1000 tasks
Due to the way Li & Lim generated the test instances, the number of tasks in these instances are different and slightly higher than the nominal value.

Here you find instance definitions and the best known solutions (to our knowledge) for the 1000 tasks instances of Li & Lim's PDPTW benchmark problems. The version reported here has a hierarchical objective: 1) Minimize number of vehicles 2) Minimize total distance. Distance and time should be calculated with double precision, total distance results are rounded to two decimals. Exact methods typically use a total distance objective and use integral or low precision distance and time calculations. Hence, results are not directly comparable.

For instance definitions, click here.

Best Known Results for PDPTW 1000-cases


The instance names in blue are hyperlinks to files with corresponding detailed solutions. They have all been checked by our solution checker. Note that many best known solutions do not have a reference to a peer reviewed publication. For these, important details on the solution algorithm, the computing time, and the experimental platform are probably not available. Further, there is no guarantee that the solutions have been produced without using external information, such as detailed solutions published earlier. We may later introduce two categories: 'properly published' and 'freestyle', the latter with no restrictions.

The instances LRC2_10_8 and LRC2_10_9 were not present in the original data sent to us by Li  & Lim. Supposedly they forgot to include them. If you happen to have these definitions, we would very much appreciate if you could forward them to top-request@sintef.no .


Instance Vehicles Distance Reference Date
lc1_10_1* 100 42488.66 SAM::OPT 23-apr-03
lc1_10_2 94 44548.51 SB 30-jan-19
lc1_10_3 78 45906.30 SCR 19-Dec-21
lc1_10_4 72 37782.17 SCR 19-Dec-21
lc1_10_5* 100 42477.40 SAM::OPT 10-aug-03
lc1_10_6 101 42838.39 SAM::OPT 11-aug-03
lc1_10_7s 100 42854.99 TS 2003
lc1_10_8 98 42949.56 Shobb 31-mar-18
lc1_10_9 90 43564.01 SCR 19-Dec-21
lc1_10_10 86 42929.15 SCR 19-Dec-21
lc2_10_1s 30 16879.24 TS 2003
lc2_10_2 30 20764.09 SCR 19-Dec-21
lc2_10_3 29 19299.48 SCR 19-Dec-21
lc2_10_4 29 17886.97 SCR 05-Nov-19
lc2_10_5k 31 17137.53 RP 25-Feb-05
lc2_10_6 30 19387.75 SCR 19-Dec-21
lc2_10_7 31 18389.37 SCR 05-Nov-19
lc2_10_8 30 17015.03 SB 30-Jan-19
lc2_10_9 30 18225.30 SCR 05-Nov-19
lc2_10_10 29 17043.64 SCR 05-Nov-19
lr1_10_1¤ 100 56744.91 MFS 22-aug-18
lr1_10_2 80 49349.84 SCR 05-Nov-19
lr1_10_3 54 41483.89 SCR 19-Dec-21
lr1_10_4 27 30788.11 NVIDIA 15-jan-24
lr1_10_5 58 59053.68 NVIDIA 06-Mar-23
lr1_10_6 46 51058.53 NVIDIA 15-jan-24
lr1_10_7 35 38563.20 HW 11-Jun-21
lr1_10_8 24 29613.27 SCR 19-Dec-21
lr1_10_9 47 54582.25 SCR 19-Dec-21
lr1_10_10 38 45510.71 SCR 19-Dec-21
lr2_10_1 17 62859.29 SCR 19-Dec-21
lr2_10_2 14 51357.30 SCR 22-Apr-21
lr2_10_3 10 42908.33 SCR 19-Dec-21
lr2_10_4 8 26595.39 SCR 22-Apr-21
lr2_10_5 13 54951.12 NVIDIA 15-jan-24
lr2_10_6 11 46253.37 SCR 19-Dec-21
lr2_10_7 8 39648.54 SCR 19-Dec-21
lr2_10_8 6 26742.31 NVIDIA 15-jan-24
lr2_10_9 12 50781.83 NVIDIA 08-Feb-23
lr2_10_10 10 44888.99 SCR 19-Dec-21
lrc1_10_1 82 49111.78 SB 30-jan-19
lrc1_10_2 71 45547.38 HW 30-Nov-20
lrc1_10_3 53 35616.85 SCR 19-Des-21
lrc1_10_4 40 27211.87 SCR 19-Des-21
lrc1_10_5 72 50323.04 HW 26-Feb-21
lrc1_10_6 67 45115.22 HW 30-Nov-20
lrc1_10_7 60 41560.52 HW 23-Dec-20
lrc1_10_8 55 40770.10 SCR 19-Dec-21
lrc1_10_9 52 40934.27 SCR 19-Dec-21
lrc1_10_10 47 36539.03 SCR 19-Dec-21
lrc2_10_1 22 34463.46 SCR 05-Nov-19
lrc2_10_2 19 38619.13 HW 10-Dec-20
lrc2_10_3 16 27218.08 HW 23-Dec-20
lrc2_10_4 11 23212.46 SCR 19-Dec-21
lrc2_10_5 16 40638.13 SCR 19-Dec-21
lrc2_10_6 17 30910.65 SCR 05-Nov-19
lrc2_10_7 15 33275.24 SCR 31-Dec-19
lrc2_10_8 - - - -
lrc2_10_9 - - - -
lrc2_10_10 11 29085.28 SCR 19-Dec-21

