Class OneMax

  • All Implemented Interfaces:
    IntegerCostOptimizationProblem<BitVector>, Problem<BitVector>

    public final class OneMax
    extends Object
    implements IntegerCostOptimizationProblem<BitVector>

    The OneMax class is an implementation of the well-known OneMax problem, often used in benchmarking genetic algorithms and other metaheuristics.

    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 value method simply counts the number of bits in the BitVector equal to 1, which is to be maximized. Thus, as a cost function, the cost method counts 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 OneMax problem was introduced by Ackley (1985). His original definition of the problem was to maximize: f(x) = 10 * CountOfOneBits(x). Thus, Ackley's original OneMax multiplied the number of 1-bits by 10. Our implementation does not multiply by 10. Doing so does not change the optimal solution or the shape of the landscape. However, it may have an effect on the behavior of some search algorithms. For example, simulated annealing decides whether or not to accept a worsening move with a probability that depends on the difference in cost between the current solution and the random neighbor, as well as on its current temperature. Keeping all else the same and scaling the cost values can lead to different acceptance probabilities (for a specific temperature value). If you want to use Ackley's original version, or any other scaling for that matter, you can use the IntegerCostFunctionScaler class for this purpose. You can do so by defining your optimization problem with something like: IntegerCostFunctionScaler<BitVector> problem = new IntegerCostFunctionScaler<BitVector>(new OneMax()); Additionally, the OneMaxAckley class specifically implements Ackley's version with the costs scaled by a factor of 10.

    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.

    • Constructor Summary

      Constructors 
      Constructor Description
      OneMax()
      Constructs a OneMax object for use in evaluating candidate solutions to the OneMax problem.
    • Constructor Detail

      • OneMax

        public OneMax()
        Constructs a OneMax object for use in evaluating candidate solutions to the OneMax problem.
    • Method Detail

      • cost

        public int cost​(BitVector candidate)
        Description copied from interface: IntegerCostOptimizationProblem
        Computes the cost of a candidate solution to the problem instance. The lower the cost, the more optimal the candidate solution.
        Specified by:
        cost in interface IntegerCostOptimizationProblem<BitVector>
        Parameters:
        candidate - The candidate solution to evaluate.
        Returns:
        The cost of the candidate solution. Lower cost means better solution.
      • minCost

        public int minCost()
        Description copied from interface: IntegerCostOptimizationProblem
        A lower bound on the minimum theoretical cost across all possible solutions to the problem instance, where lower cost implies better solution. The default implementation returns Integer.MIN_VALUE.
        Specified by:
        minCost in interface IntegerCostOptimizationProblem<BitVector>
        Returns:
        A lower bound on the minimum theoretical cost of the problem instance.
      • value

        public int value​(BitVector candidate)
        Description copied from interface: IntegerCostOptimizationProblem
        Computes the value of the candidate solution within the usual constraints and interpretation of the problem.
        Specified by:
        value in interface IntegerCostOptimizationProblem<BitVector>
        Parameters:
        candidate - The candidate solution to evaluate.
        Returns:
        The actual optimization value of the candidate solution.
      • isMinCost

        public boolean isMinCost​(int cost)
        Description copied from interface: IntegerCostOptimizationProblem
        Checks if a given cost value is equal to the minimum theoretical cost across all possible solutions to the problem instance, where lower cost implies better solution.
        Specified by:
        isMinCost in interface IntegerCostOptimizationProblem<BitVector>
        Parameters:
        cost - The cost to check.
        Returns:
        true if cost is equal to the minimum theoretical cost,