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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.ss;

import org.cicirello.math.rand.RandomIndexer;
import org.cicirello.search.ProgressTracker;
import org.cicirello.search.SolutionCostPair;
import org.cicirello.util.Copyable;

/**
 * The AcceptanceBandSampling class implements a form of stochastic sampling search that uses a
 * constructive heuristic to guide the random decisions. When making a random decision, all options
 * are evaluated with the heuristic. An acceptance band is then defined based upon the option with
 * the highest heuristic evaluation. Specifically, all options with a heuristic evaluation within B%
 * of the highest heuristic evaluation of the available options are considered equivalent. A choice
 * is then made uniformly at random from the set of equivalents.
 *
 * The search generates N random candidate solutions to the problem, using a problem-specific
 * heuristic for guidance. It evaluates each of the N candidate solutions with respect to the
 * optimization problem's cost function, and returns the best of the N candidate solutions.
 *
 * 
Although AcceptanceBandSampling itself is not restricted to permutation problems, the examples
 * that follow in this documentation focus on permutations for illustrative purposes.
 *
 * 
The acceptance bands are defined in terms of a parameter β, which must be in the interval
 * [0.0, 1.0]. Imagine that we have a set of k alternatives, a[0], a[1], ..., a[k], to pick from
 * that have heuristic values: h[0], h[1], ..., h[k]. We assume in this implementation that higher
 * heuristic values imply the options perceived better by the heuristic. We compute: h' = max {h[0],
 * h[1], ..., h[k]}. We define an acceptance threshold: T = (1.0 - beta)h'. The set S of equivalent
 * choices is then computed as: S = { a[k] | h[k] ≥ T}. We then choose uniformly at random from
 * the set S.
 *
 * 
If beta=1.0, then all alternatives are considered equivalent (we assume heuristic values are
 * non-negative) since the threshold T would be 0.0 regardless of the heuristic values. If beta=0.0,
 * then only the choices whose heuristic value is equal to the highest heuristic value are
 * considered, since in this case the threshold T is h'. This implementation allows you to specify
 * your choice of beta, and also provides a default of beta=0.1. That default means that all choices
 * within 10% of the option perceived as best by the heuristic are considered equivalent.
 *
 * 
To use this implementation of acceptance bands, you will need to implement a constructive
 * heuristic for your problem using the {@link ConstructiveHeuristic} interface.
 *
 * 
Assuming that the length of the permutation is L, and that the runtime of the constructive
 * heuristic is O(f(L)), the runtime to construct one permutation using acceptance bands is
 * O(L² f(L)). If the cost, f(L), to heuristically evaluate one permutation element is
 * simply, O(1), constant time, then the cost to heuristically construct one permutation is simply
 * O(L²).
 *
 * 
The term "acceptance bands", as we use here, was introduced to describe a stochastic sampling
 * algorithm for finding feasible solutions to a job scheduling problem, as an alternative to
 * systematic backtracking in the following paper:
 *
 * 

 *   Angelo Oddi and Stephen F. Smith. 1997. Stochastic procedures for generating feasible
 *       schedules. Proceedings of the 14th National Conference on Artificial Intelligence. AAAI
 *       Press, 308–314.
 * 
 *
 * An approach, referred to as "heuristic equivalency", has been used to randomize
 * variable-ordering/value-ordering heuristics within a systematic backtracking search. The
 * randomization technique of heuristic equivalency is the same as that of acceptance bands, but for
 * a different purpose. Heuristic equivalency was used within a backtracking search, while
 * acceptance bands was used to replace backtracking. Heuristic equivalency is described in the
 * following paper:
 *
 * 

 *   Carla P. Gomes, Bart Selman, and Henry Kautz. 1998. Boosting combinatorial search through
 *       randomization. Proceedings of the 15th National Conference on Artificial Intelligence. AAAI
 *       Press, 431–437.
 * 
 *
 * The implementation of the AcceptanceBandSampling class in our library implements the
 * stochastic sampling version, and does not involve any backtracking.
 *
 * @param  The type of object under optimization.
 * @author Vincent A. Cicirello, https://www.cicirello.org/
 */
public final class AcceptanceBandSampling>
    extends AbstractStochasticSampler {

  private final ConstructiveHeuristic heuristic;
  private final double acceptancePercentage;

  /**
   * Constructs an AcceptanceBandSampling search object. Uses a default value of beta = 0.1. This
   * default has the effect of considering all heuristic values within 10% of that of the option
   * perceived best by the heuristic to be considered equivalent. A ProgressTracker is created for
   * you.
   *
   * @param heuristic The constructive heuristic.
   * @throws NullPointerException if heuristic is null
   */
  public AcceptanceBandSampling(ConstructiveHeuristic heuristic) {
    this(heuristic, 0.1, new ProgressTracker());
  }

