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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;

/**
 * This class implements the benchmarking problem known as TwoMax. The TwoMax problem is to maximize
 * the following function: f(x) = |18*CountOfOneBits(x) - 8*n|, where x is a vector of bits of
 * length n. The global optimal solution is when x is all ones, which has a maximal value of 10*n.
 * This search landscape also has a local optima when x is all zeros, which has a value of 8*n.
 * Thus, this search landscape has two basins of attraction. The attractions basin for the global
 * optima is larger. As long as x has more than (4/9)n bits equal to a one, a strict hill climber
 * will be pulled into the global optima. However, a search that ends up at the local optima would
 * have a very steep climb to escape.
 *
 * The {@link #value value} method implements the original maximization version of the TwoMax
 * problem, as described above. The algorithms of the Chips-n-Salsa library are defined for
 * minimization, requiring a cost function. The {@link #cost cost} method implements the equivalent
 * as the following minimization problem: minimize cost(x) = 10*n - |18*CountOfOneBits(x) - 8*n|.
 * The global optima is still all 1-bits, which has a cost equal to 0. The local optima is still all
 * 0-bits, which has a cost equal to 2*n.
 *
 * The TwoMax 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 3.18.2021
 */
public final class TwoMax implements IntegerCostOptimizationProblem {

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

  @Override
  public int cost(BitVector candidate) {
    return 10 * candidate.length() - Math.abs(18 * candidate.countOnes() - 8 * candidate.length());
  }

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

  @Override
  public int value(BitVector candidate) {
    return Math.abs(18 * candidate.countOnes() - 8 * candidate.length());
  }

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