/*
 * Java Genetic Algorithm Library (jenetics-3.5.0).
 * Copyright (c) 2007-2016 Franz Wilhelmstötter
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 *
 * Author:
 *    Franz Wilhelmstötter (franz.wilhelmstoetter@gmx.at)
 */
package org.jenetics.engine;

import static java.lang.Math.round;
import static java.lang.String.format;
import static java.util.Objects.requireNonNull;
import static org.jenetics.Population.toPopulation;
import static org.jenetics.internal.util.require.probability;

import java.time.Clock;
import java.util.Iterator;
import java.util.Objects;
import java.util.concurrent.CompletableFuture;
import java.util.concurrent.Executor;
import java.util.concurrent.ForkJoinPool;
import java.util.function.Function;
import java.util.function.Predicate;
import java.util.stream.Stream;
import java.util.stream.StreamSupport;

import org.jenetics.internal.util.Concurrency;
import org.jenetics.internal.util.require;

import org.jenetics.Alterer;
import org.jenetics.Chromosome;
import org.jenetics.Gene;
import org.jenetics.Genotype;
import org.jenetics.Mutator;
import org.jenetics.Optimize;
import org.jenetics.Phenotype;
import org.jenetics.Population;
import org.jenetics.Selector;
import org.jenetics.SinglePointCrossover;
import org.jenetics.TournamentSelector;
import org.jenetics.util.Copyable;
import org.jenetics.util.Factory;
import org.jenetics.util.NanoClock;

/**
 * Genetic algorithm <em>engine</em> which is the main class. The following
 * example shows the main steps in initializing and executing the GA.
 *
 * <pre>{@code
 * public class RealFunction {
 *    // Definition of the fitness function.
 *    private static Double eval(final Genotype<DoubleGene> gt) {
 *        final double x = gt.getGene().doubleValue();
 *        return cos(0.5 + sin(x)) * cos(x);
 *    }
 *
 *    public static void main(String[] args) {
 *        // Create/configuring the engine via its builder.
 *        final Engine<DoubleGene, Double> engine = Engine
 *            .builder(
 *                RealFunction::eval,
 *                DoubleChromosome.of(0.0, 2.0*PI))
 *            .populationSize(500)
 *            .optimize(Optimize.MINIMUM)
 *            .alterers(
 *                new Mutator<>(0.03),
 *                new MeanAlterer<>(0.6))
 *            .build();
 *
 *        // Execute the GA (engine).
 *        final Phenotype<DoubleGene, Double> result = engine.stream()
 *             // Truncate the evolution stream if no better individual could
 *             // be found after 5 consecutive generations.
 *            .limit(bySteadyFitness(5))
 *             // Terminate the evolution after maximal 100 generations.
 *            .limit(100)
 *            .collect(toBestPhenotype());
 *     }
 * }
 * }</pre>
 *
 * The architecture allows to decouple the configuration of the engine from the
 * execution. The {@code Engine} is configured via the {@code Engine.Builder}
 * class and can't be changed after creation. The actual <i>evolution</i> is
 * performed by the {@link EvolutionStream}, which is created by the
 * {@code Engine}.
 * <p>
 * <em>
 *     <b>This class is thread safe:</b>
 *     No mutable state is maintained by the engine. Therefore it is save to
 *     create multiple evolution streams with one engine, which may be actually
 *     used in different threads.
 * </em>
 *
 * @see Engine.Builder
 * @see EvolutionStart
 * @see EvolutionResult
 * @see EvolutionStream
 * @see EvolutionStatistics
 * @see Codec
 *
 * @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
 * @since 3.0
 * @version 3.2
 */
public final class Engine<
        G extends Gene<?, G>,
        C extends Comparable<? super C>
>
        implements Function<EvolutionStart<G, C>, EvolutionResult<G, C>>
{

        // Needed context for population evolving.
        private final Function<? super Genotype<G>, ? extends C> _fitnessFunction;
        private final Function<? super C, ? extends C> _fitnessScaler;
        private final Factory<Genotype<G>> _genotypeFactory;
        private final Selector<G, C> _survivorsSelector;
        private final Selector<G, C> _offspringSelector;
        private final Alterer<G, C> _alterer;
        private final Predicate<? super Phenotype<G, C>> _validator;
        private final Optimize _optimize;
        private final int _offspringCount;
        private final int _survivorsCount;
        private final long _maximalPhenotypeAge;

        // Execution context for concurrent execution of evolving steps.
        private final TimedExecutor _executor;
        private final Clock _clock;

        // Additional parameters.
        private final int _individualCreationRetries;


