org.cicirello.search.operators.permutations.EdgeRecombination Maven / Gradle / Ivy

Go to download

Show more of this group Show more artifacts with this name
Show all versions of chips-n-salsa Show documentation

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.

There is a newer version: 7.0.1

Show newest version

/*
 * 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.operators.permutations;

import java.util.Arrays;
import org.cicirello.math.rand.RandomIndexer;
import org.cicirello.permutations.Permutation;
import org.cicirello.permutations.PermutationBinaryOperator;
import org.cicirello.search.operators.CrossoverOperator;

/**
 * Implementation of the Edge Recombination operator, a crossover operator for permutations. Edge
 * Recombination assumes that the permutations represent a cyclic sequence of edges. That is, if 3
 * follows 5 in the permutation, then that corresponds to an undirected edge between 3 and 5. Given
 * this assumption, it is suitable for problems where permutations do represent a sequence of edges
 * such as the traveling salesperson. However, the Chips-n-Salsa library does not limit its use to
 * such problems, and you can use it on any problem with solutions represented as permutations.
 *
 * Imagine a hypothetical graph consisting of the n elements of a permutation of length n as the
 * n vertexes of the graph. The edge set begins with the n adjacent pairs from parent p1. For
 * example, if p1 = [3, 0, 2, 1, 4], then the edge set of this graph is initialized with the
 * undirected edges: (3, 0), (0, 2), (2, 1), (1, 4), and (4, 3). Now add to that edge set any edges,
 * determined in a similar way, from parent p2, provided it doesn't already contain the relevant
 * edge. Consider p2 = [4, 3, 2, 1, 0]. Thus, we would add (3, 2), (1, 0),and (0, 4) to get an
 * undirected edge set of: { (3, 0), (0, 2), (2, 1), (1, 4), (4, 3), (3, 2), (1, 0), (0, 4) }. Child
 * c1 is initialized with the first element of parent p1, in this example p1 = [3]. We then examine
 * the adjacent vertexes to the most recently added element. The 3 is adjacent to 0, 4, and 2. We'll
 * pick one of these to add in the next spot of the permutation. We'll pick the one that is adjacent
 * to the fewest elements not yet used. 0 is adjacent to 2, 1, and 4. 4 is adjacent to 1 and 0. 2 is
 * adjacent to 0 and 1. When there is a tie, such as here with the 2 and 4, the tie is broken at
 * random. Imagine that the random tie breaker gave us 4. We now have p1 = [3, 4]. We now consider
 * the adjacent elements of 4 that are not yet in the permutation, which in this case is 0 and 1. We
 * pick the one with the fewest adjacent elements not yet in the permutation. The 0 is adjacent to 1
 * and 2. The 1 is adjacent to 0 and 2. Since we have a tie, we pick randomly. Consider for the
 * example that the random choice have us 1. We now have p1 = [3, 4, 1]. We now examine the adjacent
 * elements of 1 that are not yet in the permutation. The 1 is adjacent to 0 and 2. We pick the one
 * that is adjacent to the fewest not yet used elements. They are the only two remaining and they
 * are adjacent to each other. We thus pick randomly. Consider that the random element is 0, and we
 * now have p1 = [3, 4, 1, 0]. And at this point, there is only one element left, so the final
 * permutation is p1 = [3, 4, 1, 0, 2]. We can form the other child in a similar way, but
 * initialized with the first element of the other parent.
 *
 * 
The Edge Recombination operator uses a special data structure that its creators, Whitley et
 * al, call an edge map for efficient implementation.
 *
 * 
The worst case runtime of a call to {@link #cross cross} is O(n), where n is the length of the
 * permutations.
 *
 * The edge recombination operator was introduced in the following paper:

 * D. Whitley, T. Starkweather, and D. Fuquay. Scheduling Problems and Traveling Salesmen: The
 * Genetic Edge Recombination Operator. Proceedings of the International Conference on Genetic
 * Algorithms, 1989, pp. 133-140.
 *
 * @author Vincent A. Cicirello, https://www.cicirello.org/
 */
public final class EdgeRecombination
    implements CrossoverOperator, PermutationBinaryOperator {

  /** Constructs a edge recombination operator. */
  public EdgeRecombination() {}

  @Override
  public void cross(Permutation c1, Permutation c2) {
    if (c1.length() > 1) {
      c1.apply(this, c2);
    }
  }

  @Override
  public EdgeRecombination split() {
    // doesn't maintain any state, so safe to return this
    return this;
  }

  /**
   * See {@link PermutationBinaryOperator} for details of this method. This method is not intended
   * for direct usage. Use the {@link #cross} method instead.
   *
   * @param raw1 The raw representation of the first permutation.
   * @param raw2 The raw representation of the second permutation.
   */
  @Override
  public void apply(int[] raw1, int[] raw2) {
    EdgeMap map = new EdgeMap(raw1, raw2);
    build(raw1, new EdgeMap(map));
    build(raw2, map);
  }

  private void build(int[] raw, EdgeMap map) {
    // 0th element is as in parent, so start iteration at 1.
    for (int i = 1; i < raw.length; i++) {
      // 1. record that we used raw[i-1]
      map.used(raw[i - 1]);
      // 2. pick an adjacent element of raw[i-1] and add to raw[i]
      raw[i] = map.pick(raw[i - 1]);
    }
  }

  static final class EdgeMap {

    final int[][] adj;
    final int[] count;
    final boolean[] done;

