/*
 * Java Genetic Algorithm Library (jenetics-5.1.0).
 * Copyright (c) 2007-2019 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@gmail.com)
 */
package io.jenetics.engine;

import static java.lang.Math.round;
import static java.lang.String.format;
import static java.util.Objects.requireNonNull;
import static java.util.concurrent.CompletableFuture.supplyAsync;
import static java.util.concurrent.ForkJoinPool.commonPool;
import static io.jenetics.internal.util.require.probability;

import java.time.Clock;
import java.util.Objects;
import java.util.concurrent.CompletableFuture;
import java.util.concurrent.Executor;
import java.util.function.Function;
import java.util.function.Supplier;
import java.util.function.UnaryOperator;
import java.util.stream.Stream;

import io.jenetics.Alterer;
import io.jenetics.AltererResult;
import io.jenetics.Chromosome;
import io.jenetics.Gene;
import io.jenetics.Genotype;
import io.jenetics.Mutator;
import io.jenetics.Optimize;
import io.jenetics.Phenotype;
import io.jenetics.Selector;
import io.jenetics.SinglePointCrossover;
import io.jenetics.TournamentSelector;
import io.jenetics.internal.util.require;
import io.jenetics.util.Copyable;
import io.jenetics.util.Factory;
import io.jenetics.util.ISeq;
import io.jenetics.util.MSeq;
import io.jenetics.util.NanoClock;
import io.jenetics.util.Seq;

/**
 * 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}.
 *
 * @implNote
 *     This class is thread safe:
 *     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.
 *
 * @see Engine.Builder
 * @see EvolutionStart
 * @see EvolutionResult
 * @see EvolutionStream
 * @see EvolutionStatistics
 * @see Codec
 *
 * @author <a href="mailto:franz.wilhelmstoetter@gmail.com">Franz Wilhelmstötter</a>
 * @since 3.0
 * @version 5.1
 */
public final class Engine<
        G extends Gene<?, G>,
        C extends Comparable<? super C>
>
        implements
                Evolution<G, C>,
                Function<EvolutionStart<G, C>, EvolutionResult<G, C>>,
                EvolutionStreamable<G, C>
{

        // Problem definition.
        private final Evaluator<G, C> _evaluator;
        private final Factory<Genotype<G>> _genotypeFactory;

        // Evolution parameters.
        private final Selector<G, C> _survivorsSelector;
        private final Selector<G, C> _offspringSelector;
        private final Alterer<G, C> _alterer;
        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 Executor _executor;
        private final Clock _clock;

        // Additional parameters.
        private final Constraint<G, C> _constraint;
        private final UnaryOperator<EvolutionResult<G, C>> _mapper;


        /**
         * Create a new GA engine with the given parameters.
         *
         * @param genotypeFactory the genotype factory this GA is working with.
         * @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 constraint phenotype constraint which can override the default
         *        implementation the {@link Phenotype#isValid()} method and repairs
         *        invalid phenotypes when needed.
         * @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 evaluator the population fitness evaluator
         * @param clock the clock used for calculating the timing results
         * @throws NullPointerException if one of the arguments is {@code null}
         * @throws IllegalArgumentException if the given integer values are smaller
         *         than one.
         */
        Engine(
                final Evaluator<G, C> evaluator,
                final Factory<Genotype<G>> genotypeFactory,
                final Selector<G, C> survivorsSelector,
                final Selector<G, C> offspringSelector,
                final Alterer<G, C> alterer,
                final Constraint<G, C> constraint,
                final Optimize optimize,
                final int offspringCount,
                final int survivorsCount,
                final long maximalPhenotypeAge,
                final Executor executor,
                final Clock clock,
                final UnaryOperator<EvolutionResult<G, C>> mapper
        ) {
                _evaluator = requireNonNull(evaluator);
                _genotypeFactory = requireNonNull(genotypeFactory);
                _survivorsSelector = requireNonNull(survivorsSelector);
                _offspringSelector = requireNonNull(offspringSelector);
                _alterer = requireNonNull(alterer);
                _constraint = requireNonNull(constraint);
                _optimize = requireNonNull(optimize);

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

                _executor = requireNonNull(executor);
                _clock = requireNonNull(clock);
                _mapper = requireNonNull(mapper);
        }

        /**
         * This method is an <i>alias</i> for the {@link #evolve(EvolutionStart)}
         * method.
         *
         * @since 3.1
         *
         * @see Evolution
         *
         * @deprecated Will be removed and superseded by {@link #evolve(EvolutionStart)}
         */
        @Deprecated
        @Override
        public EvolutionResult<G, C> apply(final EvolutionStart<G, C> start) {
                return evolve(start);
        }