        /**
         * Create a new GA engine with the given parameters.
         *
         * @param genotypeFactory the genotype factory this GA is working with.
         * @param fitnessFunction the fitness function this GA is using.
         * @param fitnessScaler the fitness scaler this GA is using.
         * @param survivorsSelector the selector used for selecting the survivors
         * @param offspringSelector the selector used for selecting the offspring
         * @param alterer the alterer used for altering the offspring
         * @param validator phenotype validator which can override the default
         *        implementation the {@link Phenotype#isValid()} method.
         * @param optimize the kind of optimization (minimize or maximize)
         * @param offspringCount the number of the offspring individuals
         * @param survivorsCount the number of the survivor individuals
         * @param maximalPhenotypeAge the maximal age of an individual
         * @param executor the executor used for executing the single evolve steps
         * @param clock the clock used for calculating the timing results
         * @param individualCreationRetries the maximal number of attempts for
         *        creating a valid individual.
         * @throws NullPointerException if one of the arguments is {@code null}
         * @throws IllegalArgumentException if the given integer values are smaller
         *         than one.
         */
        Engine(
                final Function<? super Genotype<G>, ? extends C> fitnessFunction,
                final Function<? super C, ? extends C> fitnessScaler,
                final Factory<Genotype<G>> genotypeFactory,
                final Selector<G, C> survivorsSelector,
                final Selector<G, C> offspringSelector,
                final Alterer<G, C> alterer,
                final Predicate<? super Phenotype<G, C>> validator,
                final Optimize optimize,
                final int offspringCount,
                final int survivorsCount,
                final long maximalPhenotypeAge,
                final Executor executor,
                final Clock clock,
                final int individualCreationRetries
        ) {
                _fitnessFunction = requireNonNull(fitnessFunction);
                _fitnessScaler = requireNonNull(fitnessScaler);
                _genotypeFactory = requireNonNull(genotypeFactory);
                _survivorsSelector = requireNonNull(survivorsSelector);
                _offspringSelector = requireNonNull(offspringSelector);
                _alterer = requireNonNull(alterer);
                _validator = requireNonNull(validator);
                _optimize = requireNonNull(optimize);

                _offspringCount = require.nonNegative(offspringCount);
                _survivorsCount = require.nonNegative(survivorsCount);
                _maximalPhenotypeAge = require.positive(maximalPhenotypeAge);

                _executor = new TimedExecutor(requireNonNull(executor));
                _clock = requireNonNull(clock);

                if (individualCreationRetries < 0) {
                        throw new IllegalArgumentException(format(
                                "Retry count must not be negative: %d",
                                individualCreationRetries
                        ));
                }
                _individualCreationRetries = individualCreationRetries;
        }

        /**
         * Perform one evolution step with the given {@code population} and
         * {@code generation}. New phenotypes are created with the fitness function
         * and fitness scaler defined by this <em>engine</em>
         * <p>
         * <em>This method is thread-safe.</em>
         *
         * @see #evolve(EvolutionStart)
         *
         * @param population the population to evolve
         * @param generation the current generation; used for calculating the
         *        phenotype age.
         * @return the evolution result
         * @throws java.lang.NullPointerException if the given {@code population} is
         *         {@code null}
         * @throws IllegalArgumentException if the given {@code generation} is
         *         smaller then one
         */
        public EvolutionResult<G, C> evolve(
                final Population<G, C> population,
                final long generation
        ) {
                return evolve(EvolutionStart.of(population, generation));
        }

        /**
         * Perform one evolution step with the given evolution {@code start} object
         * New phenotypes are created with the fitness function and fitness scaler
         * defined by this <em>engine</em>
         * <p>
         * <em>This method is thread-safe.</em>
         *
         * @since 3.1
         * @see #evolve(org.jenetics.Population, long)
         *
         * @param start the evolution start object
         * @return the evolution result
         * @throws java.lang.NullPointerException if the given evolution
         *         {@code start} is {@code null}
         */
        public EvolutionResult<G, C> evolve(final EvolutionStart<G, C> start) {
                final Timer timer = Timer.of().start();

                final Population<G, C> startPopulation = start.getPopulation();

                // Initial evaluation of the population.
                final Timer evaluateTimer = Timer.of(_clock).start();
                evaluate(startPopulation);
                evaluateTimer.stop();

                // Select the offspring population.
                final CompletableFuture<TimedResult<Population<G, C>>> offspring =
                        _executor.async(() ->
                                selectOffspring(startPopulation),
                                _clock
                        );

                // Select the survivor population.
                final CompletableFuture<TimedResult<Population<G, C>>> survivors =
                        _executor.async(() ->
                                selectSurvivors(startPopulation),
                                _clock
                        );

                // Altering the offspring population.
                final CompletableFuture<TimedResult<AlterResult<G, C>>> alteredOffspring =
                        _executor.thenApply(offspring, p ->
                                alter(p.result, start.getGeneration()),
                                _clock
                        );

                // Filter and replace invalid and to old survivor individuals.
                final CompletableFuture<TimedResult<FilterResult<G, C>>> filteredSurvivors =
                        _executor.thenApply(survivors, pop ->
                                filter(pop.result, start.getGeneration()),
                                _clock
                        );

                // Filter and replace invalid and to old offspring individuals.
                final CompletableFuture<TimedResult<FilterResult<G, C>>> filteredOffspring =
                        _executor.thenApply(alteredOffspring, pop ->
                                filter(pop.result.population, start.getGeneration()),
                                _clock
                        );

                // Combining survivors and offspring to the new population.
                final CompletableFuture<Population<G, C>> population =
                        filteredSurvivors.thenCombineAsync(filteredOffspring, (s, o) -> {
                                        final Population<G, C> pop = s.result.population;
                                        pop.addAll(o.result.population);
                                        return pop;
                                },
                                _executor.get()
                        );

