This work seeks to explore an optimal and efficient solution for visitors to dynamically plan and assign their trips in NYC.

1. Time-based Prize Collecting
Modified Orienteering Problem
for NYC Travel Plan
TR-GY 7013 / CUSP-GX 9113: Urban Transportation & Logistics Systems – FALL 2023
Het Danak
Prajwal Chauhan
Shou Zhang
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2. Motivation
• New York City attracts numerous tourists, but due to time and budget constraints, many attractions become
challenging to visit
• By optimizing routes and recommending the optimum time to spend at each destination, the tourist
experience can be improved significantly
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3. Problem Description
• Consider a tourist visiting NYC
• They decide to visit n places on any given day
• They have two problems:
1. They are not sure about the best travel route
2. Also, they are not sure about the time they should
spend
at each location to maximize their fulfillment
• Suppose they go online to get the average time
people spend at each tourist attraction
• But this time sums up to more than the time they
have on their hand
• So, they decide to be clever about it and formulate it
as an Optimization Problem
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POIs to visit

4. Benchmark Solution
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Online recommended time to
be spent at each location and
ordered by most reviewed* (
23.33 hrs)
POIs for tourist
*https://www.yelp.com/

5. 5

6. 6

7. Solution for TSP
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Cost (travel time) Matrix
Solving using Evolutionary algo from excel, we get the following results for the shortest route
• This gives a total travel time of 1.67 hrs, which is far better than the original travel time of 4.58
hrs, 63% reduction in travel time

8. Comparing the Results
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Proposed Solution ( 1.67 hrs) Old Solution (4.53 hrs)

9. Time Spent at Each Node
•
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10. Example Functions
• Let’s assume:
• Case 1: pr=1 (low) and rank r = 1 (low)
This means this location takes less time and gives less
fulfillment
• Case 2: pr =1 but rank is high, r= 8
This location takes a longer time to give similar level of
fulfillment
• Case 3: pr=8 (high pr) but low rank, r =1
This location give higher fulfillment quicker
• Case 4: pr = 8 and rank =8
This location gives high fulfillment but also takes more time
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The x-axis represents time spent at node i and y-axis represents the reward function
Case 1. Low r, Low pr Case 2. High r, Low pr
Case 4. High r, High pr
Case 3. Low r, High pr
*Plotted in Desmos

11. Problem Formulation
•
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12. Solution (Time Budget =13:40)
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Time Budget = 13 hrs 40 mins

13. Solutions for Different Time Budget
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Time Budget = 14 hrs
Time Budget = 15 hrs
Time Budget = 12 hrs Time Budget = 12 hrs (suboptimal)
Time Budget = 15 hrs (Suboptimal)
Time Budget = 14 hrs (Suboptimal)
Considering 01:40 for travelling

14. Varying Perceived Ranks
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Time Budget = 14 hrs (old Pr) Time Budget = 14 hrs (with new Pr)
Time Budget = 14 hrs , all perceived equal

15. Formulation Using Nearest Neighbor
• Solved the TSP using Nearest Neighbor
Algorithm:
• Nearest Neighbor Tour:
[1, 6, 5, 8, 7, 9, 4, 3, 2, 1]
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Proposed Solution (2.86 hrs)

16. Comparing the Results
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Old Solution (4.53 hrs)
Nearest Neighbor (2.86 hrs)

17. Formulation
•
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18. Adding Time Windows and Subway Schedule
• By considering open/ close time &
Subway schedule, we develop a new
method to solve our Time-window TSP
• The subway schedule was implemented by
using arbitrary time frequency of each
train
• We also relaxed the constraint of visiting
all the destinations for this problem
[10, 21], # Time window for Metropolitan Museum
[7, 9], # Time window for the High Line
[8, 19], # Time window for Chelsea Market
[10,22], # Time window for Empire State building
[9,18], # Time window for Top of the Rock
[0,24], # Time window for Brooklyn Bridge
[0,24], # Time window for Grand Central Terminal
[9,21] # Time window for Statue of liberty
Adding arbitrary open and close times for locations
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19. Methodology of Current Algorithm
● We start with t= t_initial which can be set to the time the tourist leaves the hotel
● Then iteratively each node is visited, the travel time is added from the computed nearest neighbor algo and
maintained in the total passed time.
● The stay time at each location is optimized by maximizing the reward function which in this case is just a function
of time and rank
● Hence iteratively the subway schedule is followed with a constant interval assumed to start at t=0 (midnight)
● This schedule is checked each time a train is to be boarded
● Then total time passed is updated with adding travel time and the time spent at node i and adding the subway
waiting time
● By keeping track of total passed time, we determine if entry at the next location is feasible or not
● If it's feasible the node is visited and hence the time spent is added to the total passed time
● Else, next node is visited, and time spent at node i is set to zero, while the subway waiting time is added and a new
travel time from i to j is added to total passed time
● Again, the check is done if the new node is feasible to visit or not and the process repeats till the tourist is back at
hotel.
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20. Results
● We see that node 3 is not visited, as we limited its time from 8-9 AM
● The above results also provide the optimum time spent at each node
● This is zero for the depot as obviously should be and for node 3 which was not visited due to time constraint
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21. Conclusion
• We saw how planning and optimizing for Rewards as a function of time spent at destination and their
Perceived Ranks can lead to higher reward
• We also saw, how optimizing for subway schedule and opening and closing time of facilities can change the
optimum
• For future work, we can further improve the algorithms by implementing real time data and adding more
modes of transfer between locations
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22. References
• Chow, J. Y., & Liu, H. (2012). Generalized profitable tour problems for online activity routing system.
Transportation Research Record, 2284(1), 1-9.
• Yu, J., Aslam, J., Karaman, S., & Rus, D. (2015, September). Anytime planning of optimal schedules for a
mobile sensing robot. In 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems
(IROS) (pp. 5279-5286). IEEE.
• Fischetti, M., Gonzalez, J. J. S., & Toth, P. (1998). Solving the orienteering problem through branch-and-
cut. INFORMS Journal on Computing, 10(2), 133-148.
• Wu, X., Guan, H., Han, Y., & Ma, J. (2017). A tour route planning model for tourism experience utility
maximization. Advances in Mechanical Engineering, 9(10), 1687814017732309.
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23. Thank You
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