Class ThreeOptMutation
 All Implemented Interfaces:
Splittable<MutationOperator<Permutation>>
,MutationOperator<Permutation>
,UndoableMutationOperator<Permutation>
This class implements the classic 3Opt neighborhood as a mutation operator for permutations. The 3Opt neighborhood includes all twochanges and all threechanges. These originated specifically for the TSP. A twochange for the TSP removes two edges from a tour of the cities of a TSP and replaces them with two different edges such that the result is a valid tour of the cities. Likewise, a threechange removes three edges from the tour of the cities of a TSP and replaces them with three different edges. This implementation is not strictly for the TSP, and will operate on a permutation regardless of what that permutation represents. However, it assumes that the permutation represents a cyclic sequence of undirected edges, and specifically that if two elements are adjacent in the permutation that it corresponds to an undirected edge between the elements. For example, consider the permutation, p = [2, 1, 4, 0, 3], of the first 5 nonnegative integers. Now imagine that we have a graph with 5 vertexes, labeled 0 to 4. This example permutation would correspond to a set of undirected edges: { (2, 1), (1, 4), (4, 0), (0, 3), (3, 2) }. Notice that we included (3, 2) here in that the set of edges represented by the permutation is cyclic and includes an edge between the two endpoints.
The runtime (worst case and average case) of both
the mutate
and undo
methods is O(n),
where n is the length of the permutation.
For any given permutation of length n, there are n*(n3)/2 possible twochange neighbors, and 4*(n*(n1)*(n2)/6  n*(n4)  n) + n*(n4) possible threechange neighbors. Each of the possible threechanges is approximately equally likely as every other threechange. Each of the possible twochanges is approximately equally likely as every other twochange. The current implementation does not guarantee that each of the possible twochanges are equally likely as each of the possible threechanges. Currently, each twochange is slightly more likely than each threechange. Although because the number of possible threechanges grows cubicly vs quadratic growth in number of possible twochanges, the probability of a threechange increases rapidly as permutation length increases.
For permutations of length equal to 4, the ThreeOptMutation will only perform twochanges because no valid threechanges exist for that length. For permutations of length n < 4, the ThreeOptMutation operator makes no changes, as there are no twochange or threechange neighbors of permutations of that size.

Constructor Summary

Method Summary
Modifier and TypeMethodDescriptionfinal void
Mutates a candidate solution to a problem, by randomly modifying its state.split()
Generates a functionally identical copy of this object, for use in multithreaded implementations of search algorithms.final void
undo
(Permutation c) Returns a candidate solution to its previous state prior to the most recent mutation performed.

Constructor Details

ThreeOptMutation
public ThreeOptMutation()Constructs a ThreeOptMutation operator.


Method Details

mutate
Description copied from interface:MutationOperator
Mutates a candidate solution to a problem, by randomly modifying its state. The mutant that is produced is in the local neighborhood of the original candidate solution. Specified by:
mutate
in interfaceMutationOperator<Permutation>
 Parameters:
c
 The candidate solution subject to the mutation. This method changes the state of c.

undo
Description copied from interface:UndoableMutationOperator
Returns a candidate solution to its previous state prior to the most recent mutation performed.
For example, consider the following. Let c' be the current state of c. Let c'' be the state of c after mutate(c); If we then call undo(c), the state of c should revert back to c'.
The behavior of undo is undefined if c is altered by some other process between the calls to mutate and undo. The behavior is also undefined if a different candidate is given to undo then the last given to mutate. For example, if the following two statements are executed, mutate(c); undo(d);, the effect on d is undefined as it wasn't the most recently mutated candidate solution.
 Specified by:
undo
in interfaceUndoableMutationOperator<Permutation>
 Parameters:
c
 The candidate solution to revert.

split
Description copied from interface:Splittable
Generates a functionally identical copy of this object, for use in multithreaded implementations of search algorithms. The state of the object that is returned may or may not be identical to that of the original. Thus, this is a distinct concept from the functionality of theCopyable
interface. Classes that implement this interface must ensure that the object returned performs the same functionality, and that it does not share any state data that would be either unsafe or inefficient for concurrent access by multiple threads. The split method is allowed to simply return the this reference, provided that it is both safe and efficient for multiple threads to share a single copy of the Splittable object. The intention is to provide a multithreaded search with the capability to provide spawned threads with their own distinct search operators. Such multithreaded algorithms can call the split method for each thread it spawns to generate a functionally identical copy of the operator, but with independent state. Specified by:
split
in interfaceSplittable<MutationOperator<Permutation>>
 Specified by:
split
in interfaceUndoableMutationOperator<Permutation>
 Returns:
 A functionally identical copy of the object, or a reference to this if it is both safe and efficient for multiple threads to share a single instance of this Splittable object.