                // Evaluate the fitness-function and wait for result.
                final TimedResult<Population<G, C>> result = population
                        .thenApply(TimedResult.of(this::evaluate, _clock))
                        .join();

                final EvolutionDurations durations = EvolutionDurations.of(
                        offspring.join().duration,
                        survivors.join().duration,
                        alteredOffspring.join().duration,
                        filteredOffspring.join().duration,
                        filteredSurvivors.join().duration,
                        result.duration.plus(evaluateTimer.getTime()),
                        timer.stop().getTime()
                );

                final int killCount =
                        filteredOffspring.join().result.killCount +
                        filteredSurvivors.join().result.killCount;

                final int invalidCount =
                        filteredOffspring.join().result.invalidCount +
                        filteredSurvivors.join().result.invalidCount;

                return EvolutionResult.of(
                        _optimize,
                        result.result,
                        start.getGeneration(),
                        durations,
                        killCount,
                        invalidCount,
                        alteredOffspring.join().result.alterCount
                );
        }

        /**
         * This method is an <i>alias</i> for the {@link #evolve(EvolutionStart)}
         * method.
         *
         * @since 3.1
         */
        @Override
        public EvolutionResult<G, C> apply(final EvolutionStart<G, C> start) {
                return evolve(start);
        }

        // Selects the survivors population. A new population object is returned.
        private Population<G, C> selectSurvivors(final Population<G, C> population) {
                return _survivorsCount > 0
                        ?_survivorsSelector.select(population, _survivorsCount, _optimize)
                        : Population.empty();
        }

        // Selects the offspring population. A new population object is returned.
        private Population<G, C> selectOffspring(final Population<G, C> population) {
                return _offspringCount > 0
                        ? _offspringSelector.select(population, _offspringCount, _optimize)
                        : Population.empty();
        }

        // Filters out invalid and to old individuals. Filtering is done in place.
        private FilterResult<G, C> filter(
                final Population<G, C> population,
                final long generation
        ) {
                int killCount = 0;
                int invalidCount = 0;

                for (int i = 0, n = population.size(); i < n; ++i) {
                        final Phenotype<G, C> individual = population.get(i);

                        if (!_validator.test(individual)) {
                                population.set(i, newPhenotype(generation));
                                ++invalidCount;
                        } else if (individual.getAge(generation) > _maximalPhenotypeAge) {
                                population.set(i, newPhenotype(generation));
                                ++killCount;
                        }
                }

                return new FilterResult<>(population, killCount, invalidCount);
        }

        // Create a new and valid phenotype
        private Phenotype<G, C> newPhenotype(final long generation) {
                int count = 0;
                Phenotype<G, C> phenotype;
                do {
                        phenotype = Phenotype.of(
                                _genotypeFactory.newInstance(),
                                generation,
                                _fitnessFunction,
                                _fitnessScaler
                        );
                } while (++count < _individualCreationRetries &&
                                !_validator.test(phenotype));

                return phenotype;
        }

        // Alters the given population. The altering is done in place.
        private AlterResult<G, C> alter(
                final Population<G,C> population,
                final long generation
        ) {
                return new AlterResult<>(
                        population,
                        _alterer.alter(population, generation)
                );
        }

        // Evaluates the fitness function of the give population concurrently.
        private Population<G, C> evaluate(final Population<G, C> population) {
                try (Concurrency c = Concurrency.with(_executor.get())) {
                        c.execute(population);
                }
                return population;
        }

        /**
         * Create a new <b>infinite</b> evolution iterator with a newly created
         * population. This is an alternative way for evolution. It lets the user
         * start, stop and resume the evolution process whenever desired.
         *
         * @return a new <b>infinite</b> evolution iterator
         */
        public Iterator<EvolutionResult<G, C>> iterator() {
                return new EvolutionIterator<>(
                        this::evolve,
                        this::evolutionStart
                );
        }

        /**
         * Create a new <b>infinite</b> evolution stream with a newly created
         * population.
         *
         * @return a new evolution stream.
         */
        public EvolutionStream<G, C> stream() {
                return EvolutionStream.of(this::evolutionStart, this::evolve);
        }

        private EvolutionStart<G, C> evolutionStart() {
                final int generation = 1;
                final int size = _offspringCount + _survivorsCount;

                final Population<G, C> population = new Population<G, C>(size)
                        .fill(() -> newPhenotype(generation), size);

                return EvolutionStart.of(population, generation);
        }

        /**
         * Create a new <b>infinite</b> evolution stream with the given initial
         * individuals. If an empty {@code Iterable} is given, the engines genotype
         * factory is used for creating the population.
         *
         * @param genotypes the initial individuals used for the evolution stream.
         *        Missing individuals are created and individuals not needed are
         *        skipped.
         * @return a new evolution stream.
         * @throws java.lang.NullPointerException if the given {@code genotypes} is
         *         {@code null}.
         */
        public EvolutionStream<G, C> stream(
                final Iterable<Genotype<G>> genotypes
        ) {
                requireNonNull(genotypes);

                return EvolutionStream.of(
                        () -> evolutionStart(genotypes, 1),
                        this::evolve
                );
        }

