A program was developed using a genetic algorithm and automated lookup features to design an efficient passenger rail system for the eastern-half of the United States connecting large cities, metropolitan populations greater than two million, with overnight rail service. The results of the program predicted a passenger starting at the farthest point of the system boards the train at 16:02 on average and arrives at a different point of the system at 07:57 on average the following day, assuming the train travels an average speed of 70 mph. The design used actual distances by train track where possible. The system was modeled with six trains that meet at a hub and exchange passengers and continue on to their destination. The optimal solution had a total one-way minimum distance of 4334 km (2693 miles). Assuming the same ridership that currently exists on a popular train route, ticket prices would average $62 (USD) for a one-way ticket. For this system to be feasible, the government would need to own or lease one set of tracks for all the routes determined, build a hub for passengers to transfer trains near Charleston, WV, and ensure the trains are unimpeded by other trains. Installing tracks that go around cities that the trains do not stop at would be a great benefit also. With advances in communication, GPS, and train control technology, this article points out the benefits of publically available tracks to form a transportation network similar to that found in road, air, and water traffic.
This article explores the possibility of overnight train travel between major cities east of the Mississippi River in the USA. Overnight train travel is common between major European cities and some distances between major cities in the Eastern-half of the United States are similar to those between European cities. However, the time needed in the Eastern United States is long, for example, traveling from St. Louis to New York takes more than 33 hours. Traveling from Memphis to Washington DC takes more than 37 hours. Traveling from Detroit to Philadelphia has a driving distance of 940 km (584 miles) and a driving time of 8.5 hours which requires nearly 38 hours by train. Purchasing a ticket on a rail or an airplane 25 days ahead of travel results in the same price between St. Louis and New York for both forms of transportation. Airfare is 35% less than rail travel using a major airline carrier that allows a carry-on and two checked bags traveling between Memphis and Washington, DC. Airfare is 25% cheaper between Detroit and Philadelphia using the same major airline carrier.
Since the solution to the problem is challenging, possible solutions were determined using genetic algorithms, which are uniquely suited to solve difficult optimization problems. In addition, train transportation is the most cost-effective method of transporting passengers anywhere and freight overland.
Energy used to transport cargo per ton-mile has been reported [
Energy use for cargo and passengers.
Transportation type | Energy efficiency for cargo BTU/(ton-mile) | Energy efficiency for passengers BTU/(passenger-mile) |
---|---|---|
Train | 500 | 2,650 |
Ship (Barge) | 500 | N/A |
Automobile | N/A | 3,512 |
Bus | N/A | 4,235 |
Truck | 2,000 | N/A |
Aircraft | 63,000 | 3,261 |
For a successful efficient passenger rail system to be designed and ultimately constructed, some assumptions were needed in the design process. First, the US government would need to own one set of tracks for the routes shown and control train traffic on those tracks. This is similar to what the government does for road, air, and water travel. Another option would be that the government make a financial lease agreement with the private owners of the tracks to allow the passenger trains to travel uninterrupted along their route. Second, a train hub near Charleston, WV, would need to be built to accommodate six trains arriving at nearly the same time and exchanging passengers.
Genetic algorithms have been used to determine solutions for complex problems. Genetic algorithms work by proposing a solution, many times randomly generated, to a problem through a group of possible solutions. The possible solutions are evaluated based on their value of an objective function, typically something that is desired to be maximized or minimized. The candidate solutions with the best objective functions are recombined, and possibly randomly mutated, to form a new generation of solutions. The new generation of candidate solutions are then used in the next iteration. This process continues until a stopping criteria is met, which is usually based on a maximum number of iterations performed, or no change for a certain number of iterations. The solution found is not necessarily the best or global optimum; other solutions may exist depending on the initial conditions of the candidate solutions of the genetic algorithm.
Lesiak and Bojarczak [
Ngamchai and Lovell [
Chung et al. [
Zhou et al. 2017 [
Gholami and Sotskov [
Li et al. (2013) [
Wang et al. (2019) [
Xu et al. (2015) [
Khaled et al. (2015) [
Xu et al. [
Major cities were chosen in the eastern-half of the US that had a metropolitan population of 2 million or more people. Cities more north than New York City, Detroit, and Chicago were not chosen because the objective was overnight travel arriving around 08:00 the next morning and cities too far away would not meet the objective. By the same reasoning, cities more south than Atlanta, GA, and cities west of the Mississippi River were not chosen. One exception is that St. Louis, MO, was selected as it is just west of the Mississippi River but essentially lies on the Mississippi River.
