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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.problems;

import org.cicirello.search.representations.BitVector;

/**
 * The OneMaxAckley class is an implementation of the well-known OneMax problem, often used in
 * benchmarking genetic algorithms and other metaheuristics. Specifically, it implements Ackley's
 * (1985) original version of the problem.
 *
 * In the OneMax problem, the metaheuristic is searching the space of bit-strings of length n for
 * the bit-string with the most bits equal to a 1. It originated as a test problem for genetic
 * algorithms, where the standard form of a genetic algorithm represents solutions to the problem
 * with a string of bits. The OneMax problem offers a test problem with a known optimal solution, a
 * bit-string of all 1s. For example, if n=8, then the optimal solution is: 11111111. The OneMax
 * problem has no local optima, and thus should be trivially easy for hill climbers.
 *
 * 
It was originally posed as a maximization problem because it was originally defined as a
 * fitness function for a genetic algorithm. The problem was originally stated to maximize f(x) = 10
 * * CountOfOneBits(x), where x is a vector of bits of length n. The {@link #value value} method
 * returns 10 times the number of bits in the BitVector equal to 1, which is to be maximized. Thus,
 * as a cost function, the {@link #cost cost} method returns 10 times the number of bits not equal
 * to 1, where the minimum cost is thus 0, corresponding to the case of maximal number of 1-bits.
 *
 * 
The Chips-n-Salsa library also includes a version that is a simple count of the bits without
 * the multiplication by 10 in the {@link OneMax} class.
 *
 * Although commonly used by others without reference, the OneMax problem was introduced by David
 * Ackley in the following paper:

 * David H. Ackley. A connectionist algorithm for genetic search. Proceedings of the First
 * International Conference on Genetic Algorithms and Their Applications, pages 121-135, July 1985.
 *
 * @author Vincent A. Cicirello, https://www.cicirello.org/
 * @version 3.20.2021
 */
public final class OneMaxAckley implements IntegerCostOptimizationProblem {

  /**
   * Constructs a OneMaxAckley object for use in evaluating candidate solutions to the OneMax
   * problem.
   */
  public OneMaxAckley() {}

  @Override
  public int cost(BitVector candidate) {
    return 10 * candidate.countZeros();
  }

  @Override
  public int minCost() {
    return 0;
  }

  @Override
  public int value(BitVector candidate) {
    return 10 * candidate.countOnes();
  }

  @Override
  public boolean isMinCost(int cost) {
    return cost == 0;
  }
}