An arc orienteering algorithm to find the most scenic path on a large-scale road network

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1 An arc orienteering algorithm to find the most scenic path on a large-scale road network Ying Lu Cyrus Shahabi Integrated Media Systems Center, University of Southern California {ylu720, shahabi}@usc.edu 1

2 Outline Introduction Related work Baseline Proposed algorithms Experiments Conclusion 2

3 Shortest path Minimum travel costs Introduction Scenic path Most scenic path Travel cost is within a budget (e.g., 8 hours) Route a (7.5 hours) Route b (5 hours) 3

4 Shortest path Minimum travel costs Introduction Scenic path Most scenic path Travel cost is within a budget (e.g., 8 hours) Attractiveness value calculation for each arc on a road network E.g., Geo-tagged photos [TOMM 13] Route a (7.5 hours) Route b (5 hours) 4

5 Problem Definition Finding scenic path Arc Orienteering Problem (AOP) [EJOR 00] Given a directed graph G = (V, A) where a travel cost., a. cost > 0 an attractiveness value., a. value 0 Further, given a source, a destination and a traveling cost budget, AOP is to find a path from to s.t.. ( ) s.t. ( ) 5

6 Problem Definition (Cont ) 1) AOP is an NP-hard problem! 2) Fast response request on online applications Challenge: how can we solve AOP on a large-scale road network with fast response (e.g., 300 milliseconds)? 6

7 Outline Introduction Related work Baseline Proposed algorithms Experiments Conclusion 7

8 Related Work Scenic trip planning Attractiveness value calculation E.g., [TOMM 13], [GIS 14] Scenic routing algorithms 8

9 Related Work Scenic trip planning Attractiveness value calculation E.g., [TOMM 13], [GIS 14] Scenic routing algorithms Single-objective [TS 05]. ( ) Pareto [SSTD 15].. OP [EJOR 96] AOP 9

10 Related Work Scenic trip planning Attractiveness value calculation E.g., [TOMM 13], [GIS 14] Scenic routing algorithms Single-objective [TS 05]. ( ) Pareto [SSTD 15].. OP [EJOR 96] AOP Exact algo [EJOR 00] Approximate algo [IPL 15] Heuristics [Omega 11], [TR 14] [Omega 11]: Greedy Randomized Adaptive Search Procedure-based algorithm (GRASP) [TR 14]: Iterated Local Search (ILS) 10

11 Related Work Scenic trip planning Attractiveness value calculation E.g., [TOMM 13], [GIS 14] Scenic routing algorithms Single-objective [TS 05]. ( ) Pareto [SSTD 15].. OP [EJOR 96] AOP Exact algo [EJOR 00] Approximate algo [IPL 15] Heuristics [Omega 11], [TR 14] [Omega 11]: Greedy Randomized Adaptive Search Procedure-based algorithm (GRASP) [TR 14]: Iterated Local Search (ILS) baseline 11

12 Outline Introduction Related work Baseline Proposed algorithms Experiments Conclusion 12

13 Baseline ILS ILS General Framework: Init Perturb Update 13

Baseline ILS ILS General Framework: Init Perturb Update 4 1 2 3 DFS visit order s v 1 a 1. =15 v 2 v 3 2.

14 Baseline ILS ILS General Framework: Init Perturb Update DFS visit order s v 1 a 1. =15 v 2 v 3 2. =1 v 4 v 5 a 3. =18 v 6 d. = 16. = 5 Cost of each arc = 1 Cost budget = 5 a 4. =12 a 5. =1 v 7 v 8 v 9 v 10 14

Baseline ILS ILS General Framework: Remove which arcs first (start, end) Init Perturb Update 4 1 2 3 DFS visit order start s end v

15 Baseline ILS ILS General Framework: Remove which arcs first (start, end) Init Perturb Update DFS visit order start s end v 1 a 1. =15 v 2 v 3 2. =1 v 4 v 5 a 3. =18 v 6 d. = 16. = 5 Cost of each arc = 1 Cost budget = 5 a 4. =12 a 5. =1 v 7 v 8 v 9 v 10 15

Baseline ILS ILS General Framework: Remove which arcs first (start, end) Init Perturb Update DFS 4 1 2 3 DFS visit order start s end

16 Baseline ILS ILS General Framework: Remove which arcs first (start, end) Init Perturb Update DFS DFS visit order start s end v 1 a 1. =15 v 2 v 3 2. =1 v 4 v 5 a 3. =18 v 6 d. = 1. = 5 Cost of each arc = 1 Cost budget = 5 a 4. =12 a 5. =1 v 7 v 8 v 9 v 10 16