A central hub was chosen that was approximately the average latitude and longitude of each city being equally weighted. The average latitude and longitude of each city were approximately at Charleston, WV; hence, that city was chosen as the hub. It is anticipated that the trains meet at 30 minutes past midnight at the hub and passengers can change trains if needed or remain on the train if that train is going to their destination. The best solution would be for each train to continue through the hub to a final destination opposite from the hub from where it came, allowing some passengers to remain on their original train. The train would then return to their origin city during the overnight trip that begins the following day.
In the algorithm that determined the optimum routing of trains, distances between the current train stations of the selected cities were calculated using the Distance Matrix API and requesting the distance using passenger train travel, with appropriate starting times, and also driving distance [
The number of trains was chosen to allow passengers to travel to their destination by about 08:30 the following morning. Too few trains would lead to too long travel times and not reaching their destination the following morning. Too many trains are an added expense to the system. The model was run with 4, 5, 6, and 7 trains and it was determined that 6 trains were acceptable for passengers to arrive the next morning.
The solution will be shown graphically and lists acronyms of each city. Table
List of Cities used in the study.
City Acronym | Full Name of City |
---|---|
DET | Detroit, MI |
CLE | Cleveland, OH |
PIT | Pittsburgh, PA |
NYC | New York City, NY |
PHL | Philadelphia, PA |
DC | Washington, DC |
CHAR | Charlotte, NC |
ATL | Atlanta, GA |
MEM | Memphis, TN |
NASH | Nashville, TN |
STL | St. Louis, MO |
LOU | Louisville, KY |
CHI | Chicago, IL |
INDY | Indianapolis, IN |
CIN | Cincinnati, OH |
The model used was a multiple traveling salesperson genetic algorithm with a fixed starting point and open ending point [
Solution of mass transit system (total distance = 2692.9 mi (4333.8 km); iteration = 770).
Solution of mass transit system showing mode of transportation: red = train; blue = car.
Genetic algorithms many times start with a random solution set which is improved through iterations; this means that there could be more than one solution and that each solution is a local optimum. There were two other solutions that sometimes occurred, shown in the appendix. These other solutions had longer total distances and had one train traveling a much farther distance, which does not lead to all trains meeting at a hub simultaneously and also does not lead to passengers arriving at the destination by 08:30 the following day.
Table
Distance of routes and departure and arrival times of the mass transit system.
Routes | Total Distance (mi) | Total Distance (km) | Leave Furthest Point (local time) | Arrive Furthest Point the Following Day (local time) |
---|---|---|---|---|
NYC-PHL-DC-HUB | 615 | 990 | 15:42 | 9:18 |
DET-CLE-PIT-HUB | 540 | 870 | 16:47 | 8:13 |
CHI-INDY-CIN-HUB | 542 | 872 | 15:46 | 7:14 |
STL-LOU-HUB | 512 | 824 | 16:11 | 6:49 |
MEM-NASH-HUB | 607 | 976 | 14:50 | 8:10 |
ATL-CHAR-HUB | 528 | 850 | 16:57 | 8:03 |
Local departure and arrival times of each city in the mass transit system.
NYC | 15:42 | STL | 16:11 |
PHL | 17:01 | LOU | 20:56 |
DC | 18:57 | HUB | 0:30 |
HUB | 0:30 | LOU | 4:04 |
DC | 6:03 | STL | 6:49 |
PHL | 7:59 | ||
NYC | 9:18 | ||
|
|||
DET | 16:47 | MEM | 14:50 |
CLE | 19:17 | NASH | 17:54 |
PIT | 21:12 | HUB | 0:30 |
HUB | 0:30 | NASH | 5:06 |
PIT | 3:48 | MEM | 8:10 |
CLE | 5:43 | ||
DET | 8:13 | ||
|
|||
CHI | 15:46 | ATL | 16:57 |
INDY | 19:38 | CHAR | 20:42 |
CIN | 21:26 | HUB | 0:30 |
HUB | 0:30 | CHAR | 4:18 |
CIN | 3:34 | ATL | 8:03 |
INDY | 5:22 | ||
CHI | 7:14 |
Table
Expected ticket prices to ride the mass transit system based on total ridership.
