Speech by Gwénaël Rault, PhD candidate in Operational Research at Mapotempo during VeRoLog 2019. Abstract : In the context of this presentation, we focus on Asymmetric HVRP where the shortest path between two customers nodes is vehicle dependent. Moreover, the distance matrices doesn’t verify the triangular inequality. Case which is common when we consider a real road network at the fastest with the objective to minimize the total distance. The problem in itself contains a set of multiple vehicle types with a limit number on their usage, as well as a capacity limit at the parcels number they can load to deliver at the customers nodes. At this purpose, the instances provided by C. Duhamel and al(2011) and named New real life Duhamel–Lacomme–Prodhon_HVRP instances (DLP_HVRP), based on realistic distances between french cities, are considered as the main comparison set. The current approach use at first step a GRASP+ALNS metaheuristic, method known to provide good results in a short computation time. In a second step, a constraint programming model of the problem is used to shuffle the problem and provide an additional local search starting from the current solution. Data are exchanged iteratively in order to benefit from each solve step improvement. The aim behind the use of multiple models is to expose the possible synergies between those methods. Multiple solve scenarios will be presented to discuss about the multiple layout available between the two previously mentioned solve steps and show their impact on the resolution.

1. GROUPE
1
Multiple solving approaches applied to
the Heterogeneous Vehicle Routing
Problem
Flavien Lucas, Gwénaël Rault, Marc
Sevaux
June 4th 2019

2. Operations Research at Mapotempo
2
● A Generic Routing Optimization API
● Implementation of a Rich VRP model through OR-tools
● Various heuristics methods for Large VRP or Periodic VRP
● Integration of multiple solvers (CPLEX CPO, LocalSolver, Jsprit, OR-
Tools, Rados and VROOM)

3. OR-tools
https://github.com/Mapotempo
Mapotempo - Projects design
Router API
Mapotempo Web + API
Optimizer API
OSRM
OpenStreetMap
Wrapper
ORtools
VROOM
OpenStreetMap
3
RADOS*
OR-toolsOR-tools
*Collaboration Flavien Lucas

4. Resolution methods
4
● OR-Tools (Google)
Production
Constraint Programming solver, used for Rich VRP
https://github.com/google/or-tools
● VROOM (VERSO)
Production
Heuristic Library for TSP, VRP, CVRP and VRPTW, used for TSP
https://github.com/VROOM-Project/vroom

5. Set of constraints¹ available in Optimizer-API
Optimizer API
5
○ Homogeneous Fleet of Vehicles
○ Heterogeneous Fleet of Vehicles
○ Fixed Fleet of Vehicles
○ Multidepot
○ Different End Locations/Open Routes
○ Different Start and End Locations
○ Departure from Different Locations
○ Symmetric Cost Matrix
○ Asymmetric Cost Matrix
○ Vehicle Capacity
○ Multiproducts
○ Duration Constraints/Length
○ Time Windows
○ Multiple Time Windows
○ Multiple Visits
○ Multiperiod/Periodic
○ Pickup & Delivery
○ Precedence Constraints
¹Caceres Cruz, Jose & Arias, Pol & Guimarans, Daniel & Riera, Daniel & Juan, Angel. (2014). Rich Vehicle Routing Problem:
Survey. ACM Computing Surveys. 47. 1-28. 10.1145/2666003.
Problem

6. Heterogeneous VRP
6
Constraints
● Vehicle Capacity
● Heterogeneous Fleet of Vehicles
● Fixed Fleet of Vehicles
Advantages of this problem
● May represents part of bigger problems
● Have instances with real distance matrices¹
● Close to real cases met at Mapotempo
¹Christophe Duhamel, Philippe Lacomme, Caroline Prodhon, A hybrid evolutionary local search with depth first
search split procedure for the heterogeneous vehicle routing problems, Engineering Applications of Artificial
Intelligence, Volume 25, Issue 2, 2012, Pages 345-358, ISSN 0952-1976.
²R. Sadykov, E. Uchoa, A. Pessoa. "A Bucket Graph Based Labeling Algorithm with Application to Vehicle Routing"
Cadernos do LOGIS 2017/7, submitted
³Penna, Puca & Subramanian, Anand & Ochi, Luiz & Vidal, Thibaut & Prins, Christian. (2017). A hybrid heuristic for a
broad class of vehicle routing problems with heterogeneous fleet. Annals of Operations Research. 273.