17 Baseline ILS ILS General Framework: Remove which arcs first (start, end) Init Perturb Update DFS DFS visit order start s end v 1 a 1. =15 v 2 v 3 2. =1 v 4 v 5 a 3. =18 v 6 d. = 19. = 5 Cost of each arc = 1 Cost budget = 5 a 4. =12 a 5. =1 v 7 v 8 v 9 v 10 17

18 Baseline ILS ILS General Framework: Remove which arcs first (start, end) Init Perturb Update Insert which arcs first DFS DFS visit order start s end v 1 a 1. =15 v 2 v 3 2. =1 v 4 v 5 a 3. =18 v 6 d. = 19. = 5 Cost of each arc = 1 Cost budget = 5 a 4. =12 a 5. =1 v 7 v 8 v 9 v 10 18

Baseline ILS ILS General Framework: Remove which arcs first (start, end) Init Perturb Update Insert which arcs first DFS 4 1 2 3 DFS visit order 4 1 2 3 Cost of each arc = 1 Cost DFS visit budget

19 Baseline ILS ILS General Framework: Remove which arcs first (start, end) Init Perturb Update Insert which arcs first DFS DFS visit order Cost of each arc = 1 Cost DFS visit budget order = 5 start s end v 1 a 1. =15 v 2 v 3 2. =1 v 4 Arc position v 5 a 3. =18 3 (18) v 6 Neither cost nor value a 4 (10) a 4. =12 a 5. =1 v 7 a 5 (12) v 8 v 9 v 10 d. = 19. = 5 Small value improvement 19

20 Baseline ILS To avoid selecting impossible arcs Feasibility checking (,,,,,, )? s a v 1 v 2 d 20

21 Baseline ILS To avoid selecting impossible arcs Feasibility checking (,,,,,, )? s a v 1 v 2 d Check the entire graph! Slow iteration 21

22 Baseline ILS Pre-compute all-pair shortest paths Large storage requirement Real road networks dynamic Not applicable for large-scale real road network 22

23 Outline Introduction Related work Baseline Proposed algorithms Experiments Conclusion 23

24 Proposed Algorithms Overview Baseline ILS[3] drawbacks: Small value improvement Slow iteration Pre-computation Increase Speed up On-the-fly Proposed Algorithms ILS ILS(C) ILS(CE) + Criteria With Spatial techniques + Ellipse pruning + Indexing ILS(CEI) 24

25 ILS(C): ILS algorithm with Criteria ILS General Framework: Remove which arcs first (start, end) With higher ImprovePotential Init Perturb Update v 1 a 1. =15 v 2 v 3 2. =1 v 4. = 19. = 5 s v 5 a 3. =18 v 6 d Cost of each arc = 1 Cost budget = 5 a 4. =12 a 5. =1 v 7 v 8 v 9 v 10 25

26 Remove which arcs first (start, end) With higher ImprovePotential ILS(C): ILS algorithm with Criteria ILS General Framework: Init Perturb Update v 1 a 1. =15 v 2 v 3 2. =1 v 4 Insert which arcs first DFS With higher QualityRatio s v 5 a 3. =18 v 6 d. = 33. = 5 Cost of each arc = 1 Cost budget = 5 a 4. =12 a 5. =1 v 7 v 8 v 9 v 10 26

=1 v 4 Insert which arcs first DFS With higher QualityRatio s v 5 a 3. =18 v 6 d. = 33.

27 Remove which arcs first (start, end) With higher ImprovePotential ILS(C): ILS algorithm with Criteria ILS General Framework: Init Perturb Update v 1 a 1. =15 v 2 v 3 2. =1 v 4 Insert which arcs first DFS With higher QualityRatio s v 5 a 3. =18 v 6 d. = 33. = 5 Cost of each arc = 1 Cost budget = 5 Consider both cost and value a 4. =12 a 5. =1 v 7 a 4 (12) v 8 v 9 v 10 increase value improvement 27

28 ILS(C) Large search space ILS General Framework: Init Perturb Update Insert which arcs first v 1 a 1. =15 v 2 v 3 2. =1 v 4 With higher QualityRatio s v 5 a 3. =18 v 6 Search space: G a 4. =12 a 5. =1 v 7 v 8 v 9 v 10 d 28

=18 v 6 Large search space Search space: G

29 ILS(C) Large search space ILS General Framework: Init Perturb Update Insert which arcs first v 1 a 1. =15 v 2 v 3 2. =1 v 4 With higher QualityRatio s v 5 a 3. =18 v 6 Large search space Search space: G a 4. =12 a 5. =1 v 7 v 8 v 9 v 10 d Slow iteration! 29

