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Planning your route: where to start?
Lahari SenguptaRadu Mariescu-Istodor
Pasi Fränti
14.3.2019
L. Sengupta, R. Mariescu-Istodor and P. Fränti, "Planning your route: where to start?" Computational Brain & Behavior, 1 (3-4), 252-265, December 2018.
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What is O-Mopsi?
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Classical orienteeringDevices: Map and compass
Targets brought to nature for the event
• Find all controls• In pre-defined order• Fastest wins
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Mopsi orienteering (O-Mopsi)
• Find all controls• In free order• Fastest wins
Picturesof targets
Targets real objects
Smartphone and GPS
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Challenges of playing
Orienteering:• Knowing your location• Optimizing paths to targets
?
O-Mopsi:• Finding best order• Optimizing paths to targets
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Winning the game
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What matters
Order of visiting targets- Travelling salesman problem (TSP)- Human strategies: nearest neighbor, clustering- Computer strategies: optimal, optimization
Where to start playing- Remove longest edge from TSP?- Blind selection- Comparison of various heuristics
Navigating to targets- Effects of routing
250 m
228 m
250 m
228 m
Corner
? Center
Shortedge
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Order of targets
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? Bounding box
Player
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Terminal point
Terminal point
Bounding box
Optimal tour(2.9 km)
Player
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Algorithmic problem
• Minimize total distance• With N targets there are N! possible orders• Variant of travelling salesman problem (TSP)
250 m250 m
228 m
30 m
478 m 280 m
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Algorithmic problem
• Minimize total distance• With N targets there are N! possible orders• Variant of travelling salesman problem (TSP)
250 m250 m
228 m
30 m
478 m 280 m
N = 10 N!= 3,628,800
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Nearest target strategy
Optimal order
4 km
5 km
How much it matters?
12
3
1
2
3
• More targets,harder to solve
• Nearest target strategy
• 24% longer than optimal (on average)
• Median: 20%
• Minimum: 0.06%• Maximum: 109%
?
Game NT (km)
Opt. (km) Diff.
Scifest 2014 short
1.14 0.97 17%
Helsinki downtown 4.97 4.08 22%
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Navigating to the targets
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?
Fastest route?
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• Buildings and small housing in city area• Real distance on ~50% longer than bird’s distance• Can also affect the order of the targets
411 m 752 m
Routing vs. Bird’s distance
Bird distance Routing
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Effect of route network Start point changes
13.4 km
Bird distance Routing
21.4 km
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Limitations of routing
No routes viaopen plaza
No shortcuts
Limitations in street crossing
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Bird’s distance Road distance Real lifeBird’s distance Road distance Real life
Examples of the limitations
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Effect of transport mode
Routing by car
Shorter routing by walk
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Effect of starting point
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Where to start?
Before start
• Targets not visible before start (if known, can start at one target)
• No time for planning route (Time starts when game opens)
• Ony game area shown (bounding box)
• Start must be chosen blindly
After start
Bounding box
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Start point strategy 1 Center of the area
Center
?
1.105 km
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Corner
Start point strategy 2 Corner of the area
?
1.053 km
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Shortedge
Start point strategy 3 Somewhere at the shorter edge
?
976 m
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Start point matters
xmax
xminymin
ymax
Likely direction of optimal route
• Every side has at least one target• Optimal order likely to go along longer side
(rather than random zig zag)
• Heuristic: Start from the shorter side
Longer side
Shorter side
Start
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Optimal start point located:
First/last target on corners: 42%First/last target along the long side: 22 %First/last target along the short side: 29 %Some other target: 7 %
Start point statistics according to target location
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Game Area
20% of the Height
20% of The width
Game area Divided into 5x5 grid
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20% of the Height
20% of The width
Labeling grid cells Corner, middle, long and short edge
Corner Long edge Corner
Short edge Middle Short
edge
Corner Long edge Corner
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Start point examples
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Start point statistics according to grid
• Calculate optimal tour• Divide the area into 20%20% grid• Locate the start and end points of the tour in the grid
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3 km
2.2 km
Terminal point
Terminal point
Optimal tour
Closed-loop case Open-loop case
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Original problem Added large constant to start node
Phantom node added
Solve it by ConcordePhantom node removedRemoved large constant from start node
Original problemOriginal problem Added large constant to start node
Added large constant to start node
Phantom node addedPhantom node added
Solve it by ConcordeSolve it by ConcordePhantom node removedPhantom node removedRemoved large constant from start node
Removed large constant from start node
Solving the optimal tour Using Concorde algorithm
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Optimum vs. player’s choice
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Computer performance
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Location of terminal points
AR = Aspect ratio = width/height
AR=1
AR=0.5
AR=2.0
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Human performance Average performance
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Corner to same side corner
Corner to opposite long edge
Corner to opposite corner
Corner to opposite short edge Corner to adjacent long edge
Corner to adjacent short edge
Short edge to short edge
Long edge to short edge
Corner to…• opposite corner• opposite short edge• opposite long edge
45%
Corner to…• same side corner• adjacent long edge• adjacent short edge
30%
Short edge to…• short edge• long edge
17%
Most common optimal patterns
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Human performance
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Experimental setupVisible task
• Student volunteers (30)• Design and Analysis of Algorithms course
• Player selects only start point• Concorde algorithm solves
the rest of the tour
• Calculate the gap between the resulting tour and the optimum
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Experimental setupBlind task
• Player sees only the bounding box!
• Otherwise the same test setup
• Significantly more challenging
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0 %
1 %
2 %
3 %
4 %
5 %
6 %
7 %
Visible
Blind
Topgroup
Bottom group
Human performance (gap)
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0%
20%
40%
60%
80%
100%
0% 20% 40% 60% 80% 100%Exam result
Am
ount
sol
ved
(%)
High gradeLow grade
Visible
Bottom‐group
Top group
Correlation to study results Design and Analysis of Algorithms
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0%
20%
40%
60%
80%
100%
0% 10% 20% 30% 40% 50% 60%Furthest point chosen
Am
ount
sol
ved
(%)
High gradeLow grade
Visible
0%
20%
40%
60%
80%
100%
0% 20% 40% 60% 80% 100%Convex Hull point chosen
Am
ount
sol
ved
(%)
High gradeLow grade
Visible
Effect of playing strategy
Furthest pointstrategy
Points on convex hull
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Summary of affecting factors
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Exam resultCorner point
strategy
0%
10%
20%
30%
40%
50%
60%
0 % 20 % 40 % 60 % 80 % 100 %Exam result
Am
ount
sol
ved
(%)
High gradeLow grade
Blind
0%
10%
20%
30%
40%
50%
60%
70% 80% 90% 100%Corner chosen
Am
ount
sol
ved
(%)
High gradeLow grade
Blind
Blind performance
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What did we learn?
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Conclusions
• Selecting the start point surprisingly tricky
• Best human strategies: Visible: Furthest points and convex hull Blind: Corner!
• Best computer strategy (blind): Shortest edge