For a detailed explanation just google TSP or see Wikipeda.
I'll give you the basics. TSP (Traveling Salesman Problem) on which Orion is based originated in the 1800s as Irish mathematician William R. Hamilton considered a way to compute the shortest route a salesman could take upon leaving his hometown, calling on his accounts and returning home.
Later British mathematician Thomas Hinkman's work led to Karl Menger proposing a brute force algorithm (computing every possible route and selecting the one with the shortest distance).
Around 1930 Princeton mathematician Hassler Whitney named this concept TSP.
Considerable contributions in refining algorithms where made by George Dantzig, Selmer Johnson and the renown Delbert Fulkerson at Santa Monica's Rand Corporation in the 1960s.
Until this point advancements in computers and algorithms led to more and more cities or in our case, stops or individual addresses being considered for solution inclusion.
Dr. Arora broke ground when he found or rather envisioned a way to restate the TSP concept as a calculus equation to which the first branch of calculus (the derivative) would be useful.
Upon solving the equation he found that as friend(x) where x=optimal solution, approaches infinity (considering the many variables and with a permissible solution acquisition time of 1 hour) the result was 85%.
This meant that regardless of available computational power or algorithm elegance, the best result that can ever be achieved is 85%.
You should look deeper into this particularly in the field of cognitive research as scientist there have shown repeatedly that humans with no previous training can outperform the best computer and best algorithms, arriving at solutions 92 to 97 percent of optimal within 5 minutes.
The best computers would take a month to match that.
And computers don't provide an 85% result constantly. Remember 85% is the very best you'll ever get. Most times its between 30 to 60% of optimal. Just change 1 thing in a DOL and rerun Orion and see how many different results you get. Then consider the nearly infinite variables a driver takes into account each and every day.
So now, cognitive research is centered on discovering what enables humans to do such a good job with so many variables in such a short amount of time. If an algorithm could be formulated that would be half as good imagine the applications.
The defense industry has.
By the way, Dr. Arora's work has been authenticated by the mathematical and computer community. Hence the Godel Prize in 2008.
A bit long winded, I know. But check his research and you'll see that Orion is nothing but a blind alley.