Fast pareto-front calculation for 2D

optuna_dashboard/ts/components/GraphParetoFront.tsx

@@ -165,6 +165,72 @@ const makeMarker = (
   }
 }
 
+const getIsDominatedND = (normalizedValues: number[][]) => {
+  // Fallback for straight-forward pareto front algorithm (O(N^2) complexity).
+  const isDominated: boolean[] = []
+  normalizedValues.forEach((values0: number[]) => {
+    const dominated = normalizedValues.some((values1: number[]) => {
+      if (values0.every((value0: number, k: number) => values1[k] === value0)) {
+        return false
+      }
+      return values0.every((value0: number, k: number) => values1[k] <= value0)
+    })
+    isDominated.push(dominated)
+  })
+  return isDominated
+}
+
+const getIsDominated2D = (normalizedValues: number[][]) => {
+  // Fast pareto front algorithm (O(N log N) complexity).
+  const sorted = normalizedValues
+    .map((values, i) => [values[0], values[1], i])
+    .sort((a, b) =>
+      a[0] > b[0]
+        ? 1
+        : a[0] < b[0]
+        ? -1
+        : a[1] > b[1]
+        ? 1
+        : a[1] < b[1]
+        ? -1
+        : 0
+    )
+  let maxValueSeen0 = sorted[0][0]
+  let minValueSeen1 = sorted[0][1]
+
+  const isDominated: boolean[] = new Array(normalizedValues.length).fill(false)
+  sorted.forEach((values) => {
+    if (
+      values[1] > minValueSeen1 ||
+      (values[1] === minValueSeen1 && values[0] > maxValueSeen0)
+    ) {
+      isDominated[values[2]] = true
+    } else {
+      minValueSeen1 = values[1]
+    }
+    maxValueSeen0 = values[0]
+  })
+  return isDominated
+}
+
+const getIsDominated1D = (normalizedValues: number[][]) => {
+  const best_value = Math.min(...normalizedValues.map((values) => values[0]))
+  return normalizedValues.map((values) => values[0] !== best_value)
+}
+
+const getIsDominated = (normalizedValues: number[][]) => {
+  if (normalizedValues.length === 0) {
+    return []
+  }
+  if (normalizedValues[0].length === 1) {
+    return getIsDominated1D(normalizedValues)
+  } else if (normalizedValues[0].length === 2) {
+    return getIsDominated2D(normalizedValues)
+  } else {
+    return getIsDominatedND(normalizedValues)
+  }
+}
+
 const plotParetoFront = (
   study: StudyDetail,
   objectiveXId: number,
@@ -218,22 +284,11 @@ const plotParetoFront = (
     }
   })
 
-  const dominatedTrials: boolean[] = []
-  normalizedValues.forEach((values0: number[], i: number) => {
-    const dominated = normalizedValues.some((values1: number[], j: number) => {
-      if (i === j) {
-        return false
-      }
-      return values0.every((value0: number, k: number) => {
-        return values1[k] <= value0
-      })
-    })
-    dominatedTrials.push(dominated)
-  })
+  const isDominated: boolean[] = getIsDominated(normalizedValues)
 
   const plotData: Partial<plotly.PlotData>[] = [
     makeScatterObject(
-      feasibleTrials.filter((t, i) => dominatedTrials[i]),
+      feasibleTrials.filter((t, i) => isDominated[i]),
       objectiveXId,
       objectiveYId,
       infeasibleTrials.length === 0
@@ -244,7 +299,7 @@ const plotParetoFront = (
       mode
     ),
     makeScatterObject(
-      feasibleTrials.filter((t, i) => !dominatedTrials[i]),
+      feasibleTrials.filter((t, i) => !isDominated[i]),
       objectiveXId,
       objectiveYId,
       "%{text}<extra>Best Trial</extra>",