This section of the documentation discusses the pygad module.

With the pygad module, you can create, run, save, and load instances of the genetic algorithm. It solves both single-objective and multi-objective optimization problems.

The pygad module has a class named GA for building the genetic algorithm. This section explains the class constructor, its methods, functions, and attributes.

To create an instance of the pygad.GA class, the constructor accepts several parameters. These let you adjust the genetic algorithm for different types of applications.

The pygad.GA class constructor supports the parameters below, grouped by purpose. Click a parameter to expand its full description.

:::{dropdown} num_generations: Number of generations to run. :animate: fade-in-slide-down

Number of generations. :::

:::{dropdown} num_parents_mating: How many solutions are selected as parents. :animate: fade-in-slide-down

Number of solutions to be selected as parents. :::

:::{dropdown} sol_per_pop: Number of solutions in the population. :animate: fade-in-slide-down

Number of solutions (i.e. chromosomes) within the population. This parameter has no action if initial_population parameter exists. :::

:::{dropdown} num_genes: Number of genes in each solution. :animate: fade-in-slide-down

Number of genes in the solution/chromosome. This parameter is not needed if the user feeds the initial population to the initial_population parameter. :::

:::{dropdown} initial_population: Start from your own population. :animate: fade-in-slide-down

A population you provide yourself to start the run instead of a random one. It defaults to None, in which case PyGAD builds the initial population from the sol_per_pop and num_genes parameters.

If initial_population is None and either sol_per_pop or num_genes is also None, an exception is raised.

Introduced in PyGAD 2.0.0 and higher. :::

:::{dropdown} stop_criteria=None: Stop early when a condition is met. :animate: fade-in-slide-down

One or more conditions that stop the evolution early. Each criterion is a string made of a stop word and a number, like "reach_40".

Four stop words are supported:

• reach: stop when the fitness is greater than or equal to a given value. Example: "reach_40" stops once the fitness is >= 40.
• saturate: stop when the fitness does not change for a given number of generations. Example: "saturate_7" stops if the fitness stays the same for 7 generations in a row.
• time: stop when the time spent inside run() is at least the given number of seconds. Example: "time_30" stops the run after 30 seconds.
• evaluations: stop when the number of fitness function calls made inside run() reaches the given count. Example: "evaluations_1000" stops the run once 1000 calls have been made.

You can also pass a list of criteria; the run stops as soon as any one of them is met.

Added in PyGAD 2.15.0. The time and evaluations keywords were added in PyGAD 3.6.0. :::

:::{dropdown} fitness_func: Function that scores each solution. :animate: fade-in-slide-down

The function (or method) that calculates the fitness of a solution. This is the one parameter you almost always need to set.

A fitness function must accept 3 parameters:

1. The instance of the pygad.GA class.
2. A single solution.
3. The index of the solution in the population.

If you pass a method, it takes a fourth parameter for the method's class instance.

Return a single number for a single-objective problem, or a list, tuple, or numpy.ndarray for a multi-objective problem (supported since PyGAD 3.2.0).

See Preparing the fitness_func Parameter for how to build one. :::

:::{dropdown} fitness_batch_size=None: Score the solutions in batches. :animate: fade-in-slide-down

Calculates the fitness in batches instead of one solution at a time.

• 1 or None (default): the fitness function is called once per solution.
• An integer where 1 < fitness_batch_size <= sol_per_pop: solutions are grouped into batches of this size, and the fitness function is called once per batch.

See Batch Fitness Calculation for details and examples. Added in PyGAD 2.19.0. :::

:::{dropdown} gene_type=float: Data type (and precision) of the genes. :animate: fade-in-slide-down

Sets the data type (and optional precision) of the genes. It defaults to float, so every gene is a float.

You can set it to:

• One type for all genes: a numeric type such as int, float, or any numpy.int/uint/float(8-64) type. Example: gene_type=int.
• A type per gene: a list, tuple, or numpy.ndarray with one type per gene. Example: gene_type=[int, float, numpy.int8].
• A float precision: pair a float type with the number of decimal places. Example: gene_type=[float, 2].

Version history:

• PyGAD 2.9.0: a single numeric type can be used.
• PyGAD 2.14.0: a type per gene can be used.
• PyGAD 2.15.0: a precision can be set for float types. :::

:::{dropdown} gene_space=None: Allowed values or range for each gene. :animate: fade-in-slide-down

Sets the allowed values for each gene, so you can limit the search space to a range or to a set of discrete values.

You can set it to:

• The same space for all genes: a list/tuple/range/numpy.ndarray. Example: gene_space=[0.3, 5.2, -4, 8] limits every gene to those 4 values.
• A space per gene: a nested list/tuple, one sub-list per gene. Example: gene_space=[[0.4, -5], [0.5, -3.2, 8.2, -9], ...] (the first sub-list is for the first gene, and so on).
• A continuous range: a dictionary with low and high (and an optional step). Example: {'low': 2, 'high': 4} limits the gene to the range from 2 to 4.
• None for a gene: that gene is initialized from init_range_low/init_range_high, and mutated using random_mutation_min_val/random_mutation_max_val.

