Support of NSGA-II

Author: ahmedfgad

pygad/helper/nsga2.py

@@ -36,8 +36,8 @@ def get_non_dominated_set(curr_solutions):
             # Checking for if any solution dominates the current solution by applying the 2 conditions.
             # le_eq (less than or equal): All elements must be True.
             # le (less than): Only 1 element must be True.
-            le_eq = two_solutions[:, 1] <= two_solutions[:, 0]
-            le = two_solutions[:, 1] < two_solutions[:, 0]
+            le_eq = two_solutions[:, 1] >= two_solutions[:, 0]
+            le = two_solutions[:, 1] > two_solutions[:, 0]
 
             # If the 2 conditions hold, then a solution dominates the current solution.
             # The current solution is not considered a member of the dominated set.
@@ -175,8 +175,9 @@ def crowding_distance(pareto_front, fitness):
         # If there are only 2 solutions in the current pareto front, then do not proceed.
         # The crowding distance for such 2 solutions is infinity.
         if len(obj_sorted) <= 2:
+            obj_crowding_dist_list.append(obj_sorted)
             break
-    
+
         for idx in range(1, len(obj_sorted)-1):
             # Calculate the crowding distance.
             crowding_dist = obj_sorted[idx+1][1] - obj_sorted[idx-1][1]

pygad/pygad.py

@@ -2099,7 +2099,7 @@ def run(self):
                                         :] = self.last_generation_offspring_mutation
                 else:
                     self.last_generation_elitism, self.last_generation_elitism_indices = self.steady_state_selection(self.last_generation_fitness,
-                                                                                                                    num_parents=self.keep_elitism)
+                                                                                                                     num_parents=self.keep_elitism)
                     self.population[0:self.last_generation_elitism.shape[0],
                                     :] = self.last_generation_elitism
                     self.population[self.last_generation_elitism.shape[0]:, :] = self.last_generation_offspring_mutation

pygad/utils/mutation.py

@@ -474,7 +474,8 @@ def adaptive_mutation_population_fitness(self, offspring):
         if len(fitness.shape) > 1:
             # TODO This is a multi-objective optimization problem.
             # fitness[first_idx:last_idx] = [0]*(last_idx - first_idx)
-            raise ValueError('Edit adaptive mutation to work with multi-objective optimization problems.')
+            fitness[first_idx:last_idx] = numpy.zeros(shape=(last_idx - first_idx, fitness.shape[1]))
+            # raise ValueError('Edit adaptive mutation to work with multi-objective optimization problems.')
         else:
             # This is a single-objective optimization problem.
             fitness[first_idx:last_idx] = [0]*(last_idx - first_idx)
@@ -514,7 +515,13 @@ def adaptive_mutation_population_fitness(self, offspring):
                 for idx in range(batch_first_index, batch_last_index):
                     fitness[idx] = fitness_temp[idx - batch_first_index]
 
-        average_fitness = numpy.mean(fitness)
+        if len(fitness.shape) > 1:
+            # TODO This is a multi-objective optimization problem.
+            # Calculate the average of each objective's fitness across all solutions in the population.
+            average_fitness = numpy.mean(fitness, axis=0)
+        else:
+            # This is a single-objective optimization problem.
+            average_fitness = numpy.mean(fitness)
 
         return average_fitness, fitness[len(parents_to_keep):]
 