        @Override
        public EvolutionResult<G, C> evolve(final EvolutionStart<G, C> start) {
                // Create initial population if `start` is empty.
                final EvolutionStart<G, C> es = start.getPopulation().isEmpty()
                        ? evolutionStart(start)
                        : start;

                final EvolutionTiming timing = new EvolutionTiming(_clock);
                timing.evolve.start();

                // Initial evaluation of the population.
                final ISeq<Phenotype<G, C>> evaluated = timing.evaluation.timing(() ->
                        evaluate(es.getPopulation())
                );

                // Select the offspring population.
                final CompletableFuture<ISeq<Phenotype<G, C>>> offspring =
                        supplyAsync(() ->
                                timing.offspringSelection.timing(() ->
                                        selectOffspring(evaluated)
                                ),
                                _executor
                        );

                // Select the survivor population.
                final CompletableFuture<ISeq<Phenotype<G, C>>> survivors =
                        supplyAsync(() ->
                                timing.survivorsSelection.timing(() ->
                                        selectSurvivors(evaluated)
                                ),
                                _executor
                        );

                // Altering the offspring population.
                final CompletableFuture<AltererResult<G, C>> alteredOffspring =
                        offspring.thenApplyAsync(off ->
                                timing.offspringAlter.timing(() ->
                                        _alterer.alter(off, es.getGeneration())
                                ),
                                _executor
                        );

                // Filter and replace invalid and old survivor individuals.
                final CompletableFuture<FilterResult<G, C>> filteredSurvivors =
                        survivors.thenApplyAsync(sur ->
                                timing.survivorFilter.timing(() ->
                                        filter(sur, es.getGeneration())
                                ),
                                _executor
                        );

                // Filter and replace invalid and old offspring individuals.
                final CompletableFuture<FilterResult<G, C>> filteredOffspring =
                        alteredOffspring.thenApplyAsync(off ->
                                timing.offspringFilter.timing(() ->
                                        filter(off.getPopulation(), es.getGeneration())
                                ),
                                _executor
                        );

                // Combining survivors and offspring to the new population.
                final CompletableFuture<ISeq<Phenotype<G, C>>> population =
                        filteredSurvivors.thenCombineAsync(
                                filteredOffspring,
                                (s, o) -> ISeq.of(s.population.append(o.population)),
                                _executor
                        );

                // Evaluate the fitness-function and wait for result.
                final ISeq<Phenotype<G, C>> pop = population.join();
                final ISeq<Phenotype<G, C>> result = timing.evaluation.timing(() ->
                        evaluate(pop)
                );

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

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

                final int alterationCount = alteredOffspring.join().getAlterations();

                EvolutionResult<G, C> er = EvolutionResult.of(
                        _optimize,
                        result,
                        es.getGeneration(),
                        timing.toDurations(),
                        killCount,
                        invalidCount,
                        alterationCount
                );
                if (!UnaryOperator.identity().equals(_mapper)) {
                        final EvolutionResult<G, C> mapped = _mapper.apply(er);
                        er = er.with(timing.evaluation.timing(() ->
                                evaluate(mapped.getPopulation())
                        ));
                }

                timing.evolve.stop();
                return er.with(timing.toDurations());
        }

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

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

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

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

                        if (!_constraint.test(individual)) {
                                pop.set(i, _constraint.repair(individual, generation));
                                ++invalidCount;
                        } else if (individual.getAge(generation) > _maximalPhenotypeAge) {
                                pop.set(i, Phenotype.of(_genotypeFactory.newInstance(), generation));
                                ++killCount;
                        }
                }

                return new FilterResult<>(pop.toISeq(), killCount, invalidCount);
        }


        /* *************************************************************************
         * Evaluation methods.
         **************************************************************************/

        /**
         * Evaluates the fitness function of the given population with the configured
         * {@link Evaluator} of this engine and returns a new population
         * with its fitness value assigned.
         *
         * @since 5.0
         *
         * @see Evaluator
         * @see Evaluator#eval(Seq)
         *
         * @param population the population to evaluate
         * @return a new population with assigned fitness values
         * @throws IllegalStateException if the configured fitness function doesn't
         *         return a population with the same size as the input population.
         *         This exception is also thrown if one of the populations
         *         phenotype has no fitness value assigned.
         */
        public ISeq<Phenotype<G, C>> evaluate(final Seq<Phenotype<G, C>> population) {
                final ISeq<Phenotype<G, C>> evaluated = _evaluator.eval(population);

                if (population.size() != evaluated.size()) {
                        throw new IllegalStateException(format(
                                "Expected %d individuals, but got %d. " +
                                        "Check your evaluator function.",
                                population.size(), evaluated.size()
                        ));
                }
                if (!evaluated.forAll(Phenotype::isEvaluated)) {
                        throw new IllegalStateException(
                                "Some phenotypes have no assigned fitness value. " +
                                        "Check your evaluator function."
                        );
                }

                return evaluated;
        }


        /* *************************************************************************
         * Evolution Stream creation.
         **************************************************************************/