Number of riders per train | Ticket price |
---|---|
1200 | $ 46.45 |
1100 | $ 50.67 |
1000 | $ 55.74 |
900 | $ 61.93 |
800 | $ 69.67 |
700 | $ 79.62 |
600 | $ 92.89 |
It appears that overnight train travel is currently feasible between major US cities east of the Mississippi River given that the infrastructure is provided as stated in the Assumptions. The results also show that the new system is time-effective due to stopping only at major cities, traveling through the night, and passengers would depart the train downtown likely close where they wish to be for the day. The new system is also cost-effective as this method would be considerably less than air travel. One way to improve transit time would be to build tracks to bypass cities where the train does not stop. Trains must slow down through cities even if they are not stopping and it is more time-effective if they could bypass these cities without significantly slowing down. Another way to improve transit time is to convert certain tracks to high-speed travel, particularly tracks that are currently relatively straight and flat, as this is the most cost-effective. Extremely fast high-speed rail is not needed since the trains are traveling overnight; speeds could remain less than 100 mph, but sections of the track that are easy to allow higher speeds would especially help the routes that need to travel the furthest to reach the hub such as the trains leaving NYC and MEM.
If an entire transit route is too much to implement at one time, a beginning point could be starting the most popular route, likely based on the cities with the greatest population, and then expanding the system when that route becomes popular. As the system becomes more popular, an outer loop could be constructed that allows trains to travel around an outer loop of cities overnight. Passengers on these trains would not connect with other trains. Possible cities well suited for overnight travel around an outer loop would be NYC – PHL – DC – CHAR – ATL; NYC – CLE – CHI; and CHI – STL – MEM – ATL.
One downside of this travel system that might be mentioned is that the travel system only assists passengers living in large cities. However, if the system becomes successful, transportation would likely become available from small cities, or groups of small cities, to a large city arriving there shortly before the train arrives. Then, the passengers living in small cities could access this network. The current setup of train transportation that stops in many small cities does not greatly benefit the potential passengers of the small cities, because the train takes so long to reach the final destination that many potential passengers drive their own vehicle to their destination or to a major city and fly to their destination.
See Tables
The geographic coordinates used for the train stations are as follows.
Cities and Locations | Latitude | Longitude | Address | |
---|---|---|---|---|
Hub | Hub | 38.346 | -81.638 | 350 MacCorkle Avenue SE, S Side Bridge, Charleston, WV 25314 |
1 | CHI | 41.879 | -87.640 | 225 S Canal St, Chicago, IL 60606 |
2 | CIN | 39.109 | -84.535 | Cincinnati Museum Center, 1301 Western Ave, Cincinnati, OH 45203 |
3 | NYC | 40.753 | -73.977 | 42nd St, New York, NY 10017 |
4 | ATL | 33.760 | -84.386 | 1688 Peachtree St NW, Atlanta, GA 30309 |
5 | STL | 38.624 | -90.204 | 430 S 15th St, St. Louis, MO 63103 |
6 | CLE | 41.506 | -81.697 | 200 Cleveland Memorial Shoreway, Cleveland, OH 44114 |
7 | PIT | 40.445 | -79.992 | 1100 Liberty Ave, Pittsburgh, PA 15222 |
8 | MEM | 35.132 | -90.059 | 545 S Main St, Memphis, TN 38103 |
9 | NASH | 36.158 | -86.785 | 1001 Broadway, Nashville, Tennessee |
10 | CHAR | 35.241 | -80.823 | 1914 N Tryon St, Charlotte, NC 28206 |
11 | DC | 38.897 | -77.006 | 50 Massachusetts Ave NE, Washington, DC 20002 |
12 | PHL | 39.956 | -75.182 | 2955 Market St, Philadelphia, PA 19104 |
13 | LOU | 38.246 | -85.769 | 1000 West Broadway, Louisville, KY, 40203 |
14 | INDY | 39.7926 | -86.1578 | 350 South Illinois Street, Indianapolis, IN 46225 |
15 | DET | 42.368 | -83.0723 | 11 W Baltimore Ave, Detroit, MI 48202 |
Distances (miles) determined between cities. Distances by current passenger train were used if that distance was less than 1.2 times the driving distance; if it was more then the driving distance was used as the distance between those cities.
