math::probopt(3tcl)

📦

version 2.0 · 2 versions

2.0 · debian trixie, ubuntu questing, ubuntu resolute, ubuntu stonking (latest)
1.21 · debian bookworm, ubuntu noble

, in debian trixie, ubuntu questing, ubuntu resolute, ubuntu stonking

🦋 math::probopt — Probabilistic optimisation methods 🦋

okay so bestie, you've opened the math::probopt(3tcl) page from the Tcl Math Library, and honestly? it's giving "let the algorithm roll some dice until it stumbles onto your optimum". sit down, hydrate, we're doing this 💅

✨ NAME ✨

math::probopt — probabilistic optimisation methods. that's it, that's the name, no cap 🎀

🌸 SYNOPSIS 🌸

package require Tcl 8.6 9

package require TclOO

package require math::probopt 1.1

::math::probopt::pso function bounds args

::math::probopt::sce function bounds args

::math::probopt::diffev function bounds args

::math::probopt::lipoMax function bounds args

::math::probopt::adaLipoMax function bounds args

💖 DESCRIPTION 💖

so the whole point of the math::probopt package is to hand you a bunch of optimisation algorithms that run on probabilistic techniques. and because they're probabilistic, the results can literally be different from one run to the next. it's not a bug, it's the vibe. 😌

these algorithms are all well-known and well described, and the people who love them generally claim they're efficient and reliable. we're just the messenger 🫶

and because most of these algorithms have one or more tunable parameters — or even whole variations on the theme — the interface to each one accepts options so you can set those parameters or pick your variation. these come as key-value pairs, like -iterations 100. iconic format, no notes.

this manual does not offer any recommendations about these algorithms, and it doesn't give you much in the way of guidelines for the parameters either. for that, go read online articles about the algorithm in question. we're not gatekeeping, we're just not qualified to pick favourites 💀

a few notes though, because we do love a note:

with the exception of LIPO, the algorithms can deal with irregular (non-smooth) and even discontinuous functions. slay.
the results depend on the random number seeding, and they're likely not going to be very accurate — especially if the function varies slowly in the vicinity of the optimum. but hey, they do give you a good starting point for a deterministic algorithm, so it's not wasted effort 🌈

the collection consists of these algorithms:

PSO — particle swarm optimisation
SCE — shuffled complexes evolution
DE — differential evolution
LIPO — Lipschitz optimisation

the various procedures all have a uniform interface:

set result [::math::probopt::algorithm function bounds args]

and the arguments mean the following:

the argument function is the name of the procedure that evaluates the function. its interface is:

set value [function coords]

where coords is a list of coordinates at which to evaluate the function. it's supposed to return the function value. that's the whole job 🎀

the argument bounds is a list of pairs of minimum and maximum for each coordinate. this list implicitly determines the dimension of the coordinate space where the optimum is being sought. for instance, for a function like x**2 + (y-1)**4, you might specify the bounds as {{-1 1} {-1 1}} — that's two pairs for the two coordinates. math but make it cute 💅
the rest (args) is zero or more key-value pairs specifying the options. which options each algorithm supports is documented below, keep reading bestie.

the result of the various optimisation procedures is a dictionary containing at least these elements:

optimum-coordinates — a list containing the coordinates of the optimum that was found 👑
optimum-value — the function value at those coordinates
evaluations — the number of function evaluations
best-values — a list of successive best values, obtained as part of the iterations

🔥 DETAILS ON THE ALGORITHMS 🔥

the algorithms in the package are the following:

`::math::probopt::pso` function bounds args

the particle swarm optimisation algorithm runs on the idea that your candidate optimum points should swarm around the best point found so far, with variations to allow for improvements. it's giving "everyone follow the leader, but with ✨spontaneity✨".