Skip to recount
In 1960, the famed computer scientist Don Knuth wrote a technical paper by which he regarded as an integer programming mannequin for minimizing memory receive entry to latency of an IBM 650. I’ve integrated a screenshot of the 51 variable, 43 constraint worry at the raze of this put up.
Prof Knuth describes the worry and his makes an are trying to solve it in an unpublished present on his online page. Knuth dilapidated a formulation of Ralph Gomory published the same 365 days, which he somehow changed into responsive to despite the absence of email, the fetch, arxiv, or gargantuan language items. I requested ChatGPT to render an image of Gomory and Knuth pensively sitting atop a mainframe. It refused for privateness reasons. Here is the suitable it can in all probability well well moreover invent:
Knuth ran Gomory’s algorithm on an IBM 650 with lower than 10K of memory, nonetheless changed into once unable to acquire an optimal solution. Thirty-five years later (after I changed into once an undergrad), Dimitris Alevras efficiently found the optimum worth of 22996 using CPLEX on a SPARCstation 5. I’m proud to articulate I even beget coded on this kind of machine! Alveras reported that “32,200 division-and-certain nodes” had been wished to solve the worry to optimality. No CPU time is reported in Knuth’s writeup, nonetheless we are able to safely assume the answer time changed into once minutes or seemingly hours.
I grabbed the worry formulation from Knuth’s writeup and translated it into Python code (copilot changed into once purposeful for this motive). An MPS file with the mannequin could well well moreover simply also be found here.
I found that the initiate source solver SCIP changed into once in a put apart to acquire an optimal solution in two tenths of a 2nd, and that Gurobi changed into once in a put apart to solve it in lower than 0.1s.
That is yet another testament to the amazingly wonderful effectiveness of operations research!
