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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.sa;

import java.util.concurrent.ThreadLocalRandom;

/**
 * This class implements logarithmic cooling, a classic annealing schedule. This annealing schedule
 * is of theoretical interest, but in general is not practical. The classic convergence results for
 * simulated annealing depend upon logarithmic cooling. In particular, with logarithmic cooling, if
 * the temperature begins sufficiently high, then in the limit simulated annealing converges to the
 * globally optimal solution. However, the temperature cools so slowly with logarithmic cooling that
 * for any practical search length, the search remains essentially a random walk, and does not come
 * anywhere close to the limit behavior. We have included the logarithmic cooling schedule in the
 * library in the interests of being complete.
 *
 * In logarithmic cooling, the k-th temperature is defined as: t_k = c / ln(k + d),
 * where c and d are constants. The value of c should be set based on cost differences between
 * random neighbors, and d is usually set equal to 1. In our case, since we start k at 0, a value of
 * d=1 would lead to a division by 0. Additionally, to simplify initialization for the programmer
 * using this annealing schedule, our implementation sets d=e (i.e., to the base of the natural
 * logarithm). Logarithms are so slow growing that small differences in the value of d don't change
 * the behavior of the schedule in any significant way. When k=0, the denominator is thus ln(e)=1.
 * Thus, c can be set to the desired initial temperature. Therefore, our implementation redefines
 * the cooling schedule as: t_k = t₀ / ln(k + e), where e is the base of the
 * natural logarithm.
 *
 * @author Vincent A. Cicirello, https://www.cicirello.org/
 */
public final class LogarithmicCooling implements AnnealingSchedule {

  private double t;
  private final double c;
  private int stepCounter;

  /**
   * Constructs a logarithmic cooling schedule with a specified initial temperature.
   *
   * @param t0 The initial temperature, which must be positive
   * @throws IllegalArgumentException if t0 ≤ 0.0
   */
  public LogarithmicCooling(double t0) {
    if (t0 <= 0) throw new IllegalArgumentException("initial temperature must be positive");
    t = this.c = t0;
  }

  /*
   * private copy constructor for internal use only
   */
  private LogarithmicCooling(LogarithmicCooling other) {
    t = c = other.c;
  }

  /**
   * {@inheritDoc}
   *
   * @param maxEvals This cooling schedule doesn't depend upon run length, so this parameter is
   *     ignored.
   */
  @Override
  public void init(int maxEvals) {
    stepCounter = 0;
    t = c;
  }

  @Override
  public boolean accept(double neighborCost, double currentCost) {
    boolean doAccept =
        neighborCost <= currentCost
            || ThreadLocalRandom.current().nextDouble()
                < Math.exp((currentCost - neighborCost) / t);
    stepCounter++;
    t = c / StrictMath.log(StrictMath.E + stepCounter);
    return doAccept;
  }

  @Override
  public LogarithmicCooling split() {
    return new LogarithmicCooling(this);
  }

  /*
   * package-private for unit testing
   */
  double getTemperature() {
    return t;
  }
}