k: Detailed solution provided by K
s: Detailed solution provided by SAM::OPT
*: Corresponds to optimal value found by RC
¤: Corresponds to optimal value found by BBM


BBM - Baldacci, Bartolini, and Mingozzi. An Exact Algorithm for the Pickup and Delivery Problem. Operations Research 59(2), pp. 414–426 (2011).

CLS - Curtois, T., Landa-Silva, D., Qu, Y. and Laesanklang, W., 2018. Large neighbourhood search with adaptive guided ejection search for the pickup and delivery problem with time windows. EURO Journal on Transportation and Logistics, 7(2), pp.151-192.

CVB - Christiaens J. and Vanden Berghe G. A Fresh Ruin & Recreate Implementation for Capacitated Vehicle Routing Problems. To be submitted.

CVB2 - Christiaens J. and Vanden Berghe G. Preliminary title: Slack Induction by String Removals for Vehicle Routing Problems.

HW - Zhu He, Weibo Lin (linweibo@huawei.com), Fuda Ma et al. (Team of Scheduling Architecture and Algorithms, Huawei Cloud) and Zhipeng Lü (Huazhong University of Science and Technology). Cloud-oriented solvers for industrial planning and resource scheduling problems of Huawei Cloud (https://www.huaweicloud.com), unpublished.

K – Richard Kelly: Hybrid Ejection Chains and Adaptive LNS for the PDPTW. Working paper.

MFS - Evgeny Makarov, Ilya Fiks, Eugene Sorokhtin (swatmobile.io). Unpublished.

NVIDIA - (Piotr Sielski, Akif Çördük, Nicolas Blin, Hugo Linsenmaier,  Rajesh Gandham, Alex Fender) NVIDIA cuOpt : GPU accelerated Operations Research and Optimization.

OT - Piotr Sielski, Piotr Cybula, Marek Rogalski (marek.rogalski@otimo.pro), Mariusz Kok, Przemysław Pełka, Krzysztof Chaładyn. Otimo (https://otimo.pro)

RC - Ropke S. and J.-F. Cordeau. Branch and cut and price for the pickup and delivery problem with time windows. Transportation Sci. 43(3)267–286 (2009).

RP - S. Ropke & D. Pisinger, An Adaptive Large Neighborhood Search Heuristic for the Pickup and Delivery Problem with Time Windows, Technical Report, Department of Computer  Science, University of Copenhagen, 2004.

SAM::OPT - Hasle G., O. Kloster: Industrial Vehicle Routing Problems. Chapter in Hasle G., K-A Lie, E. Quak (eds): Geometric Modelling, Numerical Simulation, and Optimization. ISBN 978-3-540-68782-5, Springer 2007.

SB - Carlo Sartori, Luciana Buriol. A matheuristic approach to the PDPTW (to be submitted).

SCR - Piotr Sielski (piotr.sielski@wmii.uni.lodz.pl), Piotr Cybula, Marek Rogalski (marek.rogalski@wmii.uni.lodz.pl), Mariusz Kok, Piotr Beling, Andrzej Jaszkiewicz, Przemysław Pełka. Emapa S.A. www.emapa.pl "Development of universal methods of solving advanced VRP problems with the use of machine learning", unpublished research funded by The National Centre for Research and Development, project number: POIR.01.01.01-00-0012/19.  "Optimization of advanced VRP problem variants", unpublished. Computing grant 358 funded by Poznan Supercomputing and Networking Center.

Shobb - http://shobb.narod.ru/vrppd.html

TS - TetraSoft A/S: MapBooking Algoritm for Pickup and Delivery Solutions with Time Windows and Capacity restraints.

VR - Dmitriy Demin, Mikhail Diakov (msd@veeroute.com), Ivan Ilin, Nikita Ivanov, Viacheslav Sokolov (vs@veeroute.com) et al. VRt Global (https://veeroute.com/).

WM - Ganzhong Luo (luoganzhong@water-mirror.com), Lei Gao (gaolei@water-mirror.com), Zhixin Liu, Yaning Li, Mingxiang Chen, Qichang Chen, Nuoyi Zhu. "New Algorithms for VRPTW & PDPTW", unpublished result of WATERMIRROR AI.

Published April 18, 2008