30 To speed up iteration without loss of value improvement Road network Traditional graph Road network Spatial network 30

31 ILS(CE): ILS(C) with Ellipse pruning To avoid unnecessary checking s d llipse foci:, main axis: the remaining budget after removing a 31

32 ILS(CE): ILS(C) with Ellipse pruning To avoid unnecessary checking s d llipse foci:, main axis: the remaining budget after removing a 32

33 ILS(CE): ILS(C) with Ellipse pruning arc checking # SP computation # iteration time 33

34 ILS(CE): ILS(C) with Ellipse pruning arc checking # SP computation # iteration time Check one by one! 34

35 ILS(CE): ILS(C) with Ellipse pruning arc checking # SP computation # iteration time Check one by one! Check in a batch way 35

36 ILS(CEI): ILS(CE) with Indexing Index with Grid each cell c links a set of arcs that overlap c E.g., C(1, 5): {,,, } C(1, 5) C(6, 6) a 1 a 2 a3 a 4 C(1, 1) a.ellipse 36

37 ILS(CEI): ILS(CE) with Indexing Index with Grid each cell c links a set of arcs that overlap c E.g., C(1, 5): {,,, } C(1, 5) C(6, 6) a 1 a 2 a3 a 4 C(1, 1) a.ellipse 37

38 ILS(CEI): ILS(CE) with Indexing Index with Grid each cell c links a set of arcs that overlap c E.g., C(1, 5): {,,, } C(1, 5) C(6, 6) No need to check one by one a 1 a 2 a3 a 4 Reduce iteration time C(1, 1) a.ellipse 38

39 Outline Introduction Related work Baseline Proposed algorithms Experiments Conclusion 39

40 Experiments setup Implemented Methods Heuristics: ILS(C), ILS(CE), ILS(CEI), and Baseline ILS[TR 14] Exact algorithm: Open source optimization solver: CPLEX Metric Accuracy benchmark Accuracy percentage =.. 100% 40 21

41 Datasets LAFlickr LA road network Flickr photos: 217,391 photos Online shortest path calculation: CH [VLDB 12] FlandersBicycle [TR 14] A real bicycle network in Flanders Pre-compute all-pair shortest paths Statistics LAFlickr FlandersCycle Node# 111, Arc# 183,945 2,

42 Results on LAFlickr Dataset with online shortest path computation 42

43 Results on LAFlickr Dataset with online shortest path computation ILS(CE) and ILS(CEI) baseline, at least 20% more accurate Criteria increase value improvement spatial techniques speed up iteration 43

44 Results on LAFlickr Dataset with online shortest path computation ILS(CEI) can achieve 95% accuracy within 300 milliseconds ILS(CE) and ILS(CEI) baseline, at least 20% more accurate Criteria increase value improvement spatial techniques speed up iteration 44

45 Results on LAFlickr Dataset with online shortest path computation ILS(C) < Baseline 45

46 Results on LAFlickr Dataset with online shortest path computation ILS(C) < Baseline Search space, Arc#: Iteration time = Arc# * O(SP): Value improvement: ILS(C) > Baseline ILS(C) >> Baseline ILS(C) > Baseline dominate 46

47 Results on FlandersBicycle Dataset with shortest path pre-computation ILS(C) > Baseline Search space, Arc#: Iteration time = Arc# * O(SP): Value improvement: ILS(C) > Baseline ILS(C) > Baseline ILS(C) > Baseline dominate 47

48 Conclusion Proposed three algorithms to solve AOP with milliseconds response time: ILS(C) Two criteria Increase value improvement ILS(CE) Ellipse pruning Reduce the # of SP computation speed up iteration ILS(CEI) Grid indexing Batch checking speed up iteration 48

49 References [1] Zheng et al. GPSView: A scenic driving route planner. TOMM, 9(1):3, [2] S. P. L. Ray Deitch. The one-period bus touring problem: Solved by an effective heuristic for the orienteering tour problem and improvement algorithm. EJOR127:69 77, [3] W. Souffriau, P. Vansteenwegen, G. V. Berghe, and D. V. Oudheusden. The planning of cycle trips in the province of east flanders. Omega, 39(2): , [4] C. Verbeeck, P. Vansteenwegen, and E.-H. Aghezzaf. An extension of the arc orienteering problem and its application to cycle trip planning. Transportation research, 68:64 78,

50 Thanks! Q & A 50

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