At large $T$, the magnitude of the exponent is reduced, thus increasing The magnitude of the negative exponent gets large, and the probability of accepting an increase The trick of simulated annealing is to lower the $T$ slowly. If $f_r$ is too close to identity, you'll explore the space very slowly. The identity function would be terrible, as would any function that can't reach all possible states $S$. I said almost any fashion, because the $f_r$ must satisfy some criteria for the algorithm to work at all. If you repeat this long enough, the collection of $S$ values will satisfy the Boltzmann distribution.
If $E(S') E(S)$, accept $S'$ with probability $e^$. Has some randomness to it) and then use the following criteria to decide whether to accept the transformed state State $S$ in some (almost) arbitrary fashion to $S' = f_r(S)$ (where the $r$ subscript indicates that this transformation The gist (explained in terms of Boltzmann) is that you modify the It is well suited for theīoltzmann distribution, which was its earliest application. Monte Carlo algorithm for generating random states that satisfy a complicated probability distribution. Starting a high $T$ and gradually lowering it, we "anneal" into the lowest possible Temperatures, many different fluctuating states are possible even if their energies are high, while, as $T$ gets small, there is Sliding past the detailed physics for a moment, the basic idea is that, at high However the state and its energy are defined, we assume theīoltzmann distribution for the likelihood of any given state at any a positive contributionįor neighboring spins that are aligned). the direction of magnetic spins in a crystal lattice) and model for the energy of that state (e.g. In simulated annealing, you have some sort of Some of it will be recapitulated inline below. Try implementing this in Clojure, especially because one doesn't (or I didn't)Ĭomplex state as natural candidates for a functional lisp. Specifically, I was thinking of simulated annealing, which I'veĪlways liked because it has a nice analogy in the physical world and which has been getting a lot press recently as aĪpplication of quantum computing. Problem abstracted out into some kind of objective function. I started to wonder whether the problem could be approached as a more more general optimization, with the specifics of the Repeatedly pulls from it the most effective ones, in the sense that they match as many winners as possible, don't matchĪny losers and contribute the least to the total length of the regex when they're all |'d together. Peter's algorithm is best described by him, but, briefly, it creates a pool of regex fragments, like /r.e$ and (So Perot, Nader, Anderson et al don't figure.) Anyway, read his post beforeĬontinuing to read this, if you haven't already. Won, but not such candidates who never won. 
Solution that matches all mainstream presidential candidates who eventually Problem and then building an algorithm to search for the shortest
The hover text on the strip suggests a regex that matches all winning presidents.
Paraphrase the comic strip, is to find a regular expression that matches all members of a group of related terms, but notĪny members of a different group. Like any red-blooded American, I find regex golf fascinating.
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