Shuffle once and keep order, use SmallRng

time:   [98.196 µs 100.64 µs 103.56 µs]
change: [−13.633% −10.629% −7.6947%] (p = 0.00 < 0.05)

src-tauri/src/scheduler.rs

@@ -11,7 +11,7 @@ use crate::{
 };
 
 use log::info;
-use rand::Rng;
+use rand::{rngs::SmallRng, seq::SliceRandom, SeedableRng};
 use rayon::{
     current_thread_index,
     iter::{IntoParallelRefIterator, ParallelIterator},
@@ -132,13 +132,13 @@ impl Scheduler {
             return self.search(schedule, tracker, slot.next(), solved_in_thread);
         }
 
-        // sort candidates by current workload, add rng for tie breakers
+        let mut rng = SmallRng::from_rng(&mut rand::rng());
         let mut valid_resident_ids = self.valid_residents(slot, schedule);
-        valid_resident_ids.sort_unstable_by_key(|res_id| {
+        valid_resident_ids.shuffle(&mut rng);
+        valid_resident_ids.sort_by_key(|res_id| {
             let type_count = tracker.get_type_count(res_id, slot.shift_type());
             let workload = tracker.current_workload(res_id);
-            let tie_breaker: f64 = rand::rng().random();
-            (type_count, workload, (tie_breaker * 1000.0) as usize)
+            (type_count, workload)
         });
 
         for id in valid_resident_ids {