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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) 2002-2022 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 linear rank selection using Stochastic Universal Sampling (SUS). Linear
 * rank selection begins be determining the rank of each population member, where the least fit
 * member of the population has rank 1, and the most fit member of the population has rank N, where
 * the population size is N. During selection, the population member with rank r is chosen randomly
 * with probability proportional to: 2 - c + 2(r - 1)(c - 1)/(N - 1). The c is a real-valued
 * parameter that must be in the interval [1, 2]. When c is equal to 1, all population members are
 * equally likely chosen. When c is equal to 2, the expected number of times the most fit population
 * member will be chosen is 2, the least fit member won't be selected at all, and the expected
 * number of times the other population members will be chosen in a generation will vary between 0
 * and 2 based upon rank. To avoid a probability of 0 of choosing the least fit population member,
 * then ensure that c is less than 2. To ensure that the selection operator doesn't degenerate into
 * a uniform random selection, then set c greater than 1. The value of c can be interpreted as the
 * expected number of times the most fit population member will be selected in a generation.
 *
 * Linear rank selection was introduced by Baker (1985). According to "An Introduction to Genetic
 * Algorithms" (Melanie Mitchell, 1998), Baker recommended c = 1.1.
 *
 * 
However, whereas the standard form of linear rank selection is like spinning a carnival wheel
 * with a single pointer M times to select M members of the population, this SUS version 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 the other approach. Another consequence is
 * that SUS is typically much faster since only a single random floating point number is needed per
 * generation, compared to M random floating-point numbers.
 *
 * The runtime to select M population members from a population of size N is O(N lg N + M), which
 * includes the need to generate only a single random double, and O(M) random ints..
 *
 * @author Vincent A. Cicirello, https://www.cicirello.org/
 */
public final class LinearRankStochasticUniversalSampling extends StochasticUniversalSampling {

  private final double c;

  /**
   * Construct a linear rank selection operator that uses stochastic universal sampling.
   *
   * @param c The expected number of times the most fit population member should be selected during
   *     one generation, which must be in the interval [1.0, 2.0].
   * @throws IllegalArgumentException if c is less than 1 or greater than 2.
   */
  public LinearRankStochasticUniversalSampling(double c) {
    super();
    if (c < 1 || c > 2) throw new IllegalArgumentException("c must be int he interval [1.0, 2.0].");
    this.c = c;
  }

  @Override
  public LinearRankStochasticUniversalSampling split() {
    // Since this selection operator maintains no mutable state, it is
    // safe for multiple threads to share a single instance, so just return this.
    return this;
  }

  @Override
  final double[] computeWeightRunningSum(PopulationFitnessVector.Integer fitnesses) {
    return computeWeightRunningSumRanks(
        sortedIndexes(fitnesses), r -> 2 - c + 2 * r * (c - 1) / (fitnesses.size() - 1.0));
  }

  @Override
  final double[] computeWeightRunningSum(PopulationFitnessVector.Double fitnesses) {
    return computeWeightRunningSumRanks(
        sortedIndexes(fitnesses), r -> 2 - c + 2 * r * (c - 1) / (fitnesses.size() - 1.0));
  }
}