        /**
         * Create a new <b>infinite</b> evolution iterator with the given initial
         * individuals. If an empty {@code Iterable} is given, the engines genotype
         * factory is used for creating the population.
         *
         * @param genotypes the initial individuals used for the evolution iterator.
         *        Missing individuals are created and individuals not needed are
         *        skipped.
         * @return a new <b>infinite</b> evolution iterator
         * @throws java.lang.NullPointerException if the given {@code genotypes} is
         *         {@code null}.
         */
        public Iterator<EvolutionResult<G, C>> iterator(
                final Iterable<Genotype<G>> genotypes
        ) {
                requireNonNull(genotypes);

                return new EvolutionIterator<>(
                        this::evolve,
                        () -> evolutionStart(genotypes, 1)
                );
        }

        private EvolutionStart<G, C> evolutionStart(
                final Iterable<Genotype<G>> genotypes,
                final long generation
        ) {
                final Stream<Phenotype<G, C>> stream = Stream.concat(
                        StreamSupport.stream(genotypes.spliterator(), false)
                                .map(gt -> Phenotype.of(
                                        gt, generation, _fitnessFunction, _fitnessScaler)),
                        Stream.generate(() -> newPhenotype(generation))
                );

                final Population<G, C> population = stream
                        .limit(getPopulationSize())
                        .collect(toPopulation());

                return EvolutionStart.of(population, generation);
        }

        /**
         * Create a new <b>infinite</b> evolution stream with the given initial
         * population. If an empty {@code Population} is given, the engines genotype
         * factory is used for creating the population. The given population might
         * be the result of an other engine and this method allows to start the
         * evolution with the outcome of an different engine. The fitness function
         * and the fitness scaler are replaced by the one defined for this engine.
         *
         * @param population the initial individuals used for the evolution stream.
         *        Missing individuals are created and individuals not needed are
         *        skipped.
         * @param generation the generation the stream starts from; must be greater
         *        than zero.
         * @return a new evolution stream.
         * @throws java.lang.NullPointerException if the given {@code population} is
         *         {@code null}.
         * @throws IllegalArgumentException if the given {@code generation} is smaller
         *        then one
         */
        public EvolutionStream<G, C> stream(
                final Population<G, C> population,
                final long generation
        ) {
                requireNonNull(population);
                require.positive(generation);

                return EvolutionStream.of(
                        () -> evolutionStart(population, generation),
                        this::evolve
                );
        }

        /**
         * Create a new <b>infinite</b> evolution iterator with the given initial
         * population. If an empty {@code Population} is given, the engines genotype
         * factory is used for creating the population. The given population might
         * be the result of an other engine and this method allows to start the
         * evolution with the outcome of an different engine. The fitness function
         * and the fitness scaler are replaced by the one defined for this engine.
         *
         * @param population the initial individuals used for the evolution iterator.
         *        Missing individuals are created and individuals not needed are
         *        skipped.
         * @param generation the generation the iterator starts from; must be greater
         *        than zero.
         * @return a new <b>infinite</b> evolution iterator
         * @throws java.lang.NullPointerException if the given {@code population} is
         *         {@code null}.
         * @throws IllegalArgumentException if the given {@code generation} is smaller
         *        then one
         */
        public Iterator<EvolutionResult<G, C>> iterator(
                final Population<G, C> population,
                final long generation
        ) {
                requireNonNull(population);
                require.positive(generation);

                return new EvolutionIterator<>(
                        this::evolve,
                        () -> evolutionStart(population, generation)
                );
        }

        private EvolutionStart<G, C> evolutionStart(
                final Population<G, C> population,
                final long generation
        ) {
                final Stream<Phenotype<G, C>> stream = Stream.concat(
                        population.stream()
                                .map(p -> p.newInstance(
                                        p.getGeneration(),
                                        _fitnessFunction,
                                        _fitnessScaler)),
                        Stream.generate(() -> newPhenotype(generation))
                );

                final Population<G, C> pop = stream
                        .limit(getPopulationSize())
                        .collect(toPopulation());

                return EvolutionStart.of(pop, generation);
        }



        /* *************************************************************************
         * Property access methods.
         **************************************************************************/

        /**
         * Return the fitness function of the GA engine.
         *
         * @return the fitness function
         */
        public Function<? super Genotype<G>, ? extends C> getFitnessFunction() {
                return _fitnessFunction;
        }

        /**
         * Return the fitness scaler of the GA engine.
         *
         * @return the fitness scaler
         */
        public Function<? super C, ? extends C> getFitnessScaler() {
                return _fitnessScaler;
        }

        /**
         * Return the used genotype {@link Factory} of the GA. The genotype factory
         * is used for creating the initial population and new, random individuals
         * when needed (as replacement for invalid and/or died genotypes).
         *
         * @return the used genotype {@link Factory} of the GA.
         */
        public Factory<Genotype<G>> getGenotypeFactory() {
                return _genotypeFactory;
        }

        /**
         * Return the used survivor {@link Selector} of the GA.
         *
         * @return the used survivor {@link Selector} of the GA.
         */
        public Selector<G, C> getSurvivorsSelector() {
                return _survivorsSelector;
        }

        /**
         * Return the used offspring {@link Selector} of the GA.
         *
         * @return the used offspring {@link Selector} of the GA.
         */
        public Selector<G, C> getOffspringSelector() {
                return _offspringSelector;
        }