Version history:

• Added in PyGAD 2.5.0.
• PyGAD 2.9.0: NumPy arrays can be used.
• PyGAD 2.11.0: a dictionary can set the low and high limits.
• PyGAD 2.15.0: the "step" key was added. :::

:::{dropdown} gene_constraint=None: Functions that restrict gene values. :animate: fade-in-slide-down

A list of callables (functions), one per gene, that restrict the values a gene can take. Before a value is chosen for a gene, its callable checks that the candidate value is valid.

Added in PyGAD 3.5.0. See the Gene Constraint section for more information. :::

:::{dropdown} init_range_low=-4: Lower bound for the initial gene values. :animate: fade-in-slide-down

The lower value of the random range from which the gene values in the initial population are selected. init_range_low defaults to -4. Available in PyGAD 1.0.20 and higher. This parameter has no action if the initial_population parameter exists. :::

:::{dropdown} init_range_high=4: Upper bound for the initial gene values. :animate: fade-in-slide-down

The upper value of the random range from which the gene values in the initial population are selected. init_range_high defaults to +4. Available in PyGAD 1.0.20 and higher. This parameter has no action if the initial_population parameter exists. :::

:::{dropdown} allow_duplicate_genes=True: Allow repeated values within a solution. :animate: fade-in-slide-down

Added in PyGAD 2.13.0. If True, then a solution/chromosome may have duplicate gene values. If False, then each gene will have a unique value in its solution. :::

:::{dropdown} sample_size=100: Sample size used when searching for a valid value. :animate: fade-in-slide-down

The size of the sample of candidate values PyGAD draws when it needs to pick a gene value. It defaults to 100.

It is useful when allow_duplicate_genes=False or gene_constraint is used. If PyGAD cannot find a unique value or a value that meets a constraint, increase this parameter.

Added in PyGAD 3.5.0. See the sample_size Parameter section for more information. :::

:::{dropdown} parent_selection_type="sss": How the parents are selected. :animate: fade-in-slide-down

How the parents are selected. It defaults to "sss".

The built-in types are:

• sss: steady-state selection.
• rws: roulette wheel selection.
• sus: stochastic universal selection.
• rank: rank selection.
• random: random selection.
• tournament: tournament selection.
• nsga2: NSGA-II selection (multi-objective).
• tournament_nsga2: Tournament selection that ranks competitors with NSGA-II non-dominated sorting and crowding distance.
• nsga3: NSGA-III selection (multi-objective). Requires the nsga3_num_divisions parameter.
• tournament_nsga3: Tournament selection that ranks competitors with NSGA-III niche count instead of crowding distance. Requires the nsga3_num_divisions parameter.

You can also pass your own parent selection function (since PyGAD 2.16.0). See User-Defined Crossover, Mutation, and Parent Selection Operators. :::

:::{dropdown} K_tournament=3: Contestants per tournament selection. :animate: fade-in-slide-down

In case that the parent selection type is tournament, the K_tournament specifies the number of parents participating in the tournament selection. It defaults to 3. :::

:::{dropdown} nsga3_num_divisions=None: Number of divisions per objective axis for NSGA-III. :animate: fade-in-slide-down

Only used when parent_selection_type is 'nsga3' or 'tournament_nsga3'. It is the number of divisions per objective axis used to build the structured reference points (the p parameter from Deb & Jain 2014). The total number of reference points is C(M + p - 1, p) where M is the number of objectives. Must be a positive integer. Defaults to None.

If sol_per_pop is smaller than the resulting number of reference points, PyGAD raises a warning and grows the population to match before the generational loop starts. :::

:::{dropdown} keep_elitism=1: Keep the best solutions each generation. :animate: fade-in-slide-down

The number of best solutions (the elitism) to keep in the next generation. It defaults to 1, so only the best solution is kept.

• 0: elitism is turned off.
• A positive integer K (with 0 <= keep_elitism <= sol_per_pop): the best K solutions are kept.

If this parameter is not 0, then keep_parents has no effect.

Added in PyGAD 2.18.0. To see how keep_elitism and keep_parents work together, see How the Number of Offspring Is Decided. :::

:::{dropdown} keep_parents=-1: Keep the parents in the next generation. :animate: fade-in-slide-down

The number of parents to keep in the next population. It defaults to -1.

• -1: keep all the parents.
• 0: keep no parents.
• A positive integer: keep that many parents.

The value cannot be less than -1 or greater than sol_per_pop.

