Railway benchmark instances and their published records

Notes on the data

All instances are minimisation problems. Gap = (best known − best lower bound) ÷ |best known|, with zero gap when the bounds are equal. Size is events / activities for PESPlib and TimPassLib, trains / operations for DISPLIB, and variables / constraints for MIPLIB. The record column links to the source for each bound and describes the evidence on hover.

PESPlib: records table, read 2026-11-11. The library states that lower bounds are not verified.

TimPassLib: solutions page, read 2026-11-11. We use the lowest listed total objective and the lower bound from the passenger routing relaxation. The catalogue uses relative gaps throughout.

DISPLIB: we compare the DISPLIB 2025 competition records, Fuchs et al. (Appendix B, Tables B.8–B.15), and Stärk et al. (Appendix A, Tables 5–7). The official verifier confirms 98 of the selected upper bounds using competition solutions or the supplementary solutions from Stärk et al.. The other 14 are Wabtec values reported by Fuchs et al. for which we found no public solution files to check.

DISPLIB lower bounds come from the cited papers or the nonnegativity of the objective. We exclude reported values that conflict with verified solutions or proven optima. Fuchs et al. model resource precedence in continuous time, while the official verifier checks the order of events. The catalogue attributes the retained paper bounds to their authors. Individual lower-bound certificates have yet to be replayed for the catalogue. Table 3 of Trautsch et al. reports aggregate results and supplies no individual values.

MIPLIB: Easy and Hard are difficulty tags. Both bounds use the values marked optimal in the MIPLIB 2017 solution file, version 37. The objective at the top of the rail03 details page agrees with v37. Its downloadable solution list shows −823.4828.

Related models count as separate entries. The downloads use family to mark confirmed relationships. PESPlib and TimPassLib share the base networks R1L1–R4L4. TimPassLib adds passenger routing and its objective. PESPlib includes the corresponding variants R1L1v and R4L4v. In MIPLIB, timtab1CUTS adds constraints to timtab1, and ic97, icir97 and nh97 each have potential and tension versions. The two icir97 models have optimal values of 6325 and 6375 respectively.

DISPLIB also includes related variants. The Siemens instances have smi_headway versions with headway requirements and smi_close versions without them. The Dovrebanen, Oslo-area and Wabtec instances include different dispatching windows on the same networks. The 112 official instance files have distinct contents, and the catalogue counts each file separately. See the official DISPLIB groups.