 All Implemented Interfaces:
IntegerCostOptimizationProblem<BitVector>
,Problem<BitVector>
In the OneMax problem, the metaheuristic is searching the space of bitstrings of length n for the bitstring 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 bitstring 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 1bits.
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 1bits 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 121135, July 1985.

Constructor Summary
ConstructorDescriptionOneMax()
Constructs a OneMax object for use in evaluating candidate solutions to the OneMax problem. 
Method Summary
Modifier and TypeMethodDescriptionint
Computes the cost of a candidate solution to the problem instance.boolean
isMinCost
(int 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.int
minCost()
A lower bound on the minimum theoretical cost across all possible solutions to the problem instance, where lower cost implies better solution.int
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.IntegerCostOptimizationProblem
costAsDouble, getSolutionCostPair

Constructor Details

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


Method Details

cost
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 interfaceIntegerCostOptimizationProblem<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 interfaceIntegerCostOptimizationProblem<BitVector>
 Returns:
 A lower bound on the minimum theoretical cost of the problem instance.

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