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. 

Day 18: Soarin' Through the Day

We're Soarin', Flyin'
Hi everyone, Caroline and Courtney here! Even though we had a late night last night celebrating Animal Kingdom's first night opening, we got up early for rope-drop at Epcot for one reason: the reopening of Soarin'. The popular simulation attraction has been closed for renovations, but reopened this weekend with an updated version of its former California-themed show. The final update will be titled Soarin' Over the World, and will showcase sights from around the world. Shoutout to Dr. Bouzarth for getting us FastPasses and noticing that it would be open today! We were able to ride the attraction once right when the park opened, and again using our FastPasses, and I was very impressed. While it isn't as "thrilling" as some other attractions, the entire simulation is beautifully done.

A selfie with some of the students before Soarin'

The Mouse Himself
In between our two Soarin' expeditions, we took a quick detour to the Character Spot in Epcot. We got to meet Mickey, Goofy, and Minnie, and loved getting to interact with the characters. Goofy seemed to particularly like one member of our group.

Goofy really like Mary Lib!

We made all the guys take a picture with Minnie!

One Day, Two Parks

After our flights at Epcot, we made the trip to Magic Kingdom so that one of our independent project groups could collect more data. When we arrived, my group (Caroline), ate a quick lunch at Casey's on Main Street before heading towards Liberty Square and Frontierland. After missing the showtime for the Hall of Presidents, Dr. Hutson thought it would be a good idea to take some of us to Country Bear Jamboree. I will only say that it was a memorable experience where we also got to see some of the earliest animatronics at Disney World. After helping the Fastpass group collect some data, a few other students and I went back to Main Street for some souvenir shopping.

My group (Courtney) grabbed some food at the Colombia Harbour House then headed to Big Thunder Mountain to gather some data. Since we were only focussed on one ride, not all twelve students were needed to collect data. Therefore, we decided to go to see The Enchanted Tiki Room for the first time this trip. There were some mixed reactions, especially since the song can get stuck in your head throughout the entire day. However, I personally believe that it is a classic that you have to do once every time you go to Disney.

Some Math with our Mouse
Back at the hotel, we began analyzing our data for our independent group projects. My group (Caroline) is looking at the Rock n Rollercoaster and Expedition Everest single rider lines. Disney utilized single rider lines to make their rides more efficient, as they can even out an odd party with an individual. We are trying to analyze their efficiency while also comparing the two lines. By counting party sizes as well as wait times for both of these attractions, we have been able to track the efficiency of the single rider line. We have established a hypothesis for how fast the single rider lines should be moving for each attraction, and plan on testing it tomorrow.

My group (Courtney) spent the past few days gathering data on the Disney characters guests can meet in each park. We continued to organize our data today by the 12 different characters that we observed. We arranged the data further by looking at the time characters spent with guests to analyze the number of autographs that the characters signed from 0 to 2 or more and how this affected the time they spent with each guest. Our second half of our project looks at the number of people a character can visit within 30 minutes. We recorded the party sizes seen by each of the 12 characters to find how many people each character could see a 30 minute time span. We are looking to determine whether the number that a Disney cast member gave us, which was 80 people in 30 minutes, could be correct.

We finally got a good group picture with Mickey!

Illuminated for the Last Time
For the last time, our group went to Epcot to enjoy a delicious dinner and fireworks. When we arrived at the park, some of us went souvenir shopping and exploring at our favorite pavilions, while others took the opportunity to journey to Mars one last time. We had a great dinner at Nine Dragons. Right after dinner, we caught our last viewing of Illuminations, the Epcot firework and light show. It was just as dazzling as it was the first time, and we left the park with nothing but great pictures and memories!

Written by:

Caroline

Courtney

Day 15: Spy Kids

Hi everyone! It’s Lindsay and McKenna with your day 15 blog post. It’s hard to believe that we only have a week left! 

Morning of Math

We started off this morning with another class in Dr. Hutson and Dr. Harris’s hotel room. The morning’s subject was hypothesis testing. This is something all of us do every day, although we may not be aware of it or be making any explicit calculations. Dr. Harris introduced the concept by playing a game with cards. Zack picked 10 cards from a deck, one at a time, to see how many red cards he would draw. We were all surprised when the first four cards he drew were red, and by the 6^th or 7^th red card we were all very suspicious. After Zack had drawn his tenth red card in a row, Dr. Harris revealed to us that all of the cards in the deck except for one were red.

