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The XL set: vehicle routing with 1,000 to 10,000 customers

Beat the best-known routes on 100 capacitated vehicle routing instances with 1,000 to 10,000 customers, released for the 2026 BKS Challenge.

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1# The XL set: vehicle routing with 1,000 to 10,000 customers
2
3In January 2026 CVRPLIB released 100 new instances of the capacitated vehicle routing problem with 1,000 to 10,000 customers, together with a 30-day community challenge to find the best possible solutions. None of them is solved, and their best-known solutions are still being lowered.
4
5## Problem
6
7Each instance has a depot and up to 10,000 customers at integer points of the square $[0,1000]^2$, a demand $d_i$ per customer and a vehicle capacity $Q$. Travel costs are Euclidean distances rounded to the nearest integer. A solution is a set of routes that start and end at the depot, visit every customer exactly once in total and carry at most $Q$ each; the number of routes is free. In a name such as `XL-n5067-k201`, 5067 counts the depot and the customers and 201 is the minimum number of routes. For each of the 100 instances, find a solution cheaper than the best-known solution (BKS) listed by CVRPLIB.
8
9| Instance | Customers | $Q$ | BKS (October 2026) |
10|---|---|---|---|
11| `XL-n1048-k237` | 1,047 | 128 | 380,092 |
12| `XL-n1094-k157` | 1,093 | 7 | 112,431 |
13| `XL-n2681-k540` | 2,680 | 251 | 797,844 |
14| `XL-n8389-k2028` | 8,388 | 208 | 3,352,860 |
15| `XL-n9784-k2774` | 9,783 | 19 | 4,076,860 |
16| `XL-n10001-k1570` | 10,000 | 479 | 2,330,257 |
17
18## Background
19
20Queiroga, Martinelli, Subramanian, Uchoa and Vidal (2026) generated the XL set with the same scheme as the X set of Uchoa et al. (2017), varying depot position, customer layout, demand distribution and route length. To obtain starting values they ran five published heuristics (KGLS-XXL, SISRs, FILO and FILO2, HGS-CVRP with decomposition, and AILS-II) 60 times for two hours on each instance; AILS-II produced 93 of the 100 initial BKSs. The CVRPLib BKS Challenge then ran from 12 January 2026 for 30 days: 19 teams took part, 1,932 improved solutions were submitted, and the winning team, OptVerse-CityU, ran a portfolio of AILS-II variants with HGS-CVRP and FILO2 for about 42,600 CPU-days.
21
22## What is known
23
24- All 100 instances are open. CVRPLIB lists BKSs but no lower bounds, and the organisers describe the XL instances as beyond the reach of current exact methods.
25- During the challenge `XL-n8389-k2028` received 74 BKS updates, while `XL-n1094-k157` received none: its initial AILS-II value of 112,431 still stands.
26- Records keep falling after the challenge. On 11 September 2026 a Baidu team (Qianlong Wang and four colleagues) improved 70 XL instances at once, and in October 2026 Shiyao Bian and Martín Vizzolini lowered several more, including `XL-n10001-k1570` to 2,330,257.
27
28## What would count as progress
29
30- A solution file in CVRPLIB format (one `Route #i:` line per route, then the cost) that beats a BKS. A script checks it in seconds: each customer appears exactly once, each route load is at most $Q$, and the rounded Euclidean cost is recomputed. CVRPLIB also runs an online checker and publishes improvements on its updates page.
31- A certified lower bound for any XL instance, which would measure for the first time how far its BKS can be from optimal; proving a BKS optimal is a separate and much harder kind of progress.
32
33## References
34
351. E. Queiroga, R. Martinelli, A. Subramanian, E. Uchoa and T. Vidal (2026). The XL instances and the CVRPLib Best Known Solution Challenge. arXiv:2601.11467. https://arxiv.org/abs/2601.11467
362. E. Uchoa, D. Pecin, A. Pessoa, M. Poggi, T. Vidal and A. Subramanian (2017). New benchmark instances for the capacitated vehicle routing problem. *European Journal of Operational Research* 257, 845–858. https://doi.org/10.1016/j.ejor.2016.08.012
373. V. R. Máximo, J.-F. Cordeau and M. C. V. Nascimento (2024). AILS-II: an adaptive iterated local search heuristic for the large-scale capacitated vehicle routing problem. *INFORMS Journal on Computing* 36, 974–986. https://doi.org/10.1287/ijoc.2023.0106
384. L. Accorsi and D. Vigo (2024). Routing one million customers in a handful of minutes. *Computers & Operations Research* 164, 106562. https://doi.org/10.1016/j.cor.2024.106562
395. F. Arnold, M. Gendreau and K. Sörensen (2019). Efficiently solving very large-scale routing problems. *Computers & Operations Research* 107, 32–42. https://doi.org/10.1016/j.cor.2019.03.006
40
41## Source
42
43Imported from [CVRPLIB, XL set and BKS Challenge](https://galgos.inf.puc-rio.br/cvrplib/en/bks_challenge/overview), curated by CVRPLIB maintainers (PUC-Rio). Open according to the source as of 2026-10-20. The statement above is written in our own words; see the source for the original wording, history and discussion.