Package org.cicirello.search.problems

Class Trap

  • All Implemented Interfaces:
    OptimizationProblem<BitVector>, Problem<BitVector>
    public final class Trap
extends Object
implements OptimizationProblem<BitVector>

    This class implements Ackley's Trap function, which defines a fitness landscape with a single global optima, and a single sub-optimal local optima, such that most of the search landscape is within the attraction basin of the local optima. Thus, the local optima is a trap for a local search algorithm. The Trap function is related to the TwoMax problem, but in the TwoMax problem, more of the search space is within the attraction basin of the global optima than within that of the local optima.

    The Trap problem is to maximize the following fitness function, f(x), where x is a vector of n bits. Let z = floor((3/4)n). If CountOfOneBits(x) ≤ z, then f(x) = (8n/z)(z-c). Otherwise, f(x) = (10n/(n-z))(c-z).

    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. Only bit vectors with at least 3/4 of the bits equal to a one are within the attraction basin of the global optima.

    The value method implements the original maximization version of the Trap problem, as described above. The algorithms of the Chips-n-Salsa library are defined for minimization, requiring a cost function. The cost method implements the equivalent as the following minimization problem: minimize cost(x) = 10*n - f(x), where f(x) is the Trap function as defined above. 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 Trap problem was introduced by David Ackley in the following paper:
    David H. Ackley. An empirical study of bit vector function optimization. Genetic Algorithms and Simulated Annealing, pages 170-204, 1987.

    • Constructor Summary

      Constructors 
      Constructor Description
      Trap()
      Constructs an instance of Ackley's Trap function.

    • Constructor Detail

      • Trap

        public Trap()
        Constructs an instance of Ackley's Trap function.

    • Method Detail

      • cost

        public double cost​(BitVector candidate)
        Description copied from interface: OptimizationProblem
        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 OptimizationProblem<BitVector>
        Parameters:
        candidate - The candidate solution to evaluate.
        Returns:
        The cost of the candidate solution. Lower cost means better solution.

      • minCost

        public double minCost()
        Description copied from interface: OptimizationProblem
        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 Double.NEGATIVE_INFINITY.
        Specified by:
        minCost in interface OptimizationProblem<BitVector>
        Returns:
        A lower bound on the minimum theoretical cost of the problem instance.

      • value

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

      • isMinCost

        public boolean isMinCost​(double cost)
        Description copied from interface: OptimizationProblem
        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 OptimizationProblem<BitVector>
        Parameters:
        cost - The cost to check.
        Returns:
        true if cost is equal to the minimum theoretical cost,