Our suspicion of Dr. Harris’s deck is an example of using hypothesis testing. We started off with the assumption that half the cards in the deck were red and half were black. If this assumption were true, the likelihood of Zack drawing all red cards would have been extremely low (a 1 in 1024 chance). Statistical testing follows a similar method. We first start off with a “null hypothesis.” In the example from this morning, the null hypothesis was that the deck contained half red cards and half black cards. If the analysis makes it very unlikely that the null hypothesis is true, we reject the null hypothesis.

Lunch with Lara Larberg

After class, we headed to Pammie’s Sammies for lunch and a meeting with Furman alumna, Lara Larberg. Lara works for Universal Studios, and while the May X is called “Math and the Mouse,” we thought it would be really cool to sneak over to the “other side” to see how she uses math in her job at Universal. Lara is the Assistant Project Manager for Universal, so basically she manages over twenty interactive effects. Her most recent project is Volcano Bay, which will be opening in 2017 in Orlando. Lara graduated summa cum laude from Furman in 2006 with degrees in music and sociology. She also had a non-degreed focus and passion for theatre. It was actually her involvement with the Pauper Players that she credits for propelling her into her career.  Lara couldn’t stress enough how important her Furman education was for getting her to where she is today. She noted that although it may not seem like she is using her two degrees specifically, she is using all of the skills and connections she acquired at Furman. Furthermore, she was also quick to point out that even though she started working more with the creative side of things, she now works very closely with industrial engineers. Her work combines art and math to produce an awesome interactive experience.

Projects at the Park

After our meeting, we headed to Magic Kingdom to do a bit of spying, otherwise known as more data collection. As yesterday’s blog post mentioned, we all spent some time making observations about several characters. Today, we were able to split off into our groups to focus on our particular topics.

My (Lindsay), Mary Lib, Molly, and Maria’s group is comparing FastPass+ lines to the regular standby lines. We want to determine whether getting a FastPass actually saves you a significant amount of time. To do this, we are collecting data from the three Mountains in Magic Kingdom—Big Thunder Mountain, Splash Mountain, and Space Mountain. Since we won’t be going back to Magic Kingdom again until Tuesday (our last day!) today was our only chance to collect data. Luckily, the other groups were very supportive and helped us collected data. We collected many types of data, but my personal favorite was counting the number of people entering and exiting the line. I’m sure we all looked very suspicious sitting by ride entrances and exits counting people walking by and scribbling in notepads.

Like Johanna yesterday, I (McKenna) am in “the character group.” While the data we were gathering was the same as yesterday (number of families in line, number who entered and exited, time spent by the character with each family, and number of autographs per family), the characters were not. Today, we had the opportunity to observe Peter Pan and Aurora.

Magical Memories

After we finished meeting those characters, we took a detour to see Winnie the Pooh and Tigger, for my own personal benefit. When I was just over a year old, I went to Disney World for the first time. I had already developed an affinity for Tigger, so when I saw the long line in front of me, I just couldn’t handle it. I had to see Tigger IMMEDIATELY. I ran away from my parents, skipped all of the other people in line, and attached myself to Tigger’s leg. Since then, Tigger has remained one of my favorite characters, and I have gotten a picture with him every time. This time, I was able to tell Tigger the story of my toddler mischief, and he decided that it was his turn to attach himself to me and not let go! Mary Lib also recreated some childhood memories today. Not only did she ride Barnstormer again, but she also wore the same exact shirt that she wore while riding Barnstormer—twelve years later!

Fireworks Finale

By ten o’clock we were all finishing up with data collection and were able to catch Magic Kingdom’s end of the night fireworks show, “Wishes.” The fireworks at Disney are spectacular, probably some of the best in the world. Though we had all seen the fireworks show multiple times from the Big Thunder Mountain Railroad roller coaster, for many in the group (including the two of us) this was our first time watching the show from Main Street. The night ended with a special treat: a projection show on Cinderella’s Castle. Clips from Disney films, including classics like the Lion King and newer films like Frozen, were projected onto the castle, accompanied by music and fireworks. It was the perfect ending to another great day of math and magic.