This parameter has an effect only when keep_elitism=0 (since PyGAD 2.18.0). Since PyGAD 2.20.0, the parents' fitness from the last generation is not re-used if keep_parents=0.

To see how keep_parents and keep_elitism work together, see How the Number of Offspring Is Decided. :::

:::{dropdown} crossover_type="single_point": How parents are combined into offspring. :animate: fade-in-slide-down

The type of crossover. It defaults to "single_point".

The built-in types are:

• single_point: single-point crossover.
• two_points: two-point crossover.
• uniform: uniform crossover.
• scattered: scattered crossover (since PyGAD 2.9.0).
• sbx: simulated binary crossover. The standard real-coded operator. Requires the sbx_crossover_eta parameter.

You can also pass your own crossover function (since PyGAD 2.16.0). See User-Defined Crossover, Mutation, and Parent Selection Operators.

If crossover_type=None, the crossover step is skipped and no offspring are created, so the next generation reuses the current population (since PyGAD 2.2.2). :::

:::{dropdown} sbx_crossover_eta=30: Distribution index for SBX crossover. :animate: fade-in-slide-down

Only used when crossover_type is 'sbx'. Sets how close the children stay to the parents. A higher value means children stay closer. Must be a positive number. Defaults to 30. :::

:::{dropdown} crossover_probability=None: Chance a parent is used for crossover. :animate: fade-in-slide-down

The probability of selecting a parent for crossover. Its value must be between 0.0 and 1.0.

For each parent, a random value between 0.0 and 1.0 is generated. If that value is less than or equal to crossover_probability, the parent is selected.

Added in PyGAD 2.5.0 and higher. :::

:::{dropdown} mutation_type="random": How offspring genes are mutated. :animate: fade-in-slide-down

The type of mutation. It defaults to "random".

The built-in types are:

• random: random mutation.
• swap: swap mutation.
• inversion: inversion mutation.
• scramble: scramble mutation.
• adaptive: adaptive mutation (since PyGAD 2.10.0). See Adaptive Mutation and Use Adaptive Mutation in PyGAD.
• polynomial: polynomial mutation. The standard real-coded operator used together with SBX. Requires the polynomial_mutation_eta parameter.

You can also pass your own mutation function (since PyGAD 2.16.0). See User-Defined Crossover, Mutation, and Parent Selection Operators.

If mutation_type=None, the mutation step is skipped and the offspring are used unchanged (since PyGAD 2.2.2). :::

:::{dropdown} polynomial_mutation_eta=20: Distribution index for polynomial mutation. :animate: fade-in-slide-down

Only used when mutation_type is 'polynomial'. Sets the size of the change. A higher value means a smaller change. Must be a positive number. Defaults to 20. :::

:::{dropdown} mutation_probability=None: Per-gene chance of mutation. :animate: fade-in-slide-down

The probability of selecting a gene for mutation. Its value must be between 0.0 and 1.0.

For each gene, a random value between 0.0 and 1.0 is generated. If that value is less than or equal to mutation_probability, the gene is mutated.

If this parameter is set, you do not need mutation_percent_genes or mutation_num_genes. Added in PyGAD 2.5.0 and higher. :::

:::{dropdown} mutation_by_replacement=False: Replace the gene value instead of adding to it. :animate: fade-in-slide-down

A bool that controls how random mutation changes a gene. It works only when mutation_type="random".

• True: replace the gene with the randomly generated value.
• False (default): add the random value to the gene.

Supported in PyGAD 2.2.2 and higher. See the PyGAD 2.2.2 release notes for an example. :::

:::{dropdown} mutation_percent_genes="default": Percentage of genes to mutate. :animate: fade-in-slide-down

The percentage of genes to mutate. It defaults to the string "default", which becomes 10 (10% of the genes). The value must be > 0 and <= 100.

PyGAD uses this percentage to compute mutation_num_genes.

This parameter has no effect if mutation_probability or mutation_num_genes is set, or if mutation_type is None (since PyGAD 2.2.2). :::

:::{dropdown} mutation_num_genes=None: Number of genes to mutate. :animate: fade-in-slide-down

The number of genes to mutate. It defaults to None, meaning no number is set.

This parameter has no effect if mutation_probability is set, or if mutation_type is None (since PyGAD 2.2.2). :::

:::{dropdown} random_mutation_min_val=-1.0: Lower bound of the random mutation value. :animate: fade-in-slide-down

For random mutation, the start of the range from which a random value is drawn and added to the gene. It defaults to -1.

This parameter has no effect if mutation_type is None (since PyGAD 2.2.2). :::

:::{dropdown} random_mutation_max_val=1.0: Upper bound of the random mutation value. :animate: fade-in-slide-down

For random mutation, the end of the range from which a random value is drawn and added to the gene. It defaults to +1.

