Class TwoMax
 java.lang.Object

 org.cicirello.search.problems.TwoMax

 All Implemented Interfaces:
IntegerCostOptimizationProblem<BitVector>
,Problem<BitVector>
public final class TwoMax extends Object implements IntegerCostOptimizationProblem<BitVector>
This class implements the benchmarking problem known as TwoMax. The TwoMax problem is to maximize the following function: f(x) = 18*CountOfOneBits(x)  8*n, where x is a vector of bits of length n. 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. Thus, this search landscape has two basins of attraction. The attractions basin for the global optima is larger. As long as x has more than (4/9)n bits equal to a one, a strict hill climber will be pulled into the global optima. However, a search that ends up at the local optima would have a very steep climb to escape.
The
value
method implements the original maximization version of the TwoMax 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  18*CountOfOneBits(x)  8*n. The global optima is still all 1bits, which has a cost equal to 0. The local optima is still all 0bits, which has a cost equal to 2*n.The TwoMax 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
Constructors Constructor Description TwoMax()
Constructs a TwoMax object for use in evaluating candidate solutions to the TwoMax problem.

Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description int
cost(BitVector candidate)
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
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.IntegerCostOptimizationProblem
getSolutionCostPair




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 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
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 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,