Hub | CHI | CIN | NYC | ATL | STL | CLE | PIT | MEM | NASH | CHAR | DC | PHL | LOU | INDY | DET | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Hub | 0 | 535 | 215 | 615 | 501 | 510 | 259 | 232 | 604 | 392 | 265 | 388 | 523 | 250 | 341 | 372 |
CHI | 535 | 0 | 321 | 797 | 722 | 283 | 342 | 475 | 532 | 477 | 763 | 738 | 763 | 302 | 200 | 277 |
CIN | 215 | 321 | 0 | 647 | 463 | 351 | 256 | 292 | 487 | 276 | 483 | 603 | 577 | 101 | 127 | 265 |
NYC | 615 | 797 | 647 | 0 | 868 | 960 | 471 | 440 | 1107 | 893 | 708 | 227 | 92 | 746 | 716 | 622 |
ATL | 503 | 719 | 463 | 867 | 0 | 557 | 716 | 687 | 395 | 249 | 262 | 640 | 775 | 423 | 538 | 727 |
STL | 511 | 283 | 353 | 963 | 558 | 0 | 624 | 608 | 286 | 313 | 722 | 829 | 892 | 264 | 250 | 560 |
CLE | 257 | 341 | 255 | 470 | 715 | 625 | 0 | 134 | 874 | 528 | 520 | 397 | 483 | 353 | 319 | 174 |
PIT | 231 | 475 | 293 | 440 | 687 | 606 | 134 | 0 | 778 | 566 | 451 | 263 | 349 | 391 | 361 | 289 |
MEM | 603 | 532 | 486 | 1107 | 386 | 285 | 872 | 775 | 0 | 215 | 631 | 887 | 1019 | 388 | 470 | 809 |
NASH | 392 | 473 | 275 | 893 | 248 | 311 | 527 | 564 | 215 | 0 | 412 | 673 | 805 | 177 | 292 | 539 |
CHAR | 267 | 760 | 467 | 605 | 262 | 719 | 521 | 450 | 639 | 411 | 0 | 378 | 513 | 478 | 579 | 634 |
DC | 388 | 738 | 603 | 227 | 641 | 826 | 397 | 263 | 887 | 672 | 400 | 0 | 135 | 614 | 582 | 531 |
PHL | 523 | 763 | 577 | 92 | 776 | 890 | 483 | 349 | 1019 | 805 | 513 | 135 | 0 | 676 | 646 | 588 |
LOU | 249 | 299 | 102 | 746 | 421 | 262 | 354 | 391 | 388 | 176 | 478 | 615 | 675 | 0 | 118 | 366 |
INDY | 341 | 200 | 127 | 718 | 538 | 249 | 322 | 363 | 472 | 293 | 580 | 584 | 647 | 119 | 0 | 284 |
DET | 367 | 277 | 265 | 622 | 727 | 560 | 175 | 289 | 809 | 540 | 635 | 533 | 588 | 365 | 284 | 0 |
Mode of transportation used. T = True indicating that distance was calculated using current passenger train travel between cities; F = False indicating driving distance was used.
HUB | CHI | CIN | NYC | ATL | STL | CLE | PIT | MEM | NASH | CHAR | DC | PHL | LOU | INDY | DET | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
HUB | T | T | T | F | F | F | F | F | F | F | T | T | F | T | F | |
CHI | T | T | F | F | T | T | T | T | F | F | T | F | F | T | T | |
CIN | T | T | F | F | F | F | F | F | F | F | T | F | F | T | F | |
NYC | T | F | F | T | F | F | T | F | F | T | T | T | F | F | F | |
ATL | F | F | F | T | F | F | F | F | F | T | T | T | F | F | F | |
STL | F | T | F | F | F | T | F | F | F | F | F | F | F | F | T | |
CLE | F | T | F | F | F | T | T | T | F | F | T | T | F | F | F | |
PIT | F | T | F | T | F | F | T | F | F | F | T | T | F | F | F | |
MEM | F | T | F | F | F | F | T | F | F | F | F | F | F | F | T | |
NASH | F | F | F | F | F | F | F | F | F | F | F | F | F | F | F | |
CHAR | F | F | F | T | T | F | F | F | F | F | T | T | F | F | F | |
DC | T | T | T | T | T | F | T | T | F | F | F | T | F | F | F | |
PHL | T | F | F | T | T | F | T | T | F | F | T | T | F | F | F | |
LOU | F | F | F | F | F | F | F | F | F | F | F | F | F | F | F | |
INDY | T | T | T | F | F | F | F | F | F | F | F | F | F | F | F | |
DET | F | T | F | F | F | T | F | F | T | F | F | F | F | F | F |
The entire transit network analyzed: blue = train travel exists with a distance of 1.2 times or less of driving distance; red = driving distances used.
Solution 2: total distance = 2721.7563, iteration = 923; this solution was not selected due to the long distance of the train traveling the pink line shown.
Solution 2 of mass transit system showing mode of transportation: red = train; blue = car.
Solution 3: total distance = 2809.9095, iteration = 907; this solution was not selected due to the long distance of the train traveling the black line shown.
Solution 3 of mass transit system showing mode of transportation: red = train; blue = car.
The data used to support the findings of this study are included within the article.
The authors declare that there are no conflicts of interest regarding the publication of this paper.