        /**
         * Return the used {@link Alterer} of the GA.
         *
         * @return the used {@link Alterer} of the GA.
         */
        public Alterer<G, C> getAlterer() {
                return _alterer;
        }

        /**
         * Return the number of selected offsprings.
         *
         * @return the number of selected offsprings
         */
        public int getOffspringCount() {
                return _offspringCount;
        }

        /**
         * The number of selected survivors.
         *
         * @return the number of selected survivors
         */
        public int getSurvivorsCount() {
                return _survivorsCount;
        }

        /**
         * Return the number of individuals of a population.
         *
         * @return the number of individuals of a population
         */
        public int getPopulationSize() {
                return _offspringCount + _survivorsCount;
        }

        /**
         * Return the maximal allowed phenotype age.
         *
         * @return the maximal allowed phenotype age
         */
        public long getMaximalPhenotypeAge() {
                return _maximalPhenotypeAge;
        }

        /**
         * Return the optimization strategy.
         *
         * @return the optimization strategy
         */
        public Optimize getOptimize() {
                return _optimize;
        }

        /**
         * Return the {@link Clock} the engine is using for measuring the execution
         * time.
         *
         * @return the clock used for measuring the execution time
         */
        public Clock getClock() {
                return _clock;
        }

        /**
         * Return the {@link Executor} the engine is using for executing the
         * evolution steps.
         *
         * @return the executor used for performing the evolution steps
         */
        public Executor getExecutor() {
                return _executor.get();
        }


        /* *************************************************************************
         * Builder methods.
         **************************************************************************/

        /**
         * Create a new evolution {@code Engine.Builder} initialized with the values
         * of the current evolution {@code Engine}. With this method, the evolution
         * engine can serve as a template for an new one.
         *
         * @return a new engine builder
         */
        public Builder<G, C> builder() {
                return new Builder<>(_genotypeFactory, _fitnessFunction)
                        .alterers(_alterer)
                        .clock(_clock)
                        .executor(_executor.get())
                        .fitnessScaler(_fitnessScaler)
                        .maximalPhenotypeAge(_maximalPhenotypeAge)
                        .offspringFraction((double)_offspringCount/(double)getPopulationSize())
                        .offspringSelector(_offspringSelector)
                        .optimize(_optimize)
                        .phenotypeValidator(_validator)
                        .populationSize(getPopulationSize())
                        .survivorsSelector(_survivorsSelector)
                        .individualCreationRetries(_individualCreationRetries);
        }

        /**
         * Create a new evolution {@code Engine.Builder} for the given
         * {@link Problem}.
         *
         * @since 3.4
         *
         * @param problem the problem to be solved by the evolution {@code Engine}
         * @param <T> the (<i>native</i>) argument type of the problem fitness function
         * @param <G> the gene type the evolution engine is working with
         * @param <C> the result type of the fitness function
         * @return Create a new evolution {@code Engine.Builder}
         */
        public static <T, G extends Gene<?, G>, C extends Comparable<? super C>>
        Builder<G, C> builder(final Problem<T, G, C> problem) {
                return builder(problem.fitness(), problem.codec());
        }

        /**
         * Create a new evolution {@code Engine.Builder} with the given fitness
         * function and genotype factory.
         *
         * @param ff the fitness function
         * @param genotypeFactory the genotype factory
         * @param <G> the gene type
         * @param <C> the fitness function result type
         * @return a new engine builder
         * @throws java.lang.NullPointerException if one of the arguments is
         *         {@code null}.
         */
        public static <G extends Gene<?, G>, C extends Comparable<? super C>>
        Builder<G, C> builder(
                final Function<? super Genotype<G>, ? extends C> ff,
                final Factory<Genotype<G>> genotypeFactory
        ) {
                return new Builder<>(genotypeFactory, ff);
        }

        /**
         * Create a new evolution {@code Engine.Builder} with the given fitness
         * function and chromosome templates.
         *
         * @param ff the fitness function
         * @param chromosome the first chromosome
         * @param chromosomes the chromosome templates
         * @param <G> the gene type
         * @param <C> the fitness function result type
         * @return a new engine builder
         * @throws java.lang.NullPointerException if one of the arguments is
         *         {@code null}.
         */
        @SafeVarargs
        public static <G extends Gene<?, G>, C extends Comparable<? super C>>
        Builder<G, C> builder(
                final Function<? super Genotype<G>, ? extends C> ff,
                final Chromosome<G> chromosome,
                final Chromosome<G>... chromosomes
        ) {
                return new Builder<>(Genotype.of(chromosome, chromosomes), ff);
        }

        /**
         * Create a new evolution {@code Engine.Builder} with the given fitness
         * function and problem {@code codec}.
         *
         * @since 3.2
         *
         * @param ff the fitness function
         * @param codec the problem codec
         * @param <T> the fitness function input type
         * @param <C> the fitness function result type
         * @param <G> the gene type
         * @return a new engine builder
         * @throws java.lang.NullPointerException if one of the arguments is
         *         {@code null}.
         */
        public static <T, G extends Gene<?, G>, C extends Comparable<? super C>>
        Builder<G, C> builder(
                final Function<? super T, ? extends C> ff,
                final Codec<T, G> codec
        ) {
                return builder(ff.compose(codec.decoder()), codec.encoding());
        }


