Easier way to mass produce schedules with varying spacing/facings weighting (particularly when concerns are raised)

[samjmartin04]

Whilst the 0.5-0.5 balanced schedules are usually okay, sometimes mild concerns are raised and these may want to be improved by adjusting the weightings slightly. It would be good if you could automatically create many schedules in bulk with slightly varying spacing/facings weighting to quickly review later for the "best" one. These varied schedules would all have the same number of teams and appearances.

It could also allow you to select criteria for which ones are "best" and which concerns to avoid.

SR2025: when generating schedules for SR2025, I prioritised all teams having a min spacing of 3+, then minimising repeats, then maximising facings. I ended up generating many schedules for each number of teams and appearances by varying the spacing-facings ratio by 0.01 each time and choosing the one that fit my priority order best. Perhaps it could present the schedule(s) that have no concerns for spacing first (or no concerns at all if possible) as that would be best in this scenario.

RH2025: conversely, when generating schedules for the SRO RoboHack 2025, I prioritising facings/repeats first, then spacing. This was due to a small number of teams (9) and 2 robot matches with 8 appearances. In this scenario, every team should play every other team (and therefore play no teams twice). Repeats matter much more here with 2 robot matches as if you are facing a tough opponent, you have no other opponents to hide behind. Here it would be good to only show schedules that have "perfect facing" in the perfect sections and then prioritise by min spacings (which notably always raised at least a mild concern due to the small "ideal match spacing" from having a small number of teams).