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NSGA-II/non_dominant_sorting.py

@@ -0,0 +1,62 @@
+import numpy
+
+population = numpy.array([[20, 2.2],
+                          [60, 4.4],
+                          [65, 3.5],
+                          [15, 4.4],
+                          [55, 4.5],
+                          [50, 1.8],
+                          [80, 4.0],
+                          [25, 4.6]])
+
+def non_dominant_sorting(curr_set):
+    # List of the members of the current dominant front/set.
+    dominant_set = []
+    # List of the non-members of the current dominant front/set.
+    non_dominant_set = []
+    for idx1, sol1 in enumerate(curr_set):
+        # Flag indicates whether the solution is a member of the current dominant set.
+        is_dominant = True
+        for idx2, sol2 in enumerate(curr_set):
+            if idx1 == idx2:
+                continue
+            # Zipping the 2 solutions so the corresponding genes are in the same list.
+            # The returned array is of size (N, 2) where N is the number of genes.
+            b = numpy.array(list(zip(sol1, sol2)))
+
+            #TODO Consider repacing < by > for maximization problems.
+            # Checking for if any solution dominates the current solution by applying the 2 conditions.
+            # le_eq: All elements must be True.
+            # le: Only 1 element must be True.
+            le_eq = b[:, 1] <= b[:, 0]
+            le = b[:, 1] < b[:, 0]
+
+            # If the 2 conditions hold, then a solution dominates the current solution.
+            # The current solution is not considered a member of the dominant set.
+            if le_eq.all() and le.any():
+                # print(f"{sol2} dominates {sol1}")
+                # Set the is_dominant flag to False to not insert the current solution in the current dominant set.
+                # Instead, insert it into the non-dominant set.
+                is_dominant = False
+                non_dominant_set.append(sol1)
+                break
+            else:
+                # Reaching here means the solution does not dominant the current solution.
+                # print(f"{sol2} does not dominate {sol1}")
+                pass
+
+        # If the flag is True, then no solution dominates the current solution.
+        if is_dominant:
+            dominant_set.append(sol1)
+
+    # Return the dominant and non-dominant sets.
+    return dominant_set, non_dominant_set
+
+dominant_set = []
+non_dominant_set = population.copy()
+while len(non_dominant_set) > 0:
+    d1, non_dominant_set = non_dominant_sorting(non_dominant_set)
+    dominant_set.append(d1)
+
+for i, s in enumerate(dominant_set):
+    print(f'Dominant Front Set {i+1}:\n{s}')

docs/source/releases.rst

@@ -1361,7 +1361,7 @@ Release Date 20 June 2023
     solve the duplicates between the 2 genes by simply replacing the
     value of one gene by another gene. This release tries to solve such
     duplicates by looking for a third gene that will help in solving the
-    duplicates. These examples explain how it works. Check `this
+    duplicates. Check `this
     section <https://pygad.readthedocs.io/en/latest/pygad.html#prevent-duplicates-in-gene-values>`__
     for more information.
 
@@ -1887,6 +1887,11 @@ Research Papers using PyGAD
 
 A number of research papers used PyGAD and here are some of them:
 
+-  Alberto Meola, Manuel Winkler, Sören Weinrich, Metaheuristic
+   optimization of data preparation and machine learning hyperparameters
+   for prediction of dynamic methane production, Bioresource Technology,
+   Volume 372, 2023, 128604, ISSN 0960-8524.
+
 -  Jaros, Marta, and Jiri Jaros. "Performance-Cost Optimization of
    Moldable Scientific Workflows."