implement non-dominated sorting

Author: jbytecode

src/main/scala/nds.scala

@@ -0,0 +1,42 @@
+package org.expr.mcdm
+
+import org.expr.mcdm.Direction.{Minimize, Maximize}
+
+case class NdsResult(
+    scores: Vec
+) extends MCDMResult
+
+def dominates(p1: Vec, p2: Vec, fns: Array[Direction]): Boolean =
+  val n = p1.length
+  val notworse = (0 until n).count(i =>
+    if fns(i) == Maximize then p1(i) < p2(i)
+    else p1(i) > p2(i)
+  )
+  val better = (0 until n).count(i =>
+    if fns(i) == Maximize then p1(i) > p2(i)
+    else p1(i) < p2(i)
+  )
+  (notworse == 0) && (better > 0)
+
+def ndsranks(decmat: Mat, directions: Array[Direction]): Vec =
+
+  val (n, m) = Matrix.size(decmat)
+
+  val ranks = Matrix.zeros(n)
+
+  for i <- 0 until n do
+    for j <- 0 until n do
+      if i != j then
+        if dominates(decmat(i), decmat(j), directions) then ranks(i) += 1
+
+  ranks
+
+def nds(decmat: Mat, directions: Array[Direction]): NdsResult =
+
+  val (n, m) = Matrix.size(decmat)
+
+  val ranks = ndsranks(decmat, directions)
+
+  NdsResult(
+    scores = ranks
+  )

src/test/scala/testnds.scala

@@ -0,0 +1,76 @@
+import munit.Assertions as A
+
+import org.expr.mcdm.nds
+import org.expr.mcdm.Direction.{Maximize, Minimize}
+import org.expr.mcdm.Matrix
+
+class TestNds extends munit.FunSuite {
+  test("NDS - 1") {
+    /*
+            cases = [
+            1.0 2.0 3.0
+            2.0 1.0 3.0
+            1.0 3.0 2.0
+            4.0 5.0 6.0
+        ]
+
+
+        fns = [maximum, maximum, maximum]
+
+        result = nds(cases, fns)
+     */
+    val decisionMat = Array(
+      Array(1.0, 2.0, 3.0),
+      Array(2.0, 1.0, 3.0),
+      Array(1.0, 3.0, 2.0),
+      Array(4.0, 5.0, 6.0)
+    )
+
+    val fns = Array(
+      Maximize,
+      Maximize,
+      Maximize
+    )
+
+    val result = nds(
+      decisionMat,
+      fns
+    )
+
+    val expected_scores = Array(0.0, 0.0, 0.0, 3.0)
+
+    A.assert(
+      Matrix.elementwise_equal(result.scores, expected_scores, 1e-5),
+      "The scores do not match the expected values in nds."
+    )
+  }
+
+  test("NDS - 2") {
+
+    val decisionMat = Array(
+      Array(1.0, 2.0, 3.0, 4.0),
+      Array(2.0, 4.0, 6.0, 8.0),
+      Array(4.0, 8.0, 12.0, 16.0),
+      Array(8.0, 16.0, 24.0, 32.0)
+    )
+
+    val fns = Array(
+      Minimize,
+      Minimize,
+      Minimize,
+      Minimize
+    )
+
+    val expected_scores = Array(3.0, 2.0, 1.0, 0.0)
+
+    val result = nds(
+      decisionMat,
+      fns
+    )
+
+    A.assert(
+      Matrix.elementwise_equal(result.scores, expected_scores, 1e-5),
+      "The scores do not match the expected values in nds."
+    )
+  }
+}