        @Override
        public EvolutionStream<G, C>
        stream(final Supplier<EvolutionStart<G, C>> start) {
                return EvolutionStream.ofEvolution(
                        () -> evolutionStart(start.get()),
                        this
                );
        }

        @Override
        public EvolutionStream<G, C> stream(final EvolutionInit<G> init) {
                return stream(evolutionStart(init));
        }

        private EvolutionStart<G, C>
        evolutionStart(final EvolutionStart<G, C> start) {
                final ISeq<Phenotype<G, C>> population = start.getPopulation();
                final long gen = start.getGeneration();

                final Stream<Phenotype<G, C>> stream = Stream.concat(
                        population.stream(),
                        _genotypeFactory.instances()
                                .map(gt -> Phenotype.of(gt, gen))
                );

                final ISeq<Phenotype<G, C>> pop = stream
                        .limit(getPopulationSize())
                        .collect(ISeq.toISeq());

                return EvolutionStart.of(pop, gen);
        }

        private EvolutionStart<G, C>
        evolutionStart(final EvolutionInit<G> init) {
                final ISeq<Genotype<G>> pop = init.getPopulation();
                final long gen = init.getGeneration();

                return evolutionStart(
                        EvolutionStart.of(
                                pop.map(gt -> Phenotype.of(gt, gen)),
                                gen
                        )
                );
        }

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

        /**
         * 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 constraint of the evolution problem.
         *
         * @since 5.0
         *
         * @return the constraint of the evolution problem
         */
        public Constraint<G, C> getConstraint() {
                return _constraint;
        }

        /**
         * 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;
        }

        /**
         * Return the evolution result mapper.
         *
         * @since 4.0
         *
         * @return the evolution result mapper
         */
        public UnaryOperator<EvolutionResult<G, C>> getMapper() {
                return _mapper;
        }

        /**
         * 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 a new one.
         *
         * @return a new engine builder
         */
        public Builder<G, C> builder() {
                return new Builder<>(_evaluator, _genotypeFactory)
                        .alterers(_alterer)
                        .clock(_clock)
                        .executor(_executor)
                        .maximalPhenotypeAge(_maximalPhenotypeAge)
                        .offspringFraction((double)_offspringCount/(double)getPopulationSize())
                        .offspringSelector(_offspringSelector)
                        .optimize(_optimize)
                        .constraint(_constraint)
                        .populationSize(getPopulationSize())
                        .survivorsSelector(_survivorsSelector)
                        .mapping(_mapper);
        }


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

        /**
         * Create a new evolution {@code Engine.Builder} with the given fitness
         * function and genotype factory.
         *
         * @param ff the fitness function
         * @param gtf 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>> gtf
        ) {
                return new Builder<>(Evaluators.concurrent(ff, commonPool()), gtf);
        }

        /**
         * Create a new evolution {@code Engine.Builder} with the given fitness
         * function and problem {@code codec}.
         *
         * @since 3.2
         *
         * @param ff the fitness evaluator
         * @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());
        }

        /**
         * 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 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 builder(ff, Genotype.of(chromosome, chromosomes));
        }


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


        /**
         * Builder class for building GA {@code Engine} instances.
         *
         * @see Engine
         *
         * @param <G> the gene type
         * @param <C> the fitness function result type
         *
         * @author <a href="mailto:franz.wilhelmstoetter@gmail.com">Franz Wilhelmstötter</a>
         * @since 3.0
         * @version 5.1
         */
        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 final Evaluator<G, C> _evaluator;
                private final Factory<Genotype<G>> _genotypeFactory;

                // This are the properties which default values.
                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 Constraint<G, C> _constraint;
                private Optimize _optimize = Optimize.MAXIMUM;
                private double _offspringFraction = 0.6;
                private int _populationSize = 50;
                private long _maximalPhenotypeAge = 70;

                // Engine execution environment.
                private Executor _executor = commonPool();
                private Clock _clock = NanoClock.systemUTC();

                private UnaryOperator<EvolutionResult<G, C>> _mapper = UnaryOperator.identity();

                /**
                 * Create a new evolution {@code Engine.Builder} with the given fitness
                 * evaluator and genotype factory. This is the most general way for
                 * creating an engine builder.
                 *
                 * @since 5.0
                 *
                 * @see Engine#builder(Function, Codec)
                 * @see Engine#builder(Function, Factory)
                 * @see Engine#builder(Problem)
                 * @see Engine#builder(Function, Chromosome, Chromosome[])
                 *
                 * @param evaluator the fitness evaluator
                 * @param genotypeFactory the genotype factory
                 * @throws NullPointerException if one of the arguments is {@code null}.
                 */
                public Builder(
                        final Evaluator<G, C> evaluator,
                        final Factory<Genotype<G>> genotypeFactory
                ) {
                        _genotypeFactory = requireNonNull(genotypeFactory);
                        _evaluator = requireNonNull(evaluator);
                }

