Operations Research Blog

The Secretary problem is quite related to marriage... http://en.wikipedia.org/wiki/Secretary_problem Michael Trick, a well known Operations Research professor at CMU, wrote about applying it to his own life http://mat.tepper.cmu.edu/blog/?p=1392 [Edit:] He assumed we wanted to be married to the best possible spouse by the age of 40. The optimal strategy, given his assumptions, is to date until age 26, and then marry the first person who is the best seen so far. You'll marry the best possible person 1/e fraction of the time.

The linked post mentions a previous post [1] where he mentions that proving you have the optimal path doesn't always require N! cost: > If you have an instance of the TSP of practical interest (i.e. it makes a difference to your life if you solve it or not, and it is really a TSP, not the result of some weird set of set of reductions from some other problem), then I bet you the Concorde program of Bill Cook and others will get you a provably optimal solution in a reasonable amount of time. In fact, I would be really interested in knowing the smallest “real” instance that Concorde cannot solve in, say, one day, on a normal laptop computer. Note the "provably" before "optimal solution". 1: http://mat.tepper.cmu.edu/blog/?p=6995

I think this is just one of the pitfalls that the author points out: it is not the sheer number of possibilities that defines the difficulty of a problem. He links to his previous blog post http://mat.tepper.cmu.edu/blog/?p=6995 with a nice example: sorting. “Sorting a bunch of numbers! Hoo-wee, that’s a hard one. If I had 1000 numbers, I would have to check all orderings of the numbers to find the sorted order. That is 1000999998…21 orders and that is more than the hairs on a Hobbit’s toes.”

apropos, http://en.nothingisreal.com/wiki/Why_I_Will_Never_Have_a_Girlfriend and http://mat.tepper.cmu.edu/blog/?p=1392

Most modern solvers like CPLEX and Gurobi have built-in heuristics [1] that are automatically selected and applied without user intervention. They typically exploit the structure of the problem or encode the experiences of the developers over large problem testsets. The default heuristics for commercial solvers are actually pretty darned good these days and there's typically no need to hand-pick them. In the MIP world, they are the secret sauce to fast solution times. Hyperparameter tuning has been studied for MIPs (many papers written on this), but ultimately they are black box solutions. My experience inclines me to not even consider hyperparameters except as a last resort or unless you know something specific that a hyperparameter can exploit; there are other more high leverage things than can be done. Random perturbations to the problem have been found to be much more fruitful for forcing a diversity of branch traversal paths and have lead to significant speedups. (M. Fischetti popularized this idea in 2010s [2]) [1] https://resources.mpi-inf.mpg.de/conferences/adfocs-03/Slides/Rothberg… Also: http://transp-or.epfl.ch/zinal/2017/slides/group5.pdf [2] https://mat.tepper.cmu.edu/blog/index.php/2012/09/25/fischetti-speeds-…

Was his name Michael? http://mat.tepper.cmu.edu/blog/?p=1392