Using math to speed up school buses

June 8, 2011 By Nicolas Guérin
Credit: Carmine Savarese

( -- Optimizing school bus routes is a lot more complicated than one might think. The International School of Geneva handed their problem over to a group of EPFL mathematicians.

“Our student population is increasing rapidly,” observes Michel Chinal, Director General of the International School of Geneva. And the rising number of parents picking up and dropping off their children is creating traffic problems in the village of Founex, just outside Geneva. The bus service offered by the school is too slow. “Parents often say that they would like to sign their children up, but the bus ride is too long.” The buses pick up students in an area bounded by Morges, Geneva and neighboring France. So how can they improve the routes of 11 different buses carrying a total of 283 students to and from school? That’s the problem that was given to the in EPFL’s Discrete Optimization Group.

EPFL chemist Rainer Beck, whose child attends the school, offered to optimize the service during a meeting of the parent’s association. He asked his mathematical colleague Friedrich Eisenbrand to tackle the problem. “Coming up with a simple arithmetic algorithm is not difficult. But that’s not an efficient approach -- due to the enormous number of possible itineraries, the calculations are painfully slow. We needed to develop an algorithm that quickly rejected most routes, so that the computation could be completed before the end of the Universe,” explains Eisenbrand. With the assistance of his PhD student Adrian Bock, the mathematician came up with a solution for this complex problem. Using a few clever techniques, the calculations only take half a day to complete.

The researchers modeled student and parent satisfaction using specific parameters, such as “regret” (also called “opportunity loss”), a term used in decision theory. For this case, the regret was the difference between the ideal direct route – in a car – and the route taken by the bus. This parameter enabled the mathematicians to determine the threshold that would convince more students to take the bus. Once the calculations were finished, the gain was impressive: the largest discrepancies between the bus and car routes were cut by 25%.

Optimization is a technique that can be taken well beyond the problem of ferrying kids back and forth from school. The mathematicians are collaborating not only with world leaders in the telecommunications and airline industries to improve communications devices, but also with insurance companies to streamline their lengthy computations. Thus, in everyday life, as soon as we tap into a network, such as the Internet, we are benefiting from all the optimization work that is hidden behind it.

In addition to its evident economic advantages, this research can also help meet objectives for reducing environmental impact. “Our school is seriously concerned with pollution, and we are trying to find responsible solutions,” adds Chinal.

Explore further: Computer scientists make progress on math puzzle

More information: Decision theory:

Related Stories

Computer scientists make progress on math puzzle

October 28, 2010

( -- Two UT Dallas computer scientists have made progress on a nearly 4-decade-old mathematical puzzle, producing a proof that renowned Stanford computer scientist Don Knuth called "amazing" in his communication ...

Schools lose records; English learners pay

April 11, 2011

( -- Poor recordkeeping keeps California schools from getting all of the funding that they have coming, a failing that especially hurts English learners, according to research from the University of California, ...

When robots learn from our mistakes

May 26, 2011

( -- Robots typically acquire new capacities by imitation. Now, EPFL scientists are doing the inverse -- developing machines that can learn more rapidly and outperform humans by starting from failed or inaccurate ...

The kids are alright

May 26, 2011

Children should be seen and not heard... who says? A Philosophy academic at The University of Nottingham is challenging the adage by teaching primary school children to argue properly.

Recommended for you

From a very old skeleton, new insights on ancient migrations

October 9, 2015

Three years ago, a group of researchers found a cave in Ethiopia with a secret: it held the 4,500-year-old remains of a man, with his head resting on a rock pillow, his hands folded under his face, and stone flake tools surrounding ...

Mexican site yields new details of sacrifice of Spaniards

October 9, 2015

It was one of the worst defeats in one of history's most dramatic conquests: Only a year after Hernan Cortes landed in Mexico, hundreds of people in a Spanish-led convey were captured, sacrificed and apparently eaten.

Ancient genome from Africa sequenced for the first time

October 8, 2015

The first ancient human genome from Africa to be sequenced has revealed that a wave of migration back into Africa from Western Eurasia around 3,000 years ago was up to twice as significant as previously thought, and affected ...

Who you gonna trust? How power affects our faith in others

October 6, 2015

One of the ongoing themes of the current presidential campaign is that Americans are becoming increasingly distrustful of those who walk the corridors of power – Exhibit A being the Republican presidential primary, in which ...

1 comment

Adjust slider to filter visible comments by rank

Display comments: newest first

not rated yet Jun 23, 2011
What method is used here? There was one special problem we had where we find the shortest path for a garbage truck to pass every street in a compound. Well, sort of a graph theory and the Chinese postman Algorithm is what we used. Wonder what algo they have here. Interesting!

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.