1. OAR Lib: An Open Source Arc Routing Library
By Oliver Lum
Carmine Cerrone
Bruce Golden
Edward Wasil

2. OAR Lib (Motivation) Solution: Problem:
A (perceived) barrier to entry that coding experience in a non- modeling language is required
No centralized, standardized implementations of many routing algorithms
Existing APIs are frequently developed with graph theoretic research in mind
Realistic test data procurement
Figure generation for papers
An open-source java library aimed at new operations researchers in the field of arc-routing
An architecture for future software development in routing and scheduling
Design Philosophy: Usability First, Performance Second
OSM Integration
Gephi toolkit (open source graph visualization) Integration

3. OAR Lib (Content) Single-Vehicle Solvers Multi-Vehicle Solvers
Un/Directed Chinese Postman (UCPP/DCPP)
Mixed Chinese Postman (MCPP)
Windy Chinese Postman (WPP)
Directed Rural Postman Problem (DRPP)
Windy Rural Postman Problem (WRPP)
Multi-Vehicle Solvers
Min-Max K Windy Rural Postman Problem (MM-k WRPP)

4. OAR Lib (Content) Common Algorithms: Single-Source Shortest Paths
All-Pairs Shortest Paths
Min-Cost Matching (JNI)
Min-Cost Flow
Hierholzer’s Algorithm
(Stochastic) Minimum Spanning Tree
Minimum Spanning Arborescence (JNI)
Connectivity Tests

5. Applications Ubiquitous: Various interesting wrinkles:
Package Delivery
Snow Plowing
Military Patrols
Various interesting wrinkles:
Time-Windows
Close-Enough
Turn Penalties
Asymmetric Costs

6. The Min-Max K WRPP A natural extension of the WRPP
Objective: Minimize the max route cost
Homogenous fleet, K vehicles
Asymmetric Traversal Costs
Required and unrequired edges
Generalization of the directed, undirected, and mixed variants
Takes into account route balance, and customer satisfaction

7. The Min-Max K WRPP
= Required
= Included in route
= Untraversed
Depot

8. The Min-Max K WRPP Existing Literature:
Benavent, Enrique, et al. “Min-Max K-vehicles windy rural postman problem.” Networks 54.4 (2009):
Benavent, Enrique, Angel Corberan, Jose M. Sanchis. “A metaheuristic for the min-max windy rural postman problem with K vehicles.” Computational Management Science 7.3 (2010):
Benavent, Enrique, et al. “A branch-price-and-cut method for the min-max k-windy rural postman problem.” Networks (2014, to appear).

9. Existing Algorithm
Solve the single-vehicle variant. This produces a solution that can be represented as an ordered list of required edges (where any gaps are traversed via shortest paths).
Depot 9

10. Existing Algorithm
Set up a directed, acyclic graph with m+1 vertices, (0,1,…m) where the cost of the arc (i-1,j) is the cost of the tour starting at the depot, going to the tail of edge i, continuing along the single-vehicle solution through edge j, and then returning to the depot. 1 2 8

11. Existing Algorithm
Calculate a k-edge narrowest path from v0 to vm in the DAG, corresponding to a solution (a simple modification to Dijkstra’s single-source shortest path algorithm suffices). 1 2 3 4 5 6 7 8

12. A Partitioning Scheme
Transform the graph into a vertex-weighted graph in the following way:
Create a vertex for each edge in the original graph
Connect two vertices i and j if, in the original graph, edge I and edge j shared an endpoint 4 4 4 2 2 3 5 5 2 3 1 3 7 7 1 5 6 1
Depot 6

13. A Partitioning Scheme
Change the vertex weights to account for known dead- heading and distance to the depot. 4 4 2 5 2 3 1 3 7 5 1
Depot 6

14. A Partitioning Scheme
Partition the transformed graph into k approximately equal parts. 4 4 2 5 2 3 1 3 7 5 1
Depot 6

15. A Partitioning Scheme
Route the subgraphs induced by each partition using a single-vehicle solver. 4 4 4 2 2 2 1 3 1 3 1 3 5 5 5
Depot
Depot
Depot