        /* *************************************************************************
         * Inner classes
         **************************************************************************/

        /**
         * Builder class for building GA {@code Engine} instances.
         *
         * @see Engine
         *
         * @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
         * @since 3.0
         * @version 3.0
         */
        public static final class Builder<
                G extends Gene<?, G>,
                C extends Comparable<? super C>
        >
                implements Copyable<Builder<G, C>>
        {

                // No default values for this properties.
                private Function<? super Genotype<G>, ? extends C> _fitnessFunction;
                private Factory<Genotype<G>> _genotypeFactory;

                // This are the properties which default values.
                private Function<? super C, ? extends C> _fitnessScaler = a -> a;
                private Selector<G, C> _survivorsSelector = new TournamentSelector<>(3);
                private Selector<G, C> _offspringSelector = new TournamentSelector<>(3);
                private Alterer<G, C> _alterer = Alterer.of(
                        new SinglePointCrossover<G, C>(0.2),
                        new Mutator<>(0.15)
                );
                private Predicate<? super Phenotype<G, C>> _validator = Phenotype::isValid;
                private Optimize _optimize = Optimize.MAXIMUM;
                private double _offspringFraction = 0.6;
                private int _populationSize = 50;
                private long _maximalPhenotypeAge = 70;

                private Executor _executor = ForkJoinPool.commonPool();
                private Clock _clock = NanoClock.systemUTC();

                private int _individualCreationRetries = 10;

                private Builder(
                        final Factory<Genotype<G>> genotypeFactory,
                        final Function<? super Genotype<G>, ? extends C> fitnessFunction
                ) {
                        _genotypeFactory = requireNonNull(genotypeFactory);
                        _fitnessFunction = requireNonNull(fitnessFunction);
                }

                /**
                 * Set the fitness function of the evolution {@code Engine}.
                 *
                 * @param function the fitness function to use in the GA {@code Engine}
                 * @return {@code this} builder, for command chaining
                 */
                public Builder<G, C> fitnessFunction(
                        Function<? super Genotype<G>, ? extends C> function
                ) {
                        _fitnessFunction = requireNonNull(function);
                        return this;
                }

                /**
                 * Set the fitness scaler of the evolution {@code Engine}. <i>Default
                 * value is set to the identity function.</i>
                 *
                 * @param scaler the fitness scale to use in the GA {@code Engine}
                 * @return {@code this} builder, for command chaining
                 */
                public Builder<G, C> fitnessScaler(
                        final Function<? super C, ? extends C> scaler
                ) {
                        _fitnessScaler = requireNonNull(scaler);
                        return this;
                }

                /**
                 * The genotype factory used for creating new individuals.
                 *
                 * @param genotypeFactory the genotype factory for creating new
                 *        individuals.
                 * @return {@code this} builder, for command chaining
                 */
                public Builder<G, C> genotypeFactory(
                        final Factory<Genotype<G>> genotypeFactory
                ) {
                        _genotypeFactory = requireNonNull(genotypeFactory);
                        return this;
                }

                /**
                 * The selector used for selecting the offspring population. <i>Default
                 * values is set to {@code TournamentSelector<>(3)}.</i>
                 *
                 * @param selector used for selecting the offspring population
                 * @return {@code this} builder, for command chaining
                 */
                public Builder<G, C> offspringSelector(
                        final Selector<G, C> selector
                ) {
                        _offspringSelector = requireNonNull(selector);
                        return this;
                }

                /**
                 * The selector used for selecting the survivors population. <i>Default
                 * values is set to {@code TournamentSelector<>(3)}.</i>
                 *
                 * @param selector used for selecting survivors population
                 * @return {@code this} builder, for command chaining
                 */
                public Builder<G, C> survivorsSelector(
                        final Selector<G, C> selector
                ) {
                        _survivorsSelector = requireNonNull(selector);
                        return this;
                }

                /**
                 * The selector used for selecting the survivors and offspring
                 * population. <i>Default values is set to
                 * {@code TournamentSelector<>(3)}.</i>
                 *
                 * @param selector used for selecting survivors and offspring population
                 * @return {@code this} builder, for command chaining
                 */
                public Builder<G, C> selector(final Selector<G, C> selector) {
                        _offspringSelector = requireNonNull(selector);
                        _survivorsSelector = requireNonNull(selector);
                        return this;
                }

                /**
                 * The alterers used for alter the offspring population. <i>Default
                 * values is set to {@code new SinglePointCrossover<>(0.2)} followed by
                 * {@code new Mutator<>(0.15)}.</i>
                 *
                 * @param first the first alterer used for alter the offspring
                 *        population
                 * @param rest the rest of the alterers used for alter the offspring
                 *        population
                 * @return {@code this} builder, for command chaining
                 * @throws java.lang.NullPointerException if one of the alterers is
                 *         {@code null}.
                 */
                @SafeVarargs
                public final Builder<G, C> alterers(
                        final Alterer<G, C> first,
                        final Alterer<G, C>... rest
                ) {
                        requireNonNull(first);
                        Stream.of(rest).forEach(Objects::requireNonNull);

                        _alterer = rest.length == 0 ?
                                first :
                                Alterer.of(rest).compose(first);

