A significant development for users Linear optimisation has now been added to planner toolset! This comes in addition to the existing non-linear solver Those familiar with the FPL problem in linear optimisation might notice that this Javascript implementation might well be surprisingly fast

There a couple of new settings related to this new tool Individual autosub weights are given to you sub keeper, first, second and third outfield subs and your sub vice captain. In the non-linear solver these are calculated dynamically. By default solves are let run for up to 300s if needed. If you wish this can be reduced to 60s, which basically means the solver will return it's best found solution at that point in time. Those kinds of time periods would be for particularly challenging solves The defaults are only to be changed if necessary and will eventually make their way into the user settings page

So what exactly is the difference between the existing non-linear solver & the new linear optimiser? Generally both will provide similar outputs and often even the same, but differences can crop up. Non-Linear Solver: + Uses the fuller non-linear formula to evaluate selections (dynamic autosub calculation, eg. understanding same team GKs/binary availability) + Can output a wide range of the strongest moves it has encountered - Cannot guarantee "non-linear optimal", though it may or may not be found. The output is best found moves Linear Optimisation + Can guarantee "linear optimal" + Functions extremely well with planned future transfer etc. and easy to add future constraints - Uses the reduced linear formula to evaluate selections, hence can also not guarantee "non-linear optimal" You will see for example when you "Select" a linear optimised plan the evaluation on the main planner page will differ from the evaluation output of the solver. This is the translation from linear to non-linear

Having both tools available provides the strengths of each approach and ability to help cover the others short comings. In fact there may be future value in merging both approaches to run together In terms of which is better, there is no simple answer- at times it could be either one. In specific certain convoluted scenarios it's possible for either to run into an issue

With any conversation on mixed integer linear programming, @sertalpbilal and also @FF_Trout have to be mentioned! They have both demonstrated to the community that linear optimisation based multi-period planning is extremely powerful with their Python based developments & experimentation and are deserving of enormous credit That move to multi-period planning was one of the major advances in FPL analytics to date

Also key character in the earlier days of linear optimisation is @wiscostretford. Who had built an R-based linear optimisation tool for FPL more than 5 years ago Originally I had even hoped to use an approach like this, but ended up moving with the non-linear solver which in itself has been a beast of a challenge

The past month has been a little bit manic trying to get this across the line, and there are a number of additions I plan to make to the tool over time, but it would have been a shame not to give users time to use it for GW1 There still is some simple core work remaining too, eg. handling of selling players who have benefited price changes- but that will be quickly added in the days following GW1 as a priority Anyway, I hope this ends up proving valuable! I will be focusing on xMins and otherwise relaxing for the weekend now😅

Also special thanks to Analytics Discord, who have confirmed the world is not quite ready for MILP😂

Incredible 🐐

Can Hyperparameter Tuning deliver superior returns in trading? In this free Substack post I explore several models that are tuned to beat the buy-and-hold approach for Gold futures.

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Drafts using MILP optimiser are not getting saved despite tryimg multiple times.

I'll check this a bit later👍