This parameter has no effect if mutation_type is None (since PyGAD 2.2.2). :::

:::{dropdown} on_start=None: Called once before the run starts. :animate: fade-in-slide-down

A function (or method) called once before the run starts.

• As a function, it takes 1 parameter: the instance of the genetic algorithm.
• As a method, it takes a second parameter for the method's object.

Added in PyGAD 2.6.0. :::

:::{dropdown} on_fitness=None: Called after the fitness is calculated. :animate: fade-in-slide-down

A function (or method) called after the fitness of all solutions is calculated.

• As a function, it takes 2 parameters: a list of all the solutions' fitness values, and the instance of the genetic algorithm.
• As a method, it takes a third parameter for the method's object.

Added in PyGAD 2.6.0. :::

:::{dropdown} on_parents=None: Called after the parents are selected. :animate: fade-in-slide-down

A function (or method) called after the parents are selected.

• As a function, it takes 2 parameters: the selected parents, and the instance of the genetic algorithm.
• As a method, it takes a third parameter for the method's object.

Added in PyGAD 2.6.0. :::

:::{dropdown} on_crossover=None: Called after crossover. :animate: fade-in-slide-down

A function called each time crossover is applied. It takes 2 parameters: the instance of the genetic algorithm, and the offspring generated by crossover.

Added in PyGAD 2.6.0. :::

:::{dropdown} on_mutation=None: Called after mutation. :animate: fade-in-slide-down

A function called each time mutation is applied. It takes 2 parameters: the instance of the genetic algorithm, and the offspring after mutation.

Added in PyGAD 2.6.0. :::

:::{dropdown} on_generation=None: Called after each generation. :animate: fade-in-slide-down

A function called after each generation. It takes 1 parameter: the instance of the genetic algorithm.

If it returns the string "stop", the run() method stops without completing the remaining generations.

Added in PyGAD 2.6.0. :::

:::{dropdown} on_stop=None: Called once when the run ends. :animate: fade-in-slide-down

A function called once just before the run ends (or after the last generation). It takes 2 parameters: the instance of the genetic algorithm, and the list of the last population's fitness values.

Added in PyGAD 2.6.0. :::

:::{dropdown} save_best_solutions=False: Save the best solution of each generation. :animate: fade-in-slide-down

When True, the best solution of each generation is saved into the best_solutions attribute. When False (default), nothing is saved and best_solutions stays empty.

Supported in PyGAD 2.9.0. :::

:::{dropdown} save_solutions=False: Save every solution of each generation. :animate: fade-in-slide-down

If True, then all solutions in each generation are appended into an attribute called solutions which is NumPy array. Supported in PyGAD 2.15.0. :::

:::{dropdown} logger=None: Custom logger for the outputs. :animate: fade-in-slide-down

An instance of the logging.Logger class used to log the outputs. When set, messages are logged instead of printed with print(). If None, PyGAD creates a logger that uses a StreamHandler to write the messages to the console.

Added in PyGAD 3.0.0. See Logging Outputs for more information. :::

:::{dropdown} suppress_warnings=False: Turn warning messages on or off. :animate: fade-in-slide-down

A bool parameter to control whether the warning messages are printed or not. It defaults to False. :::

:::{dropdown} parallel_processing=None: Use threads or processes to speed up fitness. :animate: fade-in-slide-down

Runs the fitness calculation in parallel. It defaults to None (no parallel processing).

You can set it to:

• A positive integer: the number of threads. Example: parallel_processing=5 uses 5 threads (the same as ["thread", 5]).
• A list/tuple of 2 elements: the first is "process" or "thread"; the second is the number of processes or threads. Example: parallel_processing=["process", 10] uses 10 processes.

Added in PyGAD 2.17.0. See Parallel Processing in PyGAD for more information. :::

:::{dropdown} random_seed=None: Seed for reproducible runs. :animate: fade-in-slide-down

The random seed used by the NumPy and random number generators. Setting it makes runs reproducible (for example, random_seed=2). It defaults to None, which means no seed is used.

Added in PyGAD 2.18.0. :::

You do not have to set all of these parameters when you create an instance of the GA class. The most important one is fitness_func, which defines the fitness function.

It is OK to set the value of any of the 2 parameters init_range_low and init_range_high to be equal, higher, or lower than the other parameter (i.e. init_range_low is not needed to be lower than init_range_high). The same holds for the random_mutation_min_val and random_mutation_max_val parameters.

If both the mutation_type and crossover_type parameters are None, then the genetic algorithm cannot evolve at all. As a result, it cannot find a solution better than the best solution in the initial population.

The parameters are validated by calling the validate_parameters() method of the utils.validation.Validation class inside the constructor. If any parameter is not correct, an exception is raised and the valid_parameters attribute is set to False.

To keep the library modular and structured, the code is split into several scripts, where each script has one or more classes. Each class has its own purpose.