@@ -690,10 +697,30 @@ def adaptive_mutation_randomly(self, offspring):
         # Adaptive random mutation changes one or more genes in each offspring randomly.
         # The number of genes to mutate depends on the solution's fitness value.
         for offspring_idx in range(offspring.shape[0]):
-            if offspring_fitness[offspring_idx] < average_fitness:
-                adaptive_mutation_num_genes = self.mutation_num_genes[0]
+            ## TODO Make edits to work with multi-objective optimization.
+            # Compare the fitness of each offspring to the average fitness of each objective function.
+            fitness_comparison = offspring_fitness[offspring_idx] < average_fitness
+            # Check if the problem is single or multi-objective optimization.
+            if type(fitness_comparison) is bool:
+                # Single-objective optimization problem.
+                if fitness_comparison:
+                    adaptive_mutation_num_genes = self.mutation_num_genes[0]
+                else:
+                    adaptive_mutation_num_genes = self.mutation_num_genes[1]
             else:
-                adaptive_mutation_num_genes = self.mutation_num_genes[1]
+                # Multi-objective optimization problem.
+
+                # Get the sum of the pool array (result of comparison).
+                # True is considered 1 and False is 0.
+                fitness_comparison_sum = sum(fitness_comparison)
+                # Check if more than or equal to 50% of the objectives have fitness greater than the average.
+                # If True, then use the first percentage. 
+                # If False, use the second percentage.
+                if fitness_comparison_sum >= len(fitness_comparison)/2:
+                    adaptive_mutation_num_genes = self.mutation_num_genes[0]
+                else:
+                    adaptive_mutation_num_genes = self.mutation_num_genes[1]
+
             mutation_indices = numpy.array(random.sample(range(0, self.num_genes), adaptive_mutation_num_genes))
             for gene_idx in mutation_indices:
 

pygad/utils/parent_selection.py

@@ -7,17 +7,23 @@
 
 class ParentSelection:
     def steady_state_selection(self, fitness, num_parents):
-    
+
         """
-        Selects the parents using the steady-state selection technique. Later, these parents will mate to produce the offspring.
+        Selects the parents using the steady-state selection technique. 
+        This is by sorting the solutions based on the fitness and select the best ones as parents.
+        Later, these parents will mate to produce the offspring.
+
         It accepts 2 parameters:
             -fitness: The fitness values of the solutions in the current population.
             -num_parents: The number of parents to be selected.
-        It returns an array of the selected parents.
+        It returns:
+            -An array of the selected parents.
+            -The indices of the selected solutions.
         """
 
-        fitness_sorted = sorted(range(len(fitness)), key=lambda k: fitness[k])
-        fitness_sorted.reverse()
+        # Return the indices of the sorted solutions (all solutions in the population).
+        # This function works with both single- and multi-objective optimization problems.
+        fitness_sorted = nsga2.sort_solutions_nsga2(fitness=fitness)
 
         # Selecting the best individuals in the current generation as parents for producing the offspring of the next generation.
         if self.gene_type_single == True:
@@ -38,11 +44,14 @@ def rank_selection(self, fitness, num_parents):
         It accepts 2 parameters:
             -fitness: The fitness values of the solutions in the current population.
             -num_parents: The number of parents to be selected.
-        It returns an array of the selected parents.
+        It returns:
+            -An array of the selected parents.
+            -The indices of the selected solutions.
         """
 
-        # This has the index of each solution in the population.
-        fitness_sorted = sorted(range(len(fitness)), key=lambda k: fitness[k])
+        # Return the indices of the sorted solutions (all solutions in the population).
+        # This function works with both single- and multi-objective optimization problems.
+        fitness_sorted = nsga2.sort_solutions_nsga2(fitness=fitness)
 
         # Rank the solutions based on their fitness. The worst is gives the rank 1. The best has the rank N.
         rank = numpy.arange(1, self.sol_per_pop+1)
@@ -74,7 +83,9 @@ def random_selection(self, fitness, num_parents):
         It accepts 2 parameters:
             -fitness: The fitness values of the solutions in the current population.
             -num_parents: The number of parents to be selected.
-        It returns an array of the selected parents.
+        It returns:
+            -An array of the selected parents.
+            -The indices of the selected solutions.
         """
 
