001/*
002 * Java Genetic Algorithm Library (jenetics-7.1.0).
003 * Copyright (c) 2007-2022 Franz Wilhelmstötter
004 *
005 * Licensed under the Apache License, Version 2.0 (the "License");
006 * you may not use this file except in compliance with the License.
007 * You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 *
017 * Author:
018 *    Franz Wilhelmstötter (franz.wilhelmstoetter@gmail.com)
019 */
020package io.jenetics;
021
022import static java.lang.Math.exp;
023import static java.lang.String.format;
024import static io.jenetics.internal.math.Basics.normalize;
025
026import java.util.Arrays;
027
028import io.jenetics.util.Seq;
029
030/**
031 * <p>
032 * In this {@code Selector}, the probability for selection is defined as.
033 * </p>
034 * <p><img
035 *        src="./doc-files/boltzmann-formula1.svg"
036 *        alt="P(i)=\frac{\textup{e}^{b\cdot f_i}}{Z}"
037 *     >
038 * </p>
039 * where <i>b</i> controls the selection intensity, and
040 * <p><img
041 *        src="doc-files/boltzmann-formula2.svg"
042 *        alt="Z=\sum_{j=1}^{n}\textrm{e}^{f_j}"
043 *     >.
044 * </p>
045 *
046 * <i>f</i><sub><i>j</i></sub> denotes the fitness value of the
047 * <i>j<sup>th</sup></i> individual.
048 * <br>
049 * Positive values of <i>b</i> increases the selection probability of the phenotype
050 * with high fitness values. Negative values of <i>b</i> increases the selection
051 * probability of phenotypes with low fitness values. If <i>b</i> is zero the
052 * selection probability of all phenotypes is set to <sup>1</sup>/<sub>N</sub>.
053 *
054 * @param <G> the gene type.
055 * @param <N> the BoltzmannSelector requires a number type.
056 *
057 * @author <a href="mailto:franz.wilhelmstoetter@gmail.com">Franz Wilhelmstötter</a>
058 * @since 1.0
059 * @version 5.0
060 */
061public final class BoltzmannSelector<
062        G extends Gene<?, G>,
063        N extends Number & Comparable<? super N>
064>
065        extends ProbabilitySelector<G, N>
066{
067
068        private final double _b;
069
070        /**
071         * Create a new BoltzmannSelector with the given <i>b</i> value. <b>High
072         * absolute values of <i>b</i> can create numerical overflows while
073         * calculating the selection probabilities.</b>
074         *
075         * @param b the <i>b</i> value of this BoltzmannSelector
076         */
077        public BoltzmannSelector(final double b) {
078                _b = b;
079        }
080
081        /**
082         * Create a new BoltzmannSelector with a default beta of 4.0.
083         */
084        public BoltzmannSelector() {
085                this(4.0);
086        }
087
088        @Override
089        protected double[] probabilities(
090                final Seq<Phenotype<G, N>> population,
091                final int count
092        ) {
093                assert population != null : "Population must not be null. ";
094                assert !population.isEmpty() : "Population is empty.";
095                assert count > 0 : "Population to select must be greater than zero. ";
096
097                // Copy the fitness values to probabilities arrays.
098                final double[] fitness = new double[population.size()];
099
100                fitness[0] = population.get(0).fitness().doubleValue();
101                double min = fitness[0];
102                double max = fitness[0];
103                for (int i = 1; i < fitness.length; ++i) {
104                        fitness[i] = population.get(i).fitness().doubleValue();
105                        if (fitness[i] < min) min = fitness[i];
106                        else if (fitness[i] > max) max = fitness[i];
107                }
108
109                final double diff = max - min;
110                if (eq(diff, 0.0)) {
111                        // Set equal probabilities if diff (almost) zero.
112                        Arrays.fill(fitness, 1.0/fitness.length);
113                } else {
114                        // Scale fitness values to avoid overflow.
115                        for (int i = fitness.length; --i >= 0;) {
116                                fitness[i] = (fitness[i] - min)/diff;
117                        }
118
119                        // Apply the "Boltzmann" function.
120                        for (int i = fitness.length; --i >= 0;) {
121                                fitness[i] = exp(_b*fitness[i]);
122                        }
123                }
124
125                return normalize(fitness);
126        }
127
128        @Override
129        public String toString() {
130                return format("BoltzmannSelector[b=%f]", _b);
131        }
132
133}