Here is the list of scripts and the classes that the pygad.GA class extends:

1. utils/engine.py:
   1. utils.engine.GAEngine: Runs the GA loop and owns the run-time lifecycle helpers.
2. utils/validation.py
   1. utils.validation.Validation: Validates every constructor parameter and dispatches parent_selection_type / crossover_type / mutation_type to the right method.
3. utils/parent_selection.py
   1. utils.parent_selection.ParentSelection: All built-in parent selection operators, including nsga2_selection, tournament_selection_nsga2, nsga3_selection, and tournament_selection_nsga3.
4. utils/crossover.py
   1. utils.crossover.Crossover: Built-in crossover operators.
5. utils/mutation.py
   1. utils.mutation.Mutation: Built-in mutation operators.
6. utils/nsga.py
   1. utils.nsga.NSGA: Building blocks shared by NSGA-II and NSGA-III (non_dominated_sorting, get_non_dominated_set).
7. utils/nsga2.py
   1. utils.nsga2.NSGA2: NSGA-II specific primitives (crowding_distance, sort_solutions_nsga2).
8. utils/nsga3.py
   1. utils.nsga3.NSGA3: NSGA-III algorithm primitives (reference points, ideal point, extreme points, intercepts, normalization, association, niching).
9. utils/report.py
   1. utils.report.Report: Builds a PDF report of the run (generate_report).
10. helper/unique.py
    1. helper.unique.Unique: Routines that resolve duplicate genes inside a solution.
11. helper/misc.py
    1. helper.misc.Helper: Generic helpers used across the library (population dtype handling, per-gene value generation, constraint sampling, lifecycle summary).
12. visualize/plot.py
    1. visualize.plot.Plot: All plot methods. See pygad.visualize.

Since the pygad.GA class extends such classes, the attributes and methods inside them can be retrieved by instances of the pygad.GA class.

• supported_int_types: A list of the supported types for the integer numbers.
• supported_float_types: A list of the supported types for the floating-point numbers.
• supported_int_float_types: A list of the supported types for all numbers. It just concatenates the previous 2 lists.

All the parameters and functions passed to the pygad.GA class constructor are used as class attributes and methods in the instances of the pygad.GA class. In addition to such attributes, there are other attributes and methods added to the instances of the pygad.GA class.

The GA class gains the attributes of its parent classes via inheritance, making them accessible through the GA object even if they are defined externally to its specific class body.

Names that begin with an underscore (for example _bootstrap_nsga3_reference_points) are internal helpers. They are listed below for completeness but are not part of the stable API; do not rely on their signature staying the same across releases.

• generations_completed: Number of the last completed generation.
• run_completed: Set to True only after the run() method completes gracefully.
• valid_parameters: Set to True when all the parameters passed in the GA class constructor are valid.
• run_start_time: Monotonic clock value captured right before the generation loop starts. Internal.
• logger: Logger object from the logging module. Supported in PyGAD 3.0.0.

• run(): Runs the generation loop. The main entry point.
• run_loop_head(best_solution_fitness): Per-generation pre-loop bookkeeping. Internal; called from inside run(). Added in PyGAD 3.3.1.
• run_select_parents(call_on_parents=True): Select parents and call on_parents when defined. Internal; called from inside run(). Pass call_on_parents=False when refreshing the parent set at the end of run(). Added in PyGAD 3.3.1.
• run_crossover(): Apply crossover and call on_crossover when defined. Internal. Added in PyGAD 3.3.1.
• run_mutation(): Apply mutation and call on_mutation when defined. Internal. Added in PyGAD 3.3.1.
• run_update_population(): Replace self.population with the crossed-over and mutated offspring. Internal. Added in PyGAD 3.3.1.
• summary(...): Prints a Keras-like summary of the PyGAD lifecycle. Added in PyGAD 2.19.0. See Print Lifecycle Summary.

• population: A NumPy array that initially holds the initial population and is later updated after each generation.
• initial_population: Frozen copy of the initial population, set after initialize_population runs.
• pop_size: A (sol_per_pop, num_genes) tuple describing the population shape.
• gene_type_single: True when every gene shares the same dtype; False when gene_type is a list/tuple/numpy.ndarray. Added in PyGAD 2.14.0.
• gene_space_unpacked: Unpacked version of gene_space. For example, range(1, 5) becomes [1, 2, 3, 4]; {'low': 2, 'high': 4} becomes a finite sample. Added in PyGAD 3.1.0.

