Optimizer MILP: explore memory as a hard bound instead of a weighted cost term

[milindsrivastava1997]

Context

The planned mip_assign (cross-AQE sharing MILP, #650) minimizes the existing weighted objective from optimizer/cost_model.rs:

w_ingest_mem·mem_active + w_ingest_cpu·cpu_ingest + w_query_mem·mem_query + w_query_cpu·cpu_query

The memory weights convert bytes into the same units as CPU-seconds with an assumed price ratio (~1e6, see CostWeights docs). That ratio is a guess, and it means the solver trades memory against CPU at an exchange rate nobody has calibrated.

sketch-bench PR #129 (rqe-optimizer) takes a different approach: it minimizes CPU only (ingest + query + merge) and treats memory as a hard constraint, adding a continuous variable M ≥ working-set(a,g) for every assignment and an optional M ≤ budget limit.

Proposal to explore

• Remove the memory terms from the objective, i.e. CostWeights { ingest_mem: 0, query_mem: 0, .. } or remove the fields.
• Add memory bounds as constraints instead. Candidates:
  • Peak query working set (PR Re-organize code in repo to be more OSS friendly #129's definition): M ≥ groups × n_windows × mem_bytes_per_instance for every selected (a,g); M ≤ max_query_memory_bytes.
  • Total ingest memory: Σ_g u[g] · n_concurrent(g) · groups(g) · mem_bytes_per_instance ≤ max_ingest_memory_bytes. This is linear in u[g] and needs no extra variable; arguably the number an operator budgets for.
• Decide where the budget(s) come from: asap-planner CLI flag vs. a ControllerConfig field.

Questions to answer

• Does the CPU-only + memory-bound formulation give materially different plans from the weighted one on real workloads?
• Which memory quantity (query working set, ingest/active, retained storage) should be bounded?
• Should greedy follow the same change so the mip_cost ≤ greedy_cost test invariant still holds?

References

• No cross-AQE sharing — greedy deploys one sketch per AQE even when they could share #650 (cross-AQE sharing MILP)
• sketch-bench PR Re-organize code in repo to be more OSS friendly #129: rqe-optimizer/src/milp.rs (MilpBounds, peak-memory variable)
• .design_docs/optimizer-mip-formulation.md
• asap-planner-rs/src/optimizer/cost_model.rs

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