7. OR-Tools HVRP model
7
Data Variables
Constraints Objective

8. OR-Tools HVRP resolution
8
● First solution
○ Built-In heuristic : Savings
○ External tool
● Guided Local Search

9. HVRP instances
9
96 Instances proposed by C. Duhamel, P. Lacomme & C. Prodhon¹
● true distance between french cities
● with 20 to 300 serviced nodes, corresponding to the French districts
● strongly heterogeneous list of vehicles
● no linear dependence between vehicles capacity and fixed cost
● include nightmare instances with up to 250 nodes and 7 vehicles types
¹Christophe Duhamel, Philippe Lacomme, Caroline Prodhon, A hybrid evolutionary local search with depth first
search split procedure for the heterogeneous vehicle routing problems, Engineering Applications of Artificial
Intelligence, Volume 25, Issue 2, 2012, Pages 345-358, ISSN 0952-1976.
http://fc.isima.fr/%7Elacomme/hvrp/hvrp.html

10. OR-Tools HVRP model results
10
Instance Nodes BKS OR-tools
1st sol
Ortools
cost
time(s) gap Rados cost time(s) gap R+O cost time gap
DLP_92 35 564.39*¹ ² 647.5 569.97 3.51 0.99 569.79 1.03 0.96 569.79 0.1 0.96
DLP_11 95 3367.41*¹ ² 5817.13 3505.4 64.79 4.1 3493.74 15.38 3.75 3450.33 9.89 2.46
DLP_17 105 5362.83*¹ ² - 5673.22 273.73 5.79 6110.72 15.74 13.95 5717.82 289.55 6.62
DLP_47 111 16156.12*¹ 23592.6 17144.77 625.86 6.12 19628.3 11.07 21.49 16736.16 467.32 3.59
DLP_30 112 6278.62*¹ 10986.4 6459.4 337.67 2.88 6670.18 9.26 6.24 6536.88 140.72 4.11
DLP_72 186 5870.43*¹ 10829.2 6321.48 263.63 7.68 6588.09 30.3 12.22 6162.71 65.7 4.98
DLP_57 163 44781.64² 57779.7 46727 981.57 4.34 49825.69 20.24 11.26 46347.26 328.36 3.5
DLP_62 225 22987¹ - 24887.7 649.18 8.27 28299.68 27.63 23.11 24635.43 768.78 7.17
DLP_27 220 8423¹ - 9084.47 669.55 7.85 9854.58 23.43 17 8856.91 1147.27 5.15
*Optimality proven
¹R. Sadykov, E. Uchoa, A. Pessoa. "A Bucket Graph Based Labeling Algorithm with Application to Vehicle Routing"
Cadernos do LOGIS 2017/7, submitted
²Penna, Puca & Subramanian, Anand & Ochi, Luiz & Vidal, Thibaut & Prins, Christian. (2017). A hybrid heuristic for a broad class of
vehicle routing problems with heterogeneous fleet. Annals of Operations Research. 273.

11. Next Improvements
11
● Explore various starting points
● Use rules deduced¹ from solutions provided by RADOS
● Add perturbation mechanisms
Multiple-Swap², Multiple-Shift², Multiple-K-Split³, Merge⁴
¹Arnold Florian, Gendreau Michel, Sörensen Kenneth. (2019). Efficiently solving very large-scale routing problems. Computers &
Operations Research.
²Penna, P. H. V., Subramanian, A., & Ochi, L. S. (2013). An iterated local search heuristic for the heterogeneous
fleet vehicle routing problem. Journal of Heuristics, 19(2), 201–232.
³Silva, M. M., Subramanian, A., & Ochi, L. S. (2015). An iterated local search heuristic for the split delivery
vehicle routing problem. Computers & Operations Research, 53, 234–249.
⁴Penna, Puca & Subramanian, Anand & Ochi, Luiz & Vidal, Thibaut & Prins, Christian. (2017). A hybrid heuristic for a broad class of
vehicle routing problems with heterogeneous fleet. Annals of Operations Research. 273.

12. A new variant: Clustered HVRP
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● Goals
○ Match the organizational expectations
○ Break the complexity (10,000+ nodes
to serve)
● Cluster generation
○ First level of sectors deduced from
geographical frontiers
○ Second level of sectors deduced
from constraints and density with a
clustering method

13. Clustered HVRP
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● Consider clusters as single node
● Solve with cluster nodes to estimate the vehicle fleet
● Recompute each route with real nodes
● Perform exchanges, insertions or removal of clusters instead of single
nodes
● Open/Close routes with the available fleet

14. 2 Echelon HVRP
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● Goals
○ Match the organizational expectations
○ Supply the satellite depots
○ Delegate final delivery to the most fitted
vehicle
● Modeling
○ High Level HVRP to supply the satellite
depots
○ Location Routing Problem to select the
most advantageous satellite depots
○ Low Level HVRP to deliver the final
customers from the satellite depots Main depot
Satellite depot
Customers

15. HVRP for 2 Echelon VRP
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● High level HVRP : Supply of the
Satellite Depots
● Low level HVRPs : Routes from
Satellite Depots to final customers (if we
can consider each sub-problem individually)

16. Conclusion & Perspectives
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● OR-Tools works well as Local Search Tool
● Integration with RADOS
● HVRP as initialization of a new variant: Clustered HVRP
● 2 Echelon HVRP
● Having an efficient HVRP resolution method is a requirements to
consider sophisticated business cases
● Solve instances with 10,000+ nodes

17. IT’S TIME TO RETHINK YOUR ROUTES
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CONTACT
Gwénaël Rault
OR Developer & PhD Student
www.linkedin.com/in/rgwenael
17
OR-tools
Optimizer API
Wrapper
ORtools
VROOM RADOS