  /**
   * Constructs an AcceptanceBandSampling search object. Uses a default value of beta = 0.1. This
   * default has the effect of considering all heuristic values within 10% of that of the option
   * perceived best by the heuristic to be considered equivalent.
   *
   * @param heuristic The constructive heuristic.
   * @param tracker A ProgressTracker
   * @throws NullPointerException if heuristic or tracker is null
   */
  public AcceptanceBandSampling(ConstructiveHeuristic heuristic, ProgressTracker tracker) {
    this(heuristic, 0.1, tracker);
  }

  /**
   * Constructs an AcceptanceBandSampling search object. A ProgressTracker is created for you.
   *
   * @param heuristic The constructive heuristic.
   * @param beta The acceptance band parameter. When making a decision, if h is the max of the
   *     heuristic evaluations of all of the options, then the search will consider all options
   *     whose heuristic evaluation is at least h(1.0 - beta) as equivalent and choose uniformly at
   *     random from among those equivalent options. The value of beta must satisfy: 0.0 ≤ beta
   *     ≤ 1.0. If beta is closer to 0.0, then heuristic values must be closer to the heuristic
   *     value of the perceived best option to be considered equivalent to it. If beta is 1.0, then
   *     all options will be considered equivalent.
   * @throws NullPointerException if heuristic is null
   * @throws IllegalArgumentException if beta is less than 0.0 or greater than 1.0.
   */
  public AcceptanceBandSampling(ConstructiveHeuristic heuristic, double beta) {
    this(heuristic, beta, new ProgressTracker());
  }

  /**
   * Constructs an AcceptanceBandSampling search object.
   *
   * @param heuristic The constructive heuristic.
   * @param beta The acceptance band parameter. When making a decision, if h is the max of the
   *     heuristic evaluations of all of the options, then the search will consider all options
   *     whose heuristic evaluation is at least h(1.0 - beta) as equivalent and choose uniformly at
   *     random from among those equivalent options. The value of beta must satisfy: 0.0 ≤ beta
   *     ≤ 1.0. If beta is closer to 0.0, then heuristic values must be closer to the heuristic
   *     value of the perceived best option to be considered equivalent to it. If beta is 1.0, then
   *     all options will be considered equivalent.
   * @param tracker A ProgressTracker
   * @throws NullPointerException if heuristic or tracker is null
   * @throws IllegalArgumentException if beta is less than 0.0 or greater than 1.0.
   */
  public AcceptanceBandSampling(
      ConstructiveHeuristic heuristic, double beta, ProgressTracker tracker) {
    super(heuristic.getProblem(), tracker);
    this.heuristic = heuristic;
    if (beta < 0.0 || beta > 1.0) {
      throw new IllegalArgumentException("beta must be in the interval: [0.0, 1.0].");
    }
    acceptancePercentage = 1.0 - beta;
  }

  /*
   * private for use by split method
   */
  private AcceptanceBandSampling(AcceptanceBandSampling other) {
    super(other);
    heuristic = other.heuristic;
    acceptancePercentage = other.acceptancePercentage;
  }

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

  /*
   * package-private rather than private to support unit testing
   */
  int choose(double[] values, int k, double max, int[] equivalents) {
    double threshold = max * acceptancePercentage;
    int n = 0;
    for (int i = 0; i < k; i++) {
      if (values[i] >= threshold) {
        equivalents[n] = i;
        n++;
      }
    }
    return equivalents[RandomIndexer.nextInt(n)];
  }

  @Override
  SolutionCostPair sample() {
    IncrementalEvaluation incEval = heuristic.createIncrementalEvaluation();
    int n = heuristic.completeLength();
    Partial p = heuristic.createPartial(n);
    double[] v = new double[n];
    int[] equivalents = new int[n];
    while (!p.isComplete()) {
      int k = p.numExtensions();
      if (k == 1) {
        if (incEval != null) {
          incEval.extend(p, p.getExtension(0));
        }
        p.extend(0);
      } else {
        double max = Double.NEGATIVE_INFINITY;
        for (int i = 0; i < k; i++) {
          v[i] = heuristic.h(p, p.getExtension(i), incEval);
          if (v[i] > max) max = v[i];
        }
        int which = choose(v, k, max, equivalents);
        if (incEval != null) {
          incEval.extend(p, p.getExtension(which));
        }
        p.extend(which);
      }
    }
    T complete = p.toComplete();
    return evaluateAndPackageSolution(complete);
  }
}