[cchianel]

Some additional optimization resources (for metaheuristics, where you only have the objective/score function and no derivative):

- "Essentials of Metaheuristics" by Sean Luke https://cs.gmu.edu/~sean/book/metaheuristics/

- "Clever Algorithms" by Jason Brownlee https://cleveralgorithms.com/

Timefold uses the metaheuristic algorithms in these books (Tabu Search, Late Acceptance, Simulated Annealing, etc.) to find near-optimal solutions quickly from a score function (typically defined in a Java stream-like/SQL-like syntax so score calculation can be done incrementally to improve score calculation speed).

You can see simplified diagrams of these algorithms in action in Timefold's docs: https://docs.timefold.ai/timefold-solver/latest/optimization....

Disclosure: I work for Timefold.

[abhgh]

Timefold looks very interesting. This might be irrelevant but have you looked at stuff like InfoBax [1]?

[1] https://willieneis.github.io/bax-website/

[cchianel]

I haven't; from a quick reading, InfoBax is for when you have an expensive function and want to do limited evaluations. Timefold works with cheap functions and does many evaluations. Timefold does this via Constraint Streams, so a function like:

    var score = 0;
    for (var shiftA : solution.getShifts()) {
        for (var shiftB : solution.getShifts()) {
            if (shiftA != shiftB && shiftA.getEmployee() == shiftB.getEmployee() && shiftA.overlaps(shiftB)) {
                score -= 1;
            }
        }
    }
    return score

usually takes shift * shift evaluations of overlaps, we only check the shifts affected by the change (changing it from O(N^2) to O(1) usually).

That being said, it might be useful for a move selector. I need to give it a more in depth reading.

[abhgh]

Thanks for the example. Yes, true, this is for expensive functions - to be precise functions that depend on data that is hard to gather, so you interleave the process of computing the value of the function with gathering strategically just as much data as is needed to compute the function value. The video on their page [1] is quite illustrative: calculate shortest path on a graph where the edge weights are expensive to obtain. Note how the edge weights they end up obtaining forms a narrow band around the shortest path they find.

[1] https://willieneis.github.io/bax-website/