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Benchmarks
All computations done on a machine using an Intel Xeon E5-1620 CPU @ 3.50GHz, 4c/8t.
The Solomon benchmark is used as a reference in most research papers including time window constraints.
All required instances and scripts are available to reproduce results.
56 instances with 100 jobs, grouped in classes C (clustered), R (random), RC (mix of both), and 1 or 2 for short or long planning horizon.
Using v1.9.0 with -x 5 and comparing to best known solutions targeting cumulated travel time (more on objectives).
| Computing times | (ms) |
|---|---|
| Average | 425 |
| Median | 484 |
| Longest | 652 |
| Quality | |
|---|---|
| Best known solutions | 14 (25.0%) |
| Minimum gap | +0.00% |
| Median gap | +1.11% |
| Average gap | +1.75% |
| Worst gap | +8.61% |
Comparison to best known solutions (BKS) targeting cumulated travel time (CTT). Cumulated number of vehicles (CNV) is only reported for the record.
| Class | C1 | C2 | R1 | R2 | RC1 | RC2 | Total |
|---|---|---|---|---|---|---|---|
| BKS CNV | 10.0 | 3.0 | 13.25 | 5.36 | 12.88 | 6.25 | 485 |
| BKS CTT | 828.38 | 589.86 | 1175.75 | 878.41 | 1340.02 | 1004.21 | 54,699 |
| VROOM CNV | 10.0 | 3.0 | 13.33 | 4.36 | 13.12 | 5.25 | 469 |
| VROOM CTT | 828.38 | 589.86 | 1190.03 | 911.56 | 1359.48 | 1038.89 | 55,668 |
| CTT gap | +0.00% | +0.00% | +1.21% | +3.77% | +1.45% | +3.45% | +1.77 |
All required instances and scripts are available to reproduce results on the Cordeau et al. (1997) dataset.
33 instances with capacity constraints and a number of jobs ranging from 48 to 360 (average 176), with vehicles starting from 2 to 9 depots.
Using v1.10.0 with -x 5.
| Computing times | (ms) |
|---|---|
| Average | 1310 |
| Median | 423 |
| Longest | 5564 |
| Quality | |
|---|---|
| Best known solutions | 5 (15.2%) |
| Minimum gap | +0.00% |
| Median gap | +1.67% |
| Average gap | +1.82% |
| Worst gap | +5.02% |
The Li & Lim 100 benchmark is derived from the Solomon instances with the addition of pickup and delivery constraints.
All required instances and scripts are available to reproduce results.
56 instances with around 100 jobs, grouped in classes C (clustered), R (random), RC (mix of both), and 1 or 2 for short or long planning horizon.
Using v1.9.0 with -x 5.
| Computing times | (ms) |
|---|---|
| Average | 140 |
| Median | 130 |
| Longest | 283 |
We target cumulated travel time (CTT), but best known results are only reported for approaches using the number of vehicles as the first optimization objective. For a meaningful comparison we rule out instances lc103, lc104, lc109 andlr211 for which we provide solutions that are better in term of CTT but use one more vehicle than the reported "best known solution".
| CTT comparison | |
|---|---|
| Best known solutions | 24 (46.2%) |
| Minimum gap | +0.00% |
| Median gap | +0.09% |
| Average gap | +1.22% |
| Worst gap | +9.86% |
CVRPLIB is a set of benchmark instances for single-depot CVRP. We use all instances described using euclidean distance (EDGE_WEIGHT_TYPE = EUC_2D), from classes A, B, E, F, M, P and X.
All required instances and scripts are available to reproduce results.
- 189 instances
- Sizes ranging from 15 to 1,000 jobs
- Average size around 240 jobs
- Number of vehicles ranging from 2 to 207
- Average capacity tightness (total job demand / total vehicle capacity): 0.95
Using v1.9.0.
| Exploration level | 0 (fastest) | 5 (best) |
|---|---|---|
| Median computing time | 41ms | 707ms |
| Longest computing time | 2.4s | 132.5s |
| Jobs assigned | 99.6% | 99.9% |
| Solutions with all jobs | 158 (83.6%) | 170 (90.0%) |
| Best known solutions | 13 (6.9%) | 42 (22.2%) |
Only reported for instances with all jobs assigned, so cost comparison makes sense.
| Exploration level | 0 (fastest) | 5 (best) |
|---|---|---|
| Minimum gap | +0.00% | +0.00% |
| Median gap | +2.84% | +0.99% |
| Average gap | +3.25% | +1.73% |
| Worst gap | +16.41% | +11.00% |
TSPLIB is the reference benchmark for TSP. We use all instances described using euclidean distance (EDGE_WEIGHT_TYPE = EUC_2D).
All required instances and scripts are available to reproduce results.
- 78 instances
- Sizes ranging from 50 to 18,511 points
- Average size around 1,170 points
Using v1.8.0.
- Median computing time: 35 ms
- Average gap to optimal solution: +2.69%
- Worst gap to optimal solution: +6.21%
| Instance | Size | Computing time | Gap |
|---|---|---|---|
| kroB100 | 100 | 5ms | +0.26% |
| a280 | 280 | 18ms | +1.12% |
| rat575 | 575 | 61ms | +3.35% |
| u1060 | 1,060 | 294ms | +3.04% |
| u2152 | 2,152 | 1824ms | +4.77% |
| rl5915 | 5,915 | 25s | +1.92% |
| usa13509 | 13,509 | 14m18s | +2.81% |
| d18512 | 18,512 | 35m37s | +2.99% |