• initialize_population(allow_duplicate_genes, gene_type, gene_constraint): Build the initial population, apply gene types and constraints, resolve duplicates when not allowed.
• initialize_parents_array(shape): Allocate an empty parents (or offspring) array with the right dtype.
• change_population_dtype_and_round(population): Cast a 2D population to the dtype encoded in self.gene_type and round non-integer genes.
• change_gene_dtype_and_round(gene_index, gene_value): Same as above, but for a single gene value.
• round_genes(solutions): Round genes in a 2D array according to self.gene_type precision.
• get_initial_population_range(gene_index): Return the [init_range_low, init_range_high] window for a specific gene.
• get_random_mutation_range(gene_index): Return the [random_mutation_min_val, random_mutation_max_val] window for a specific gene.
• get_gene_dtype(gene_index): Return the (type, precision) pair for a specific gene.
• generate_gene_value(...): Sample a single gene value from the gene space or from the configured range.
• generate_gene_value_from_space(...): Sample a single gene value from gene_space.
• generate_gene_value_randomly(...): Sample a single gene value from the configured numeric range.

• last_generation_fitness: Fitness values of the solutions in the last generation. Added in PyGAD 2.12.0.
• previous_generation_fitness: Fitness of the population one step before last_generation_fitness. Used to skip re-evaluating solutions PyGAD has already seen. Added in PyGAD 2.16.2.
• best_solutions_fitness: List of best-solution fitness per generation.
• best_solutions: A NumPy array of the best solution per generation. Only populated when save_best_solutions=True.
• best_solutions_fitness: Fitness for every entry in best_solutions.
• solutions: All visited solutions when save_solutions=True.
• solutions_fitness: Fitness for every entry in solutions.
• best_solution_generation: Generation at which the best fitness was reached. -1 until run() completes.

• cal_pop_fitness(): Compute the fitness of every solution in the current population, reusing previously calculated values where possible.
• best_solution(pop_fitness=None): Return the best solution, its fitness, and its population index.
• adaptive_mutation_population_fitness(offspring): Average fitness used by adaptive mutation to split solutions into low / high quality.

• last_generation_parents: Parents selected in the last generation. Added in PyGAD 2.12.0.
• last_generation_parents_indices: Indices of the selected parents in self.population. Added in PyGAD 2.15.0.

• select_parents(fitness, num_parents): Active parent-selection method. Bound during validation according to parent_selection_type.
• steady_state_selection(fitness, num_parents): Steady-state selection.
• rank_selection(fitness, num_parents): Rank-based selection.
• random_selection(fitness, num_parents): Random selection.
• tournament_selection(fitness, num_parents): K-tournament selection.
• roulette_wheel_selection(fitness, num_parents): Roulette-wheel selection.
• stochastic_universal_selection(fitness, num_parents): SUS selection.
• wheel_cumulative_probs(probs, num_parents): Build the [start, end) ranges used by RWS and SUS.

• pareto_fronts: List of the Pareto fronts of the last generation when running a multi-objective problem. Each front is a NumPy array of (population_index, fitness_vector) pairs. Added in PyGAD 3.2.0.

• non_dominated_sorting(fitness): Sort the population into Pareto fronts. Defined in utils.nsga.NSGA and shared with NSGA-III.
• get_non_dominated_set(curr_solutions): Split the current set of solutions into a dominated and non-dominated subset. Defined in utils.nsga.NSGA.
• crowding_distance(pareto_front, fitness): Per-solution crowding distance inside a Pareto front. Defined in utils.nsga2.NSGA2.
• sort_solutions_nsga2(fitness, find_best_solution=False): Sort population indices best-to-worst using Pareto fronts and crowding distance for MOO; descending fitness for SOO. Defined in utils.nsga2.NSGA2.
• nsga2_selection(fitness, num_parents): NSGA-II parent selection. Defined in utils.parent_selection.ParentSelection.
• tournament_selection_nsga2(fitness, num_parents): K-tournament with non-dominated rank + crowding distance as tiebreakers. Defined in utils.parent_selection.ParentSelection.

• nsga3_num_divisions: Stored value of the nsga3_num_divisions constructor parameter. Used when building the reference grid.
• nsga3_reference_points: Structured grid of reference points on the unit simplex. A 2D NumPy array of shape (n_points, num_objectives) where each row sums to 1. Built once before the generation loop starts (_bootstrap_nsga3_reference_points). Re-used for every generation.

• nsga3_generate_reference_points(num_objectives, num_divisions): Build the Das-Dennis grid.
• nsga3_compute_ideal_point(fitness): Best fitness per objective across the input rows (column max under maximization).
• nsga3_find_extreme_points(fitness, ideal_point, epsilon=NSGA3_ASF_EPSILON): For each objective, find the row that best represents the corner of that axis using the ASF.
• nsga3_compute_intercepts(extreme_points, ideal_point, fallback_fitness): Fit a hyperplane through the extreme points and return per-axis intercepts. Falls back to the nadir on singular systems.
• nsga3_normalize_fitness(fitness, ideal_point, intercepts): Scale each fitness row to the unit hypercube and clip outliers to [0, 1].
• nsga3_associate_to_reference_points(normalized, reference_points): For every normalized row, find the closest reference line and the perpendicular distance to it.
• nsga3_niching_select(critical_front_indices, critical_front_associations, critical_front_distances, accepted_associations, num_reference_points, num_to_select): Niching loop that picks survivors from the critical front to preserve diversity across reference points.

