The Genetics of Touring

Each student has written three blog posts at this point, so it's now the professors' turn to take over! Yesterday, we started the day with an optional trip to Hollywood Studios to allow students to collect project data. Unfortunately, the park had Extra Magic Hours that morning, so WDW resort guests could enter the park an hour before we could, which made for long lines early in the day. After some time to work on projects back in the hotel in the afternoon, we headed to Animal Kingdom to enjoy another evening in the park. 

The Genetics of Touring

Last week, the students participated in a race to see which team could accomplish a list of 19 tasks in the Magic Kingdom most efficiently.  The tasks ranged from riding an attraction to getting a picture taken with a character.  Differing from the Traveling Tourist Problem at Epcot two years ago, we allowed teams some flexibility in the attractions that they visited.  Here is a list of possible events:

The winning group's tour of the Magic Kingdom.

Required                                

Space Mountain       

Buzz Lightyear’s Spin            

Seven Dwarfs Mine Train 

Dumbo   

Haunted Mansion 

Peter Pan’s Flight           

Under the Sea - Voyage of the Little Mermaid

Splash Mountain              

Big Thunder Mountain Railroad

Pirates of the Caribbean           

Jungle Cruise         

Group Photo with a costumed character  

Group Photo with Walt Disney 

Fantasyland (Pick 3)
It’s a Small World
Winnie the Pooh

The winning group, Zack, Mary Lib, and Johanna.

Mad Tea Party
Hall of Presidents
Enchanted Tales with Belle
Barnstormer
Prince Charming’s Royal Carousel
Mickey’s Philharmagic

Tomorrowland (Pick 2)
Astro Orbitors
Stitch’s Great Escape
Monster’s Inc. Laugh Floor
Carousel of Progress
Tomorrowland Speedway

Adventureland (Pick 1)
Magic Carpets of Aladdin
Country Bear Jamboree
Enchanted Tiki Room

The students were assigned into groups of three and were given data on the expected wait, walk, and ride times in the Magic Kingdom that day (supplied by tourningplans.com).  They had an afternoon to design a tour of the chosen 19 attractions and were allowed time in the park to perform reconnaissance.  The following day we raced, and (drumroll, please) the winning team was Johanna, Mary Lib, and Zack who finished the tour in just under 6 hours.  Their tour is shown above.

Johanna, Mary Lib, and Zack flying with Dumbo.

After the race, the students learned to model the problem using networks and also learned that the problem they were trying to solve is a variation of the Traveling Salesman Problem.  This problem of trying to find an efficient tour of a given list of locations is one that is researched by logistics companies like FedEx and UPS.  A variety of algorithms exist to try to produce optimal, or near-optimal, solutions to these types of problems.  One such method is to use what are known as genetic algorithms.  These algorithms mimic natural selection in that a variety of solutions are produced (called a population) and their tour length (called their fitness) are calculated.  A solution for this problem is just a sequence of attractions in the order that they are visited (called a tour).  Solutions are then subjected to one of two types of operations to produce new, child solutions.  The first type of operation is called a mutator.  These operators take a member of the population and augment it in some way, such as switching the order in which you visit two (or more) attractions.  The second type of operation is called a crossover operator.  These operators take two members of the population and produce a child that resembles both parents.  For instance, a crossover operator might take two members of the population and find the attractions that are sequenced in a common position in both parents and include those attractions in those positions in the child.  The remaining attractions are then randomly placed in the remaining sequence positions in the child.  Every time a child is produced its fitness is calculated and if it is better fit than the least-fit solution in the population, that child replaces the least-fit solution in the population.  These operations reoccur for a fixed number of iterations (usually quite large) and the most-fit solution from the population is chosen as the “optimal” solution. 

The winning group at the finish line and
home of Dole Whip, Aloha Isle.

The second project for the students in the course involved inventing mutators and crossovers for a genetic algorithm to find the optimal solution of an abbreviated Traveling Tourist Problem involving only ten rides.  In fact, the example mutation and crossover operators described above are ones that students came up with.  Here are examples of other inventive operators that the students generated.

Crossover Example

1. Define Parent 1 as the parent with the single highest wait time.
2. Find the sequenced attractions that match in P1 and P2.  Include these attractions in these sequenced slots in the child.  Then take P1’s highest non-matching wait time and swap it with other attractions until it is in the location in P2’s sequence of the highest non-matching wait time.
3. Continue to find a nonmatching ride whose wait time is the highest and switch it with the lowest remaining wait time of the other parent. 

Mutator Example (Frame Shift)

Move an attraction from sequence spot j to sequence spot k and then shift all of the attractions in between sequence spots j and k one slot to the right or left depending on j’s relative position to k.

After running their genetic algorithms on the subset of rides that they were given, the group consisting of Johana, Mary Lib, Alyssa, and Molly found a tour that could be traversed in 284 minutes.  The sequence of attractions in this tour was

1. Seven Dwarfs Mine Train
2. Peter Pan's Flight
3. Haunted Mansion
4. Jungle Cruise
5. Buzz Lightyear
6. Dumbo
7. Space Mountain
8. Splash Mountain
9. Pirates of the Caribbean
10. Big Thunder Mountain Railroad

After studying these genetic algorithms, our group met with Len Testa, President of Touring Plans and co-author of The Unofficial Guide to Walt Disney World, which has sold more than 4 million copies worldwide.  Testa’s company, Touring Plans, employs an analytic approach to travel, helping its subscribers not only find good park tours, but also finding affordable options for park tickets, finding the quietest hotel rooms, etc.  His company employs mathematicians, statisticians, and computer scientists to model and produce solutions to many problems related to travel.  Len spoke with our students about the evolutionary algorithms (such as genetic algorithms) that his company employ to produce tours for users in a quick amount of time.  The time that the students put into to developing an intuition about the problem and creating mutation and crossover operators paid off when they saw how Touring Plans employs these types of algorithms to produce solutions to real-world problems.  They came away with an appreciation for the mathematical sophistication that Touring Plans brings to their solution approaches.  For some students this was an experience that caused them to remark that they wished they had brought a resume to the talk to give to Testa.  For the professors, we give many thanks to Len Testa for inspiring a group of students to continue to develop their mathematical creativity and problem-solving skills to make a difference for others.