                        return this;
                }

                /**
                 * The phenotype validator used for detecting invalid individuals.
                 * Alternatively it is also possible to set the genotype validator with
                 * {@link #genotypeFactory(Factory)}, which will replace any
                 * previously set phenotype validators.
                 *
                 * <p><i>Default value is set to {@code Phenotype::isValid}.</i></p>
                 *
                 * @since 3.1
                 *
                 * @see #genotypeValidator(Predicate)
                 *
                 * @param validator the {@code validator} used for validating the
                 *        individuals (phenotypes).
                 * @return {@code this} builder, for command chaining
                 * @throws java.lang.NullPointerException if the {@code validator} is
                 *         {@code null}.
                 */
                public Builder<G, C> phenotypeValidator(
                        final Predicate<? super Phenotype<G, C>> validator
                ) {
                        _validator = requireNonNull(validator);
                        return this;
                }

                /**
                 * The genotype validator used for detecting invalid individuals.
                 * Alternatively it is also possible to set the phenotype validator with
                 * {@link #phenotypeValidator(Predicate)}, which will replace any
                 * previously set genotype validators.
                 *
                 * <p><i>Default value is set to {@code Genotype::isValid}.</i></p>
                 *
                 * @since 3.1
                 *
                 * @see #phenotypeValidator(Predicate)
                 *
                 * @param validator the {@code validator} used for validating the
                 *        individuals (genotypes).
                 * @return {@code this} builder, for command chaining
                 * @throws java.lang.NullPointerException if the {@code validator} is
                 *         {@code null}.
                 */
                public Builder<G, C> genotypeValidator(
                        final Predicate<? super Genotype<G>> validator
                ) {
                        requireNonNull(validator);

                        _validator = pt -> validator.test(pt.getGenotype());
                        return this;
                }

                /**
                 * The optimization strategy used by the engine. <i>Default values is
                 * set to {@code Optimize.MAXIMUM}.</i>
                 *
                 * @param optimize the optimization strategy used by the engine
                 * @return {@code this} builder, for command chaining
                 */
                public Builder<G, C> optimize(final Optimize optimize) {
                        _optimize = requireNonNull(optimize);
                        return this;
                }

                /**
                 * Set to a fitness maximizing strategy.
                 *
                 * @since 3.4
                 *
                 * @return {@code this} builder, for command chaining
                 */
                public Builder<G, C> maximizing() {
                        return optimize(Optimize.MAXIMUM);
                }

                /**
                 * Set to a fitness minimizing strategy.
                 *
                 * @since 3.4
                 *
                 * @return {@code this} builder, for command chaining
                 */
                public Builder<G, C> minimizing() {
                        return optimize(Optimize.MINIMUM);
                }

                /**
                 * The offspring fraction. <i>Default values is set to {@code 0.6}.</i>
                 *
                 * @param fraction the offspring fraction
                 * @return {@code this} builder, for command chaining
                 * @throws java.lang.IllegalArgumentException if the fraction is not
                 *         within the range [0, 1].
                 */
                public Builder<G, C> offspringFraction(final double fraction) {
                        _offspringFraction = probability(fraction);
                        return this;
                }

                /**
                 * The number of individuals which form the population. <i>Default
                 * values is set to {@code 50}.</i>
                 *
                 * @param size the number of individuals of a population
                 * @return {@code this} builder, for command chaining
                 * @throws java.lang.IllegalArgumentException if {@code size < 1}
                 */
                public Builder<G, C> populationSize(final int size) {
                        if (size < 1) {
                                throw new IllegalArgumentException(format(
                                        "Population size must be greater than zero, but was %s.", size
                                ));
                        }
                        _populationSize = size;
                        return this;
                }

                /**
                 * The maximal allowed age of a phenotype. <i>Default values is set to
                 * {@code 70}.</i>
                 *
                 * @param age the maximal phenotype age
                 * @return {@code this} builder, for command chaining
                 * @throws java.lang.IllegalArgumentException if {@code age < 1}
                 */
                public Builder<G, C> maximalPhenotypeAge(final long age) {
                        if (age < 1) {
                                throw new IllegalArgumentException(format(
                                        "Phenotype age must be greater than one, but was %s.", age
                                ));
                        }
                        _maximalPhenotypeAge = age;
                        return this;
                }

                /**
                 * The executor used by the engine.
                 *
                 * @param executor the executor used by the engine
                 * @return {@code this} builder, for command chaining
                 */
                public Builder<G, C> executor(final Executor executor) {
                        _executor = requireNonNull(executor);
                        return this;
                }

                /**
                 * The clock used for calculating the execution durations.
                 *
                 * @param clock the clock used for calculating the execution durations
                 * @return {@code this} builder, for command chaining
                 */
                public Builder<G, C> clock(final Clock clock) {
                        _clock = requireNonNull(clock);
                        return this;
                }

                /**
                 * The maximal number of attempt before the {@code Engine} gives up
                 * creating a valid individual ({@code Phenotype}). <i>Default values is
                 * set to {@code 10}.</i>
                 *
                 * @since 3.1
                 *
                 * @param retries the maximal retry count
                 * @throws IllegalArgumentException if the given retry {@code count} is
                 *         smaller than zero.
                 * @return {@code this} builder, for command chaining
                 */
                public Builder<G, C> individualCreationRetries(final int retries) {
                        if (retries < 0) {
                                throw new IllegalArgumentException(format(
                                        "Retry count must not be negative: %d",
                                        retries
                                ));
                        }
                        _individualCreationRetries = retries;
                        return this;
                }

