Optimality of the Porto PMF packing

Determine whether the proportional mean fairlet packing returned for the Porto-SES test data is globally optimal over the generated proposal pool, rather than merely feasible with a nonzero mixed-integer-programming optimality gap.

Background

The secondary proportional mean fairlet (PMF) diagnostic constructs a finite proposal pool of candidate blocks and solves a set-packing mixed-integer program for the selected Porto-SES station plan. The solver returned 174 disjoint blocks, while its upper bound was 184, producing a 5.7% gap before reaching the deterministic node limit.

Consequently, the reported PMF result satisfies the fixed feasibility and inclusion requirements but is not certified as optimal within the generated proposal pool. The unresolved issue concerns optimization over that sampled pool only; it does not require extending the question to the complete set of geometrically possible blocks.

References

The result meets all fixed requirements; the reported gap leaves optimality unresolved.

— Freeze, Validate, Report: Auditing Urban Station Plans with Common Evidence  (2609.39064 - Teusch et al., 30 Sep 2026) in Section 6.4, subsection “Secondary PMF results, bounds, and pool ablation”