         if self.gene_type_single == True:
@@ -96,35 +107,68 @@ def tournament_selection(self, fitness, num_parents):
         It accepts 2 parameters:
             -fitness: The fitness values of the solutions in the current population.
             -num_parents: The number of parents to be selected.
-        It returns an array of the selected parents.
+        It returns:
+            -An array of the selected parents.
+            -The indices of the selected solutions.
         """
-    
+
+        # Return the indices of the sorted solutions (all solutions in the population).
+        # This function works with both single- and multi-objective optimization problems.
+        fitness_sorted = nsga2.sort_solutions_nsga2(fitness=fitness)
+
         if self.gene_type_single == True:
             parents = numpy.empty((num_parents, self.population.shape[1]), dtype=self.gene_type[0])
         else:
             parents = numpy.empty((num_parents, self.population.shape[1]), dtype=object)
-    
+
         parents_indices = []
-    
+
         for parent_num in range(num_parents):
+            # Generate random indices for the candiadate solutions.
             rand_indices = numpy.random.randint(low=0.0, high=len(fitness), size=self.K_tournament)
-            K_fitnesses = fitness[rand_indices]
-            selected_parent_idx = numpy.where(K_fitnesses == numpy.max(K_fitnesses))[0][0]
+            # K_fitnesses = fitness[rand_indices]
+            # selected_parent_idx = numpy.where(K_fitnesses == numpy.max(K_fitnesses))[0][0]
+
+            # Find the rank of the candidate solutions. The lower the rank, the better the solution.
+            rand_indices_rank = [fitness_sorted.index(rand_idx) for rand_idx in rand_indices]
+            # Select the solution with the lowest rank as a parent.
+            selected_parent_idx = rand_indices_rank.index(min(rand_indices_rank))
+
+            # Append the index of the selected parent.
             parents_indices.append(rand_indices[selected_parent_idx])
+            # Insert the selected parent.
             parents[parent_num, :] = self.population[rand_indices[selected_parent_idx], :].copy()
-    
+
         return parents, numpy.array(parents_indices)
-    
+
     def roulette_wheel_selection(self, fitness, num_parents):
 
         """
         Selects the parents using the roulette wheel selection technique. Later, these parents will mate to produce the offspring.
         It accepts 2 parameters:
             -fitness: The fitness values of the solutions in the current population.
             -num_parents: The number of parents to be selected.
-        It returns an array of the selected parents.
+        It returns:
+            -An array of the selected parents.
+            -The indices of the selected solutions.
         """
-    
+
+        ## Make edits to work with multi-objective optimization.
+        ## The objective is to convert the fitness from M-D array to just 1D array.
+        ## There are 2 ways:
+            # 1) By summing the fitness values of each solution. 
+            # 2) By using only 1 objective to create the roulette wheel and excluding the others.
+
+        # Take the sum of the fitness values of each solution.
+        if len(fitness.shape) > 1:
+            # Multi-objective optimization problem.
+            # Sum the fitness values of each solution to reduce the fitness from M-D array to just 1D array.
+            fitness = numpy.sum(fitness, axis=1)
+        else:
+            # Single-objective optimization problem.
+            pass
+
+        # Reaching this step extends that fitness is a 1D array.
         fitness_sum = numpy.sum(fitness)
         if fitness_sum == 0:
             self.logger.error("Cannot proceed because the sum of fitness values is zero. Cannot divide by zero.")
@@ -170,7 +214,9 @@ def wheel_cumulative_probs(self, probs, num_parents):
             probs_start[min_probs_idx] = curr
             curr = curr + probs[min_probs_idx]
             probs_end[min_probs_idx] = curr
-            probs[min_probs_idx] = 99999999999
+            # Replace 99999999999 by float('inf')
+            # probs[min_probs_idx] = 99999999999
+            probs[min_probs_idx] = float('inf')
 
         # Selecting the best individuals in the current generation as parents for producing the offspring of the next generation.
         if self.gene_type_single == True:
@@ -187,14 +233,34 @@ def stochastic_universal_selection(self, fitness, num_parents):
         It accepts 2 parameters:
             -fitness: The fitness values of the solutions in the current population.
             -num_parents: The number of parents to be selected.
-        It returns an array of the selected parents.
+        It returns:
+            -An array of the selected parents.
+            -The indices of the selected solutions.
         """
 