• nsga3_selection(fitness, num_parents): NSGA-III parent selection.
• tournament_selection_nsga3(fitness, num_parents): K-tournament with niche count + perpendicular distance as tiebreakers.
• _nsga3_pick_critical_front_survivors(...): Run normalization and niching on P_next ∪ critical_front and return the picked survivors. Internal.
• _nsga3_pick_tournament_winner(...): Decide the winner of one K-tournament round under NSGA-III rules. Internal.
• _nsga3_build_parents(final_indices, num_parents): Copy the chosen rows out of the population into a new parents array. Internal.

• _bootstrap_nsga3_reference_points(): Build the reference-point grid once, right after the first fitness evaluation. Calls _nsga3_grow_population when sol_per_pop is smaller than the reference count.
• _nsga3_grow_population(required_size, num_objectives): Append random solutions to self.population, update sol_per_pop / pop_size / num_offspring, re-evaluate fitness.
• _nsga3_generate_extra_random_solutions(count): Build count random solutions respecting the gene space, init range, gene type, gene constraints, and allow_duplicate_genes rules.
• _nsga3_generate_single_random_gene(gene_idx, partial_solution): Sample a single gene value using initial-population settings (not mutation settings).
• _nsga3_apply_gene_constraints(population): Enforce gene_constraint on the new rows.
• _nsga3_resolve_duplicate_genes(population): Resolve duplicate genes in the new rows when allow_duplicate_genes=False.

• NSGA3_ASF_EPSILON: Off-axis weight used by the ASF inside nsga3_find_extreme_points.
• NSGA3_INTERCEPT_NEAR_ZERO: Threshold under which an intercept gap is treated as zero.
• _nsga3_pick_target_reference_point(niche_counts, critical_front_associations, remaining_positions): Choose the next reference point for the niching loop. Internal.
• _nsga3_pick_candidate_at_reference(candidates_at_target, critical_front_distances, niche_count_at_target): Choose a candidate at a given reference point. Internal.
• _nsga3_enumerate_compositions(num_objectives, num_divisions): Yield every non-negative integer tuple summing to num_divisions. Internal.

• _nsga3_validate_multi_objective_fitness(fitness, supported_int_float_types, method_name): Raise when the GA was set to NSGA-III but the fitness function returned scalars.
• _nsga3_accumulate_fronts(pareto_fronts, num_parents): Walk the Pareto fronts and split them into the accepted set + the critical front.

• last_generation_offspring_crossover: Offspring after crossover. Added in PyGAD 2.12.0.

• crossover(): Active crossover operator. Bound during validation according to crossover_type.
• single_point_crossover(parents, offspring_size): Single-point crossover.
• two_points_crossover(parents, offspring_size): Two-point crossover.
• uniform_crossover(parents, offspring_size): Uniform crossover.
• scattered_crossover(parents, offspring_size): Scattered crossover.
• sbx_crossover(parents, offspring_size): Simulated binary crossover. Uses self.sbx_crossover_eta.

• last_generation_offspring_mutation: Offspring after mutation. Added in PyGAD 2.12.0.
• last_generation_offspring_mutation_indices: Indices of mutated offspring inside self.population.

• mutation(): Active mutation operator. Bound during validation according to mutation_type.
• random_mutation(offspring): Random mutation (replaces or adds a uniform random value).
• swap_mutation(offspring): Swap mutation.
• inversion_mutation(offspring): Inversion mutation.
• scramble_mutation(offspring): Scramble mutation.
• adaptive_mutation(offspring): Adaptive mutation. Uses adaptive_mutation_population_fitness.
• polynomial_mutation(offspring): Polynomial mutation. Uses self.polynomial_mutation_eta.
• mutation_change_gene_dtype_and_round(...): Round and re-cast a mutated gene to the configured dtype/precision.

• last_generation_elitism: Elitism solutions from the last generation. Added in PyGAD 2.18.0.
• last_generation_elitism_indices: Population indices of last_generation_elitism. Added in PyGAD 2.19.0.