                /**
                 * 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 constraint is used for detecting invalid individuals
                 * and repairing them.
                 *
                 * <p><i>Default implementation uses {@code Phenotype::isValid} for
                 * validating the phenotype.</i></p>
                 *
                 * @since 5.0
                 *
                 * @param constraint phenotype constraint which can override the default
                 *        implementation the {@link Phenotype#isValid()} method and repairs
                 *        invalid phenotypes when needed.
                 * @return {@code this} builder, for command chaining
                 */
                public Builder<G, C> constraint(final Constraint<G, C> constraint) {
                        _constraint = constraint;
                        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>
                 * This method call is equivalent to
                 * {@code survivorsFraction(1 - offspringFraction)} and will override
                 * any previously set survivors-fraction.
                 *
                 * @see #survivorsFraction(double)
                 *
                 * @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 survivors fraction. <i>Default values is set to {@code 0.4}.</i>
                 * This method call is equivalent to
                 * {@code offspringFraction(1 - survivorsFraction)} and will override
                 * any previously set offspring-fraction.
                 *
                 * @since 3.8
                 *
                 * @see #offspringFraction(double)
                 *
                 * @param fraction the survivors 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> survivorsFraction(final double fraction) {
                        _offspringFraction = 1.0 - probability(fraction);
                        return this;
                }

                /**
                 * The number of offspring individuals.
                 *
                 * @since 3.8
                 *
                 * @param size the number of offspring individuals.
                 * @return {@code this} builder, for command chaining
                 * @throws java.lang.IllegalArgumentException if the size is not
                 *         within the range [0, population-size].
                 */
                public Builder<G, C> offspringSize(final int size) {
                        if (size < 0) {
                                throw new IllegalArgumentException(format(
                                        "Offspring size must be greater or equal zero, but was %s.",
                                        size
                                ));
                        }

                        return offspringFraction((double)size/(double)_populationSize);
                }

                /**
                 * The number of survivors.
                 *
                 * @since 3.8
                 *
                 * @param size the number of survivors.
                 * @return {@code this} builder, for command chaining
                 * @throws java.lang.IllegalArgumentException if the size is not
                 *         within the range [0, population-size].
                 */
                public Builder<G, C> survivorsSize(final int size) {
                        if (size < 0) {
                                throw new IllegalArgumentException(format(
                                        "Survivors must be greater or equal zero, but was %s.",
                                        size
                                ));
                        }

                        return survivorsFraction((double)size/(double)_populationSize);
                }

                /**
                 * 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 result mapper, which allows to change the evolution result after
                 * each generation.
                 *
                 * @since 4.0
                 * @see EvolutionResult#toUniquePopulation()
                 *
                 * @param mapper the evolution result mapper
                 * @return {@code this} builder, for command chaining
                 * @throws NullPointerException if the given {@code resultMapper} is
                 *         {@code null}
                 */
                public Builder<G, C> mapping(
                        final Function<
                                ? super EvolutionResult<G, C>,
                                EvolutionResult<G, C>
                        > mapper
                ) {
                        _mapper = requireNonNull(mapper::apply);
                        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<>(
                                _evaluator instanceof ConcurrentEvaluator
                                        ? ((ConcurrentEvaluator<G, C>)_evaluator).with(_executor)
                                        : _evaluator,
                                _genotypeFactory,
                                _survivorsSelector,
                                _offspringSelector,
                                _alterer,
                                _constraint == null
                                        ? RetryConstraint.of(_genotypeFactory)
                                        : _constraint,
                                _optimize,
                                getOffspringCount(),
                                getSurvivorsCount(),
                                _maximalPhenotypeAge,
                                _executor,
                                _clock,
                                _mapper
                        );
                }

                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 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 constraint of the evolution problem.
                 *
                 * @since 5.0
                 *
                 * @return the constraint of the evolution problem
                 */
                public Constraint<G, C> getConstraint() {
                        return _constraint;
                }

                /**
                 * 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 evolution result mapper.
                 *
                 * @since 4.0
                 *
                 * @return the evolution result mapper
                 */
                public UnaryOperator<EvolutionResult<G, C>> getMapper() {
                        return _mapper;
                }

                /**
                 * 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<G, C>(_evaluator, _genotypeFactory)
                                .alterers(_alterer)
                                .clock(_clock)
                                .executor(_executor)
                                .maximalPhenotypeAge(_maximalPhenotypeAge)
                                .offspringFraction(_offspringFraction)
                                .offspringSelector(_offspringSelector)
                                .constraint(_constraint)
                                .optimize(_optimize)
                                .populationSize(_populationSize)
                                .survivorsSelector(_survivorsSelector)
                                .mapping(_mapper);
                }

        }

}