+        ## Make edits to work with multi-objective optimization.
+        ## The objective is to convert the fitness from M-D array to just 1D array.
+        ## There are 2 ways:
+            # 1) By summing the fitness values of each solution. 
+            # 2) By using only 1 objective to create the roulette wheel and excluding the others.
+
+        # Take the sum of the fitness values of each solution.
+        if len(fitness.shape) > 1:
+            # Multi-objective optimization problem.
+            # Sum the fitness values of each solution to reduce the fitness from M-D array to just 1D array.
+            fitness = numpy.sum(fitness, axis=1)
+        else:
+            # Single-objective optimization problem.
+            pass
+
+        # Reaching this step extends that fitness is a 1D array.
         fitness_sum = numpy.sum(fitness)
         if fitness_sum == 0:
             self.logger.error("Cannot proceed because the sum of fitness values is zero. Cannot divide by zero.")
             raise ZeroDivisionError("Cannot proceed because the sum of fitness values is zero. Cannot divide by zero.")
+
         probs = fitness / fitness_sum
+
         probs_start = numpy.zeros(probs.shape, dtype=float) # An array holding the start values of the ranges of probabilities.
         probs_end = numpy.zeros(probs.shape, dtype=float) # An array holding the end values of the ranges of probabilities.
 
@@ -206,7 +272,9 @@ def stochastic_universal_selection(self, fitness, num_parents):
             probs_start[min_probs_idx] = curr
             curr = curr + probs[min_probs_idx]
             probs_end[min_probs_idx] = curr
-            probs[min_probs_idx] = 99999999999
+            # Replace 99999999999 by float('inf')
+            # probs[min_probs_idx] = 99999999999
+            probs[min_probs_idx] = float('inf')
 
         pointers_distance = 1.0 / self.num_parents_mating # Distance between different pointers.
         first_pointer = numpy.random.uniform(low=0.0, 
@@ -234,8 +302,6 @@ def stochastic_universal_selection(self, fitness, num_parents):
     def tournament_selection_nsga2(self,
                                    fitness,
                                    num_parents
-                                   # pareto_fronts,
-                                   # solutions_fronts_indices, 
                                    ):
 
         """
@@ -253,7 +319,9 @@ def tournament_selection_nsga2(self,
             -pareto_fronts: A nested array of all the pareto fronts. Each front has its solutions.
             -solutions_fronts_indices: A list of the pareto front index of each solution in the current population.
     
-        It returns an array of the selected parents alongside their indices in the population.
+        It returns:
+            -An array of the selected parents.
+            -The indices of the selected solutions.
         """
 
         if self.gene_type_single == True:
@@ -263,19 +331,15 @@ def tournament_selection_nsga2(self,
 
         # The indices of the selected parents.
         parents_indices = []
-    
+
         # TODO If there is only a single objective, each pareto front is expected to have only 1 solution.
-        # TODO Make a test to check for that behaviour.
+        # TODO Make a test to check for that behaviour and add it to the GitHub actions tests.
         pareto_fronts, solutions_fronts_indices = nsga2.non_dominated_sorting(fitness)
 
         # Randomly generate pairs of indices to apply for NSGA-II tournament selection for selecting the parents solutions.
         rand_indices = numpy.random.randint(low=0.0, 
                                             high=len(solutions_fronts_indices), 
                                             size=(num_parents, self.K_tournament))
-        # rand_indices[0, 0] = 5
-        # rand_indices[0, 1] = 3
-        # rand_indices[1, 0] = 1
-        # rand_indices[1, 1] = 6
 
         for parent_num in range(num_parents):
             # Return the indices of the current 2 solutions.
@@ -346,7 +410,7 @@ def tournament_selection_nsga2(self,
                         else:
                             # If the random number is >= 0.5, then select the second solution.
                             selected_parent_idx = current_indices[1]
-    
+
             # Insert the selected parent index.
             parents_indices.append(selected_parent_idx)
             # Insert the selected parent.
@@ -358,8 +422,6 @@ def tournament_selection_nsga2(self,
     def nsga2_selection(self,
                         fitness,
                         num_parents
-                        # pareto_fronts,
-                        # solutions_fronts_indices
                         ):
 
         """
@@ -378,7 +440,9 @@ def nsga2_selection(self,
             -pareto_fronts: A nested array of all the pareto fronts. Each front has its solutions.
             -solutions_fronts_indices: A list of the pareto front index of each solution in the current population.
     
-        It returns an array of the selected parents alongside their indices in the population.
+        It returns:
+            -An array of the selected parents.
+            -The indices of the selected solutions.
         """
 
         if self.gene_type_single == True:

pygad/visualize/__init__.py

@@ -1,3 +1,3 @@
 from pygad.visualize import plot
 
-__version__ = "1.0.0"
+__version__ = "1.1.0"