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Chips-n-Salsa is a Java library of customizable, hybridizable, iterative, parallel, stochastic, and self-adaptive local search algorithms. The library includes implementations of several stochastic local search algorithms, including simulated annealing, hill climbers, as well as constructive search algorithms such as stochastic sampling. Chips-n-Salsa now also includes genetic algorithms as well as evolutionary algorithms more generally. The library very extensively supports simulated annealing. It includes several classes for representing solutions to a variety of optimization problems. For example, the library includes a BitVector class that implements vectors of bits, as well as classes for representing solutions to problems where we are searching for an optimal vector of integers or reals. For each of the built-in representations, the library provides the most common mutation operators for generating random neighbors of candidate solutions, as well as common crossover operators for use with evolutionary algorithms. Additionally, the library provides extensive support for permutation optimization problems, including implementations of many different mutation operators for permutations, and utilizing the efficiently implemented Permutation class of the JavaPermutationTools (JPT) library. Chips-n-Salsa is customizable, making extensive use of Java's generic types, enabling using the library to optimize other types of representations beyond what is provided in the library. It is hybridizable, providing support for integrating multiple forms of local search (e.g., using a hill climber on a solution generated by simulated annealing), creating hybrid mutation operators (e.g., local search using multiple mutation operators), as well as support for running more than one type of search for the same problem concurrently using multiple threads as a form of algorithm portfolio. Chips-n-Salsa is iterative, with support for multistart metaheuristics, including implementations of several restart schedules for varying the run lengths across the restarts. It also supports parallel execution of multiple instances of the same, or different, stochastic local search algorithms for an instance of a problem to accelerate the search process. The library supports self-adaptive search in a variety of ways, such as including implementations of adaptive annealing schedules for simulated annealing, such as the Modified Lam schedule, implementations of the simpler annealing schedules but which self-tune the initial temperature and other parameters, and restart schedules that adapt to run length.

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/*
 * Chips-n-Salsa: A library of parallel self-adaptive local search algorithms.
 * Copyright (C) 2002-2021  Vincent A. Cicirello
 *
 * This file is part of Chips-n-Salsa (https://chips-n-salsa.cicirello.org/).
 *
 * Chips-n-Salsa is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * Chips-n-Salsa is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see .
 */

package org.cicirello.search.evo;

/**
 * This class implements a variation of Stochastic Universal Sampling (SUS) that we call Biased
 * Stochastic Universal Sampling (Biased SUS), which integrates the use of a bias function with SUS
 * to enable transforming fitness values prior to the stochastic selection decisions. In this Biased
 * SUS, a member of the population is chosen randomly with probability proportional to a bias
 * function of its fitness relative to the total of such biased fitness of the population. For
 * example, if the fitness of population member i is f_i, then the probability of
 * selecting population member i is: bias(f_i) / ∑_j bias(f_j),
 * for j ∈ { 1, 2, ..., N }, where N is the population size, and bias is a bias function.
 *
 * As an example bias function, consider: bias(x) = x², which would square each
 * fitness value x.
 *
 * 
SUS and this Biased SUS are similar to fitness proportional selection and a biased variation
 * of fitness proportional selection. However, whereas fitness proportional selection is like
 * spinning a carnival wheel with a single pointer M times to select M members of the population,
 * SUS instead is like spinning a carnival wheel that has M equidistant pointers a single time to
 * select all M simultaneously. One statistical consequence of this is that it reduces the variance
 * of the selected copies of population members as compared to fitness proportional selection (and
 * its biased variation). Another consequence is that SUS and Biased SUS are typically much faster
 * since only a single random floating point number is needed per generation, compared to M random
 * floating-point numbers for fitness proportional selection. However, SUS and Biased SUS then must
 * randomize the ordering of the population to avoid all of the copies of a single population member
 * from being in sequence so that parent assignment is random, whereas fitness proportional
 * selection has this property built in.
 *
 * 
This selection operator requires positive fitness values. Behavior is undefined if any
 * fitness values are less than or equal to 0. If your fitness values may be negative, you can
 * use {@link FitnessShifter}, which transforms fitness values such that minimum fitness equals 1.
 *
 * 
The runtime to select M population members from a population of size N is O(N + M), which
 * includes the need to generate only a single random double, and O(M) ints. This assumes that the
 * bias function has a constant runtime.
 *
 * For the more common standard version of SUS, see the {@link StochasticUniversalSampling}
 * class.
 *
 * @author Vincent A. Cicirello, https://www.cicirello.org/
 */
public class BiasedStochasticUniversalSampling extends StochasticUniversalSampling {

  private final FitnessBiasFunction bias;

  /**
   * Construct a biased stochastic universal sampling operator.
   *
   * @param bias A bias function
   */
  public BiasedStochasticUniversalSampling(FitnessBiasFunction bias) {
    this.bias = bias;
  }

  @Override
  public BiasedStochasticUniversalSampling split() {
    // The FitnessBiasFunction interface's contract is that implementations
    // must be threadsafe and thread efficient, so assume that the only state,
    // the bias function, meets that contract.
    return this;
  }

  @Override
  double[] computeWeightRunningSum(PopulationFitnessVector.Integer fitnesses) {
    double[] p = new double[fitnesses.size()];
    p[0] = bias.bias(fitnesses.getFitness(0));
    for (int i = 1; i < p.length; i++) {
      p[i] = p[i - 1] + bias.bias(fitnesses.getFitness(i));
    }
    return p;
  }

  @Override
  double[] computeWeightRunningSum(PopulationFitnessVector.Double fitnesses) {
    double[] p = new double[fitnesses.size()];
    p[0] = bias.bias(fitnesses.getFitness(0));
    for (int i = 1; i < p.length; i++) {
      p[i] = p[i - 1] + bias.bias(fitnesses.getFitness(i));
    }
    return p;
  }
}