                /**
                 * Builds an new {@code Engine} instance from the set properties.
                 *
                 * @return an new {@code Engine} instance from the set properties
                 */
                public Engine<G, C> build() {
                        return new Engine<>(
                                _fitnessFunction,
                                _fitnessScaler,
                                _genotypeFactory,
                                _survivorsSelector,
                                _offspringSelector,
                                _alterer,
                                _validator,
                                _optimize,
                                getOffspringCount(),
                                getSurvivorsCount(),
                                _maximalPhenotypeAge,
                                _executor,
                                _clock,
                                _individualCreationRetries
                        );
                }

                private int getSurvivorsCount() {
                        return _populationSize - getOffspringCount();
                }

                private int getOffspringCount() {
                        return (int)round(_offspringFraction*_populationSize);
                }

                /**
                 * Return the used {@link Alterer} of the GA.
                 *
                 * @return the used {@link Alterer} of the GA.
                 */
                public Alterer<G, C> getAlterers() {
                        return _alterer;
                }

                /**
                 * Return the {@link Clock} the engine is using for measuring the execution
                 * time.
                 *
                 * @since 3.1
                 *
                 * @return the clock used for measuring the execution time
                 */
                public Clock getClock() {
                        return _clock;
                }

                /**
                 * Return the {@link Executor} the engine is using for executing the
                 * evolution steps.
                 *
                 * @since 3.1
                 *
                 * @return the executor used for performing the evolution steps
                 */
                public Executor getExecutor() {
                        return _executor;
                }

                /**
                 * Return the fitness function of the GA engine.
                 *
                 * @since 3.1
                 *
                 * @return the fitness function
                 */
                public Function<? super Genotype<G>, ? extends C> getFitnessFunction() {
                        return _fitnessFunction;
                }

                /**
                 * Return the fitness scaler of the GA engine.
                 *
                 * @since 3.1
                 *
                 * @return the fitness scaler
                 */
                public Function<? super C, ? extends C> getFitnessScaler() {
                        return _fitnessScaler;
                }

                /**
                 * Return the used genotype {@link Factory} of the GA. The genotype factory
                 * is used for creating the initial population and new, random individuals
                 * when needed (as replacement for invalid and/or died genotypes).
                 *
                 * @since 3.1
                 *
                 * @return the used genotype {@link Factory} of the GA.
                 */
                public Factory<Genotype<G>> getGenotypeFactory() {
                        return _genotypeFactory;
                }

                /**
                 * Return the maximal allowed phenotype age.
                 *
                 * @since 3.1
                 *
                 * @return the maximal allowed phenotype age
                 */
                public long getMaximalPhenotypeAge() {
                        return _maximalPhenotypeAge;
                }

                /**
                 * Return the offspring fraction.
                 *
                 * @return the offspring fraction.
                 */
                public double getOffspringFraction() {
                        return _offspringFraction;
                }

                /**
                 * Return the used offspring {@link Selector} of the GA.
                 *
                 * @since 3.1
                 *
                 * @return the used offspring {@link Selector} of the GA.
                 */
                public Selector<G, C> getOffspringSelector() {
                        return _offspringSelector;
                }

                /**
                 * Return the used survivor {@link Selector} of the GA.
                 *
                 * @since 3.1
                 *
                 * @return the used survivor {@link Selector} of the GA.
                 */
                public Selector<G, C> getSurvivorsSelector() {
                        return _survivorsSelector;
                }

                /**
                 * Return the optimization strategy.
                 *
                 * @since 3.1
                 *
                 * @return the optimization strategy
                 */
                public Optimize getOptimize() {
                        return _optimize;
                }

                /**
                 * Return the number of individuals of a population.
                 *
                 * @since 3.1
                 *
                 * @return the number of individuals of a population
                 */
                public int getPopulationSize() {
                        return _populationSize;
                }

                /**
                 * Return the maximal number of attempt before the {@code Engine} gives
                 * up creating a valid individual ({@code Phenotype}).
                 *
                 * @since 3.1
                 *
                 * @return the maximal number of {@code Phenotype} creation attempts
                 */
                public int getIndividualCreationRetries() {
                        return _individualCreationRetries;
                }

                /**
                 * Create a new builder, with the current configuration.
                 *
                 * @since 3.1
                 *
                 * @return a new builder, with the current configuration
                 */
                @Override
                public Builder<G, C> copy() {
                        return new Builder<>(_genotypeFactory, _fitnessFunction)
                                .alterers(_alterer)
                                .clock(_clock)
                                .executor(_executor)
                                .fitnessScaler(_fitnessScaler)
                                .maximalPhenotypeAge(_maximalPhenotypeAge)
                                .offspringFraction(_offspringFraction)
                                .offspringSelector(_offspringSelector)
                                .phenotypeValidator(_validator)
                                .optimize(_optimize)
                                .populationSize(_populationSize)
                                .survivorsSelector(_survivorsSelector)
                                .individualCreationRetries(_individualCreationRetries);
                }

        }
}