Written by: Lindsay Eddy and McKenna Luzynski

Time Flies When You're Having Fun... With Math!

Hello! It’s Johanna and Alex here. We can’t believe that we only have nine days left in our Math and the Mouse adventure and can't wait to share another day's worth.

Mind your P's and "Queues"

Johanna's group presenting their winning strategy

We were given a late start to the day, and while some of us used it to catch up on sleep, others used it to put the last touches on our second project. We started our day out by giving presentations of our genetic algorithm projects. My group (Johanna) had the shortest optimal path, making it around ten of Magic Kingdom’s biggest attractions in just 284 minutes. All the groups had fun coming up with different algorithms to try to figure out the best path. It was interesting to see that all three groups had some close similarities and big differences in their approaches. After our presentations, we learned about queuing theory, which is the mathematics behind lines at places as fantastic as Disney and as ordinary as grocery stores. Because there are so many opportunities to wait in line at Disney, it is directly applicable to what we have witnessed in the parks. Queuing theory basically uses throughput, total number of people in the line at the start of the period, and the probability of a person entering or exiting the line in that period to calculate the wait time. 

At the end of class, we all discussed our initial data collection from the parks yesterday. From this we brainstormed ideas for final projects. In the end, we split into three groups, each group focusing on a project idea of their choice. In some way or another, all of us are using queuing theory as part of our projects. Both of us are in the same group, and we are studying the wait lines for various Disney characters throughout the parks. We found interest in this project after noticing the high demand for some characters and how families (including ourselves) were turned away after a certain point. Other groups are studying single rider lines or how efficient the FastPass line is compared to the standby line. These projects are still in the works, so tune in later for more details!

Hollywood Studios

We took time from collecting data to take one goofy picture

In the afternoon, the group headed to Hollywood Studios for more data collection and a little free time. At the beginning, many of us split up in the single rider line at Rock 'n' Roller Coaster to collect data. Some data we wrote down in line were the actual wait time in the single rider line (from start to finish) and the party numbers going on to the ride. While many of us got great data (some of us went through multiple times), the group didn't let our FastPasses go to waste! Today we used FastPasses for Rock 'n' Roller Coaster, Tower of Terror, and Star Tours, all of the group's favorites. 

I (Johanna) along with three others in our group had a very eclectic afternoon. After riding Rock 'n' Roller Coaster, we collected queuing data on Sophia the First and Jake the Neverland Pirate in the Disney Junior section of Hollywood Studios. We spent a relaxing afternoon wandering around the park, going through all the gift shops to find souvenirs for our families. We also rode Toy Story Mania and saw The Voyage of the Little Mermaid, where I discovered that Ursula is just as terrifying now as she was when I was little. 

Some of the best ice cream sandwiches around!

Show ready with the Mickey hat atop my head

I (Alex) and a few others had an afternoon full of Disney Princesses! After collecting data and riding some of the thrill rides, we saw Beauty and the Beast Live, Frozen Sing-a-Long, and The Voyage of the Little Mermaid. It's not surprising that we were all singing classic Disney songs for the rest of the night. To top it off a few of us even treated ourselves to ice cream sandwiches which were bigger than our hands! We've made a goal to try and finish an entire one by the end of this trip (probably a lot easier said then done). I also used some of the afternoon to practice for my Fantasmic audition for Mickey Mouse, which has now become my career goal ever since seeing the show!

Look who spotted Chewbacca!

The Star Wars fanatics in the group used time after collecting data to explore the new Star Wars area and even get a photo with Chewbacca. We stayed in the park until closing and ended the day with watching the Star Wars themed fireworks show. Even after watching it again, the fireworks never cease to amaze us!

Big News for Dr. Bouzarth!

Congratulations to Dr. Bouzarth who received tenure today! In honor of her huge accomplishment, the group gave her a personalized movie clapperboard from Hollywood Studios so that she could remember the day. We all signed it at the park and presented it to her at the end of the evening. We are all so lucky to have amazing professors leading this experience and giving us memories of a lifetime.

Written By:

Alex Doxey

Johanna Swab