    /*
     * Assumes length is greater than 1
     */
    EdgeMap(int[] raw1, int[] raw2) {
      adj = new int[raw1.length][4];
      count = new int[raw1.length];
      done = new boolean[raw1.length];
      boolean[][] in = new boolean[raw1.length][raw1.length];
      adj[raw1[0]][0] = raw1[raw1.length - 1];
      in[raw1[0]][raw1[raw1.length - 1]] = true;
      for (int i = 1; i < raw1.length; i++) {
        adj[raw1[i]][0] = raw1[i - 1];
        in[raw1[i]][raw1[i - 1]] = true;
      }
      if (raw1.length <= 2) {
        Arrays.fill(count, 1);
      } else {
        Arrays.fill(count, 2);
        adj[raw1[raw1.length - 1]][1] = raw1[0];
        in[raw1[raw1.length - 1]][raw1[0]] = true;
        for (int i = 1; i < raw1.length; i++) {
          adj[raw1[i - 1]][1] = raw1[i];
          in[raw1[i - 1]][raw1[i]] = true;
        }
        if (!in[raw2[0]][raw2[raw2.length - 1]]) {
          adj[raw2[0]][count[raw2[0]]] = raw2[raw2.length - 1];
          in[raw2[0]][raw2[raw2.length - 1]] = true;
          count[raw2[0]]++;
        }
        if (!in[raw2[raw2.length - 1]][raw2[0]]) {
          adj[raw2[raw2.length - 1]][count[raw2[raw2.length - 1]]] = raw2[0];
          in[raw2[raw2.length - 1]][raw2[0]] = true;
          count[raw2[raw2.length - 1]]++;
        }
        for (int i = 1; i < raw2.length; i++) {
          if (!in[raw2[i]][raw2[i - 1]]) {
            adj[raw2[i]][count[raw2[i]]] = raw2[i - 1];
            in[raw2[i]][raw2[i - 1]] = true;
            count[raw2[i]]++;
          }
          if (!in[raw2[i - 1]][raw2[i]]) {
            adj[raw2[i - 1]][count[raw2[i - 1]]] = raw2[i];
            in[raw2[i - 1]][raw2[i]] = true;
            count[raw2[i - 1]]++;
          }
        }
      }
    }

    EdgeMap(EdgeMap other) {
      count = other.count.clone();
      // deliberately not cloning done... this copy constructor
      // only used on the initial EdgeMap, so nothing done
      done = new boolean[count.length];
      adj = new int[other.adj.length][];
      for (int i = 0; i < adj.length; i++) {
        adj[i] = other.adj[i].clone();
      }
    }

    final int pick(int from) {
      if (count[from] == 1) {
        return adj[from][0];
      }
      if (count[from] > 0) {
        int[] minIndexes = new int[4];
        int num = 1;
        for (int i = 1; i < count[from]; i++) {
          if (count[adj[from][i]] < count[adj[from][minIndexes[0]]]) {
            minIndexes[0] = i;
            num = 1;
          } else if (count[adj[from][i]] == count[adj[from][minIndexes[0]]]) {
            minIndexes[num] = i;
            num++;
          }
        }
        if (num > 1) {
          // The num can be at most 3, so nextBiasedInt's lack of rejection sampling
          // should introduce an extremely negligible bias away from uniformity.
          return adj[from][minIndexes[RandomIndexer.nextBiasedInt(num)]];
        }
        return adj[from][minIndexes[0]];
      }
      // IS IT POSSIBLE TO GET HERE?
      // IS IT POSSIBLE FOR NONE AVAILABLE?
      // IF NOT, THEN ABOVE IF STATEMENT NOT NEEDED AND CAN JUST DO THE BLOCK.
      // ALSO WOULDN'T NEED THE DONE ARRAY AT ALL.
      // NOTE: Test cases include unit tests of this specific method that include
      // an extra call after the permutation is complete to artificially create a
      // scenario that ends up here. Try to confirm if a real scenario exists.
      return anyRemaining();
    }

    final void used(int element) {
      for (int i = 0; i < count[element]; i++) {
        remove(adj[element][i], element);
      }
      done[element] = true;
    }

    final void remove(int list, int element) {
      int i = 0;
      // guaranteed to be in list
      while (adj[list][i] != element) {
        i++;
      }
      count[list]--;
      adj[list][i] = adj[list][count[list]];
    }

    final int anyRemaining() {
      int[] minIndexes = new int[adj.length];
      int num = 0;
      for (int i = 0; i < done.length; i++) {
        if (!done[i]) {
          if (num == 0) {
            minIndexes[0] = i;
            num = 1;
          } else if (count[i] == count[minIndexes[0]]) {
            minIndexes[num] = i;
            num++;
          } else if (count[i] < count[minIndexes[0]]) {
            minIndexes[0] = i;
            num = 1;
          }
        }
      }
      if (num > 1) {
        // The num should be very small, so nextBiasedInt's lack of rejection sampling
        // should introduce an extremely negligible bias away from uniformity. In fact, this
        // case is believed extremely statistically rare.
        return minIndexes[RandomIndexer.nextBiasedInt(num)];
      }
      if (num == 1) {
        return minIndexes[0];
      }
      return -1;
    }
  }
}