?

Every option could literally be free, cost tens of millions, or anything in-between. Parts documentation is already woefully incomplete as it is, trying to automate routing it by requiring people to provide data describing basically the entire world just isn't realistic.

I think using the vision decoder baked into modern LLMs is the way to go. Have the LLM iterate; make sure it can assert placement qualities and understands the hard requirements. I think it can be done.

I wonder how a MIP solver would fare in this?