16. Cross-Section of Helsinki, Finland
Test Instance:
Cross-Section of Helsinki, Finland
|V|=1230
|E|=1468
= Required Edge
= Unrequired Edge
= Depot

17. Existing Approach Route 1

18. Existing Approach Route 2

19. Partitioning Approach

20. Results Instance |V| |E| Partition Obj. Benavent Obj. % Diff
San Francisco
705
844
11645
10188
14.3
Washington D.C.
592
663
10742
10649
.87
London, UK
845
994
6116
5866
4.2
Istanbul, TR
629
780
7388
7516
-1.7
Perth, AUS
535
597
7379
6970
5.8
Auckland, AUS
1045
1130
13655
13368
2.1
Helsinki, FI
1230
1468
6640
6866
-2.5
Vienna, AU
483
557
3875
3947
-1.9
Paris, FR
1931
2256
14862
N/A
Calgary, CA
1733
2283
22644

21. Conclusions / Future Work
Advantages:
Capable of solving large instances
Service contiguity – adjacent links are more likely to be serviced by the same vehicle
Memory usage – the widest path calculation in the existing algorithm is extremely memory intensive ( order )
Future Work:
Incorporate / apply existing improvement procedures to both procedures and compare.
Exploring relationship between number of vehicles, and tuning parameters

22. Cross-Section of Greenland
A Large Instance
Test Instance:
Cross-Section of Greenland
|V|=3047
|E|=3285
Runtime: s

23. References
Ahr, Dino, and Gerhard Reinelt. "New heuristics and lower bounds for the Min-Max k-Chinese PostmanProblem." Algorithms|ESA Springer Berlin Heidelberg,
Benavent, Enrique, et al. "New heuristic algorithms for the windy rural postman problem." Computers& operations research (2005):
Campos, V., and J. V. Savall. "A computational study of several heuristics for the DRPP." ComputationalOptimization and Applications 4.1 (1995):
minimumCostFlow2
Edmonds, Jack, and Ellis L. Johnson. "Matching, Euler tours and the Chinese postman." Mathematicalprogramming 5.1 (1973):

24. References
Eiselt, Horst A., Michel Gendreau, and Gilbert Laporte. "Arc routing problems, part II: The ruralpostman problem." Operations Research 43.3 (1995):
Derigs, Ulrich. Optimization and operations research. Eolss Publishers Company Limited, 2009.
Dussault, Benjamin, et al. "Plowing with precedence: A variant of the windy postman problem."Computers & Operations Research (2012).
Frederickson, Greg N. "Approximation algorithms for some postman problems." Journal of the ACM(JACM) 26.3 (1979):

25. References
Grotschel, Martin, and Zaw Win. "A cutting plane algorithm for the windy postman problem." Math-ematical Programming (1992):
Hierholzer, Carl, and Chr Wiener. "Uber die Moglichkeit, einen Linienzug ohne Wiederholung und ohneUnterbrechung zu umfahren." Mathematische Annalen 6.1 (1873):
Karypis, George, and Vipin Kumar. "A fast and high quality multilevel scheme for partitioning irregulargraphs." SIAM Journal on scientic Computing 20.1 (1998):
Kolmogorov, Vladimir. "Blossom V: a new implementation of a minimum cost perfect matching algo-rithm." Mathematical Programming Computation 1.1 (2009):
Lau, Hang T. A Java library of graph algorithms and optimization. CRC Press, 2010.
Letchford, Adam N., Gerhard Reinelt, and Dirk Oliver Theis. "A faster exact separation algorithm forblossom inequalities." Integer programming and combinatorial optimization. Springer Berlin Heidelberg,

26. References
Padberg, Manfred W., and M. Ram Rao. "Odd minimum cut- sets and b-matchings." Mathematics ofOperations Research 7.1 (1982):
Thimbleby, Harold. "The directed chinese postman problem." Software: Practice and Experience 33.11(2003):
Win, Zaw. "On the windy postman problem on Eulerian graphs." Mathematical Programming (1989):
Yaoyuenyong, Kriangchai, Peerayuth Charnsethikul, and Vira Chankong. "A heuristic algorithm for themixed Chinese postman problem." Optimization and Engineering 3.2 (2002):