Module org.cicirello.chips_n_salsa
Package org.cicirello.search.problems

Class Trap

java.lang.Object
org.cicirello.search.problems.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.

  • Method Summary

    Modifier and Type
    Method
    Description
    double
    cost(BitVector candidate)
    Computes the cost of a candidate solution to the problem instance.
    boolean
    isMinCost(double cost)
    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.
    double
    minCost()
    A lower bound on the minimum theoretical cost across all possible solutions to the problem instance, where lower cost implies better solution.
    double
    value(BitVector candidate)
    Computes the value of the candidate solution within the usual constraints and interpretation of the problem.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

    Methods inherited from interface org.cicirello.search.problems.OptimizationProblem

    costAsDouble, getSolutionCostPair

  • Constructor Details

    • Trap

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

  • Method Details

    • 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,