Package org.cicirello.search.problems
Class PolynomialRootFinding
 java.lang.Object

 org.cicirello.search.problems.PolynomialRootFinding

 All Implemented Interfaces:
OptimizationProblem<SingleReal>
,Problem<SingleReal>
public final class PolynomialRootFinding extends Object implements OptimizationProblem<SingleReal>
This class defines polynomial root finding as an optimization problem, enabling solving via simulated annealing or other metaheuristic optimization algorithms. In polynomial rootfinding, we have an equation of the form: 0 = c_{0} + c_{1}*x + c_{2}*x^{2} + ... + c_{N}*x^{N}. The problem is to find a value of x, known as a root or as a zero, that satisfies the equation. This class represents rootfinding as an optimization problem where one must find a value of x to minimize the value of: abs(c_{0} + c_{1}*x + c_{2}*x^{2} + ... + c_{N}*x^{N}).


Field Summary
Fields Modifier and Type Field Description static double
DEFAULT_PRECISION
The default for the precision of the result.

Constructor Summary
Constructors Constructor Description PolynomialRootFinding(double[] coefficients)
Defines a problem for finding a root of a polynomial equation of the form: 0 = c_{0} + c_{1}*x + c_{2}*x^{2} + ...PolynomialRootFinding(double[] coefficients, double precision)
Defines a problem for finding a root of a polynomial equation of the form: 0 = c_{0} + c_{1}*x + c_{2}*x^{2} + ...PolynomialRootFinding(double a, double b, double c)
Defines a problem for finding a root of a quadratic equation of the form: 0 = a*x^{2} + b*x + c.PolynomialRootFinding(double a, double b, double c, double precision)
Defines a problem for finding a root of a quadratic equation of the form: 0 = a*x^{2} + b*x + c.

Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description double
cost(SingleReal 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(SingleReal 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




Field Detail

DEFAULT_PRECISION
public static final double DEFAULT_PRECISION
The default for the precision of the result. See Also:
isMinCost(double)
, Constant Field Values


Constructor Detail

PolynomialRootFinding
public PolynomialRootFinding(double a, double b, double c)
Defines a problem for finding a root of a quadratic equation of the form: 0 = a*x^{2} + b*x + c. The problem defined is to find a value of x that satisfies the above equation. Uses theDEFAULT_PRECISION
for the precision of the result, i.e., any x such thatDEFAULT_PRECISION
≥ abs( a*x^{2} + b*x + c). Parameters:
a
 The coefficient of the quadratic term.b
 The coefficient of the linear term.c
 The constant term. See Also:
isMinCost(double)

PolynomialRootFinding
public PolynomialRootFinding(double a, double b, double c, double precision)
Defines a problem for finding a root of a quadratic equation of the form: 0 = a*x^{2} + b*x + c. The problem defined is to find a value of x that satisfies the above equation. Programmer can specify the precision of the result, i.e., finds any x such that precision ≥ abs( a*x^{2} + b*x + c). Parameters:
a
 The coefficient of the quadratic term.b
 The coefficient of the linear term.c
 The constant term.precision
 The precision of the result. See Also:
isMinCost(double)

PolynomialRootFinding
public PolynomialRootFinding(double[] coefficients)
Defines a problem for finding a root of a polynomial equation of the form: 0 = c_{0} + c_{1}*x + c_{2}*x^{2} + ... + c_{N}*x^{N}. The problem defined is to find a value of x that satisfies the above equation. Uses theDEFAULT_PRECISION
for the precision of the result, i.e., any x such thatDEFAULT_PRECISION
≥ abs(c_{0} + c_{1}*x + c_{2}*x^{2} + ... + c_{N}*x^{N}). Parameters:
coefficients
 An array of the coefficients of the polynomial. The degree of the polynomial is equal to coefficients.length  1. The value of coefficients[i] is the coefficient of the x^{i} term. Thus, coefficients[0] is the constant term. The length of coefficients must be at least 2. Throws:
IllegalArgumentException
 if coefficients.length < 2NullPointerException
 if coefficients is null See Also:
isMinCost(double)

PolynomialRootFinding
public PolynomialRootFinding(double[] coefficients, double precision)
Defines a problem for finding a root of a polynomial equation of the form: 0 = c_{0} + c_{1}*x + c_{2}*x^{2} + ... + c_{N}*x^{N}. The problem defined is to find a value of x that satisfies the above equation. Programmer can specify the precision of the result, i.e., finds any x such that precision ≥ abs(c_{0} + c_{1}*x + c_{2}*x^{2} + ... + c_{N}*x^{N}). Parameters:
coefficients
 An array of the coefficients of the polynomial. The degree of the polynomial is equal to coefficients.length  1. The value of coefficients[i] is the coefficient of the x^{i} term. Thus, coefficients[0] is the constant term. The length of coefficients must be at least 2.precision
 The precision of the result. Throws:
IllegalArgumentException
 if coefficients.length < 2NullPointerException
 if coefficients is null See Also:
isMinCost(double)


Method Detail

cost
public double cost(SingleReal 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<SingleReal>
 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<SingleReal>
 Returns:
 A lower bound on the minimum theoretical cost of the problem instance.

isMinCost
public 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. Specified by:
isMinCost
in interfaceOptimizationProblem<SingleReal>
 Parameters:
cost
 The cost to check. Returns:
 true if abs(cost) is ≤ precision.
 See Also:
DEFAULT_PRECISION

value
public double value