Class Plateaus
 java.lang.Object

 org.cicirello.search.problems.Plateaus

 All Implemented Interfaces:
OptimizationProblem<BitVector>
,Problem<BitVector>
public final class Plateaus extends Object implements OptimizationProblem<BitVector>
This class implements Ackley's Plateaus problem, an artificial search landscape over the space of bitstrings that is characterized by large flat regions known as plateaus. This is specifically an implementation of Ackley's 1987 version of the problem (he described a similar problem in an earlier 1985 paper).
The Plateaus problem involves maximizing the following function. Divide the bits of the bit string into four equal sized parts. For each of the four parts, check whether all bits in the segment are equal to a 1, and if so, then that segment contributes 2.5*n to the fitness function, where n is the length of the entire bit string (if there are any 0s in the segment, then that segment doesn't contribute anything to the fitness function). Since there are four segments the optimum occurs when the entire bit string is all 1s, which has a maximum fitness of 10*n. The entire search space only has 5 possible fitness values: 0, 2.5*n, 5*n, 7.5*n, and 10*n.
The
value
method implements the original maximization version of the Plateaus problem, as described above. The algorithms of the ChipsnSalsa library are defined for minimization, requiring a cost function. Thecost
method implements the equivalent as the following minimization problem: minimize cost(x) = 10*n  f(x), where f(x) is the Plateaus function as defined above. The global optima is still all 1bits, which has a cost equal to 0.The Plateaus 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 170204, 1987.


Constructor Summary
Constructors Constructor Description Plateaus()
Constructs an instance of Ackley's Plateaus problem.

Method Summary
All Methods Instance Methods Concrete Methods 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
getSolutionCostPair




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 interfaceOptimizationProblem<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 interfaceOptimizationProblem<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 interfaceOptimizationProblem<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 interfaceOptimizationProblem<BitVector>
 Parameters:
cost
 The cost to check. Returns:
 true if cost is equal to the minimum theoretical cost,

