[Lowerbounds, Upperbounds]

Algorithms are everywhere.

I don’t know how, but my 15-year-old HP 20S calculator just “died” a week ago. As I am looking for a replacement, I learned that the legendary keyboard on HP calculators is now history, at least in the scientific series. Sigh…

When I was a high school student in Hong Kong, I had a couple Casio, a Sharp and I finally landed on the HP 20S because of its tactile feedback keyboard. In an exam, having tactile feedback takes away the “did I push that key hard enough?” guessing. I guess someone may say that 20S is not RPN and so it is not cool. But then Hong Kong has its own list of approved calculators and the 20S is the already most advanced HP calculator on the list. Basically we disallow any calculator that can graph or store alphabets.

And now I know why the other companies don’t have a similar keyboard. As Google just told me, HP holds a patent on it.

No wonder a used HP 32SII can sell for \$229.

Update: I must add that the HP 33S (the 32SII replacement) does have tactile feedback, but according to reviews, it is not reliable.

In the past, the ics file exported by WP-iCal would sometimes crash Rainlendar. Well, I just found out that the latest version of Rainlendar 0.22.1 seems to have fixed this problem.

The content of the ics file still needs some tweaks, but it’s already quite usable.

https://diamond.aladdin.cs.cmu.edu/dav/calendar/aladdin.ics

Look Before You Book: Computer Science in the Airline Industry

Todd Williamson
Senior Computer Scientist
ITA Software,Inc.

Mauldin Auditorium (NSH 1305)
Refreshments 12:15 pm
Talk 12:30 pm

A provably hard optimization problem involving ambiguous data. Communication with dubious hardware via arcane protocols. Real-time software constraints, with a very low tolerance for processing errors. No, it’s not a new robotics project, it’s the world of airline pricing and distribution. As anyone who does much flying soon learns, the airline industry has (largely unwittingly) made the problem of finding the lowest fare and successfully booking it a daunting problem.

At any moment there are between 2,000 and 10,000 commercial airliners in the sky, part of a dense network that provides, for example, more than 100,000 practical paths from Boston to the San Francisco area every day. At its core, finding a sequence of flights that meets the user’s stated time constraints is a path-planning problem which can be solved with well-known techniques. But the airfare search problem is much more complex than that. In fact, the airlines’ price structure is so rich that finding the cheapest price for a simple round-trip journey is in the general case provably undecidable. Even if one bounds the size of solutions to a small number of flights there may be more than 1020 reasonable answers to a simple travel query. The problem is compounded by the fact that airline revenue management systems are constantly and dynamically adjusting the prices for each flight along a discretized scale.

This talk will introduce the structure of the airline industry, how tickets are priced and sold, and some of the reasoning behind the complexity in airline price structures. Simple combinatorics show that the low fare search problem is in general too large to solve optimally in a reasonable amount of time or space. Once the user chooses a solution to purchase, a robust distributed transaction must be executed, involving the exchange of messages with several airline databases and keeping a synchronized local copy. The talk will outline how we attack these problems with algorithms spanning the fields of graph theory, parsing, databases, optimization, and distributed systems.

Finally, the talk will introduce some recent projects at ITA, both deployed and in development, showing how we’re continuing to tackle challenging problems and revolutionize the travel industry.

Speaker Biography
———————
Todd Williamson is currently a Senior Computer Scientist at ITA Software, Inc., where he works on challenging travel planning problems. He received his Ph.D. in Robotics from CMU in 1998, working on the NAVLAB project. His dissertation was about using real-time stereo vision to detect obstacles on the road. He spent 4 years as the Vice President of R&D for Zaxel Systems, Inc., where he invented and implemented a real-time method for doing “Virtualized Reality”.

Friday, February 10, 2006
1:30 p.m. Posner Hall 151

Anureet Saxena
Ph.D. Student, Tepper School of Business
Carnegie Mellon University

Optimizing Over the Split Closure

The polyhedron defined by all the split cuts obtainable directly (i.e. without iterated cut generation) from the LP-relaxation P of a mixed integer program (MIP) is termed the split closure of the MIP. This paper deals with the problem of optimizing over the split closure. This is accomplished by repeatedly solving the following separation problem: given a fractional point, say x, find a rank-1 split cut violated by x or show that none exists. We show that this separation problem can be formulated as a parametric mixed integer linear program (PMILP) with a single parameter in the objective function and the right hand side. We develop an algorithmic framework to deal with the resulting PMILP by creating and maintaining a dynamically updated grid of parameter values, and use the corresponding mixed integer programs to generate rank 1 split cuts. Our approach was implemented in the COIN-OR framework using the CPLEX 9.0 as the general purpose MIP solver. We report our computational results on well-known benchmark instances from MIPLIB 3.0 and Capacitated Warehouse Location Problems from OR-Lib.

Our computational results show that rank-1 split cuts close more than 98% of the duality gap on 14 out of 33 mixed integer instances from MIPLIB 3.0. More than 75% of the duality gap can be closed on additional 11 instances. Rank-1 split cuts close more than 75% of the duality gap on 13 out of 25 pure integer programming instances from MIPLIB 3.0. On average, rank 1 split cuts close about 71% of the duality gap on these instances. We also report our results on two sets of real-world Capacitated Warehouse Location Problem (CWLP) instances from OR-Lib. The first set has 37 instances, each one having 50 customers and 16-50 warehouses. The second set has 12 instances with 1000 customers and 100 warehouses. The split closure closes 100% of the duality gap on all the 37 instances from the first set, and on average about 93% of the duality gap on the 12 instances from the second set.

We also gathered statistics on the support size of the disjunctions generated (which affects the density of the resulting cut) and the average size (absolute value) of their coefficients. They turn out to be surprisingly small.

This is a joint work with Egon Balas.