• validate_gene_constraint_callable_output(selected_values, values): Sanity-check the return value of a user-defined gene_constraint.
• filter_gene_values_by_constraint(values, solution, gene_idx): Run gene_constraint[gene_idx] and return the filtered list.
• get_valid_gene_constraint_values(...): Sample candidate values until one satisfies the gene constraint.
• solve_duplicate_genes_randomly(...): Resolve duplicate genes by sampling new values from the random range.
• solve_duplicate_genes_by_space(...): Resolve duplicate genes by sampling new values from gene_space.
• solve_duplicates_deeply(...): Slow, exhaustive fallback for duplicate resolution.
• unique_int_gene_from_range(...): Pick an integer gene that does not already appear in the solution.
• unique_float_gene_from_range(...): Pick a float gene that does not already appear in the solution.
• unique_gene_by_space(...): Pick a unique value from gene_space.
• unique_genes_by_space(...): Pick unique values for several genes from gene_space.
• select_unique_value(...): Sample one value uniformly at random from a list of candidates.
• find_two_duplicates(solution): Locate the first pair of duplicated indices in a solution.
• unpack_gene_space(...): Materialize the unpacked gene_space (used to build gene_space_unpacked).

• save(filename): Pickle the GA instance to disk (uses cloudpickle).
• generate_report(filename, ...): Build a PDF report of the run. See generate_report() below.
• push_to_vilvik(...): Optional convenience wrapper around the Vilvik SDK.

Note that the attributes with names starting with last_generation_ are updated after each generation.

The next sections discuss the methods available in the pygad.GA class.

The save() method in the pygad.GA class saves the genetic algorithm instance as a pickled object.

Accepts the following parameter:

• filename: Name of the file to save the instance. No extension is needed.

(generate-report)=

Builds a PDF report of the current GA run. It bundles the configuration table, a run-summary table, the best solution, and every applicable plot. Requires the optional report extra:

pip install pygad[report]

Call it after run() finishes. A minimal example:

ga_instance.run()
ga_instance.generate_report("my_run")  # writes my_run.pdf next to the script

Parameters:

• filename (str, required): Output path. .pdf is appended automatically if missing.
• title (str or None, default None): Title shown on the first page. Defaults to "PyGAD run report".
• sections (iterable of str or None, default None): Sections to include and their order. Valid entries are "title", "configuration", "run_summary", "best_solution", "plots", and "notes". When None, every section is included in their default order.
• include_plots (iterable of str, "all", or None, default None): Plots to embed under the "plots" section. None or "all" auto-selects every plot whose preconditions are met by this run. Pass a list of plot method names to include only those.
• figure_size_inches ((float, float), default (7.0, 4.5)): Width and height (in inches) used when each plot is drawn for the report.
• notes (str or None, default None): Free-form text rendered in the optional "notes" section.
• page_size (str, default "letter"): Either "letter" or "A4".

The report skips any plot whose preconditions are not met. For example, plot_pareto_front_curve is included only for multi-objective runs with 2 or 3 objectives; plot_non_dominated_hypervolume is included only when save_solutions=True is set on the GA. A full example lives at examples/example_generate_report.py.

The title page shows the PyGAD logo. The image ships with the package, so it works without network access. If the image file is missing, the report is built without it.

Besides the methods available in the pygad.GA class, this section discusses the functions available in pygad. Up to this time, there is only a single function named load().

Reads a saved instance of the genetic algorithm. This is not a method but a function that is indented under the pygad module. So, it could be called by the pygad module as follows: pygad.load(filename).

Accepts the following parameter:

• filename: Name of the file holding the saved instance of the genetic algorithm. No extension is needed.

Returns the genetic algorithm instance.

::::{grid} 1 2 2 2 :gutter: 3

:::{grid-item-card} Steps to Use PyGAD :link: steps_to_use :link-type: doc

A step-by-step walkthrough to build and run the genetic algorithm. :::

:::{grid-item-card} Life Cycle of PyGAD :link: lifecycle :link-type: doc

How a generation runs and where each callback is called. :::

::::

This section gives the complete code of some examples that use pygad. Each subsection builds a different example.

::::{grid} 1 2 2 2 :gutter: 3

:::{grid-item-card} Linear Model - Single Objective :link: pygad_example_linear :link-type: doc :::

:::{grid-item-card} Linear Model - Multi-Objective :link: pygad_example_multi_objective :link-type: doc :::

:::{grid-item-card} Reproducing Images :link: pygad_example_reproducing_images :link-type: doc :::

::::

For a 2-cluster problem, the code is available here. For a 3-cluster problem, the code is here. The 2 examples are using artificial samples.

Soon a tutorial will be published at Paperspace to explain how clustering works using the genetic algorithm with examples in PyGAD.

The code is available at the CoinTex GitHub project. CoinTex is an Android game written in Python using the Kivy framework. Find CoinTex at Google Play: https://play.google.com/store/apps/details?id=coin.tex.cointexreactfast

Check this Paperspace tutorial for how the genetic algorithm plays CoinTex: https://blog.paperspace.com/building-agent-for-cointex-using-genetic-algorithm. Check also this YouTube video showing the genetic algorithm while playing CoinTex.

:::{toctree} :hidden:

steps_to_use lifecycle pygad_example_linear pygad_example_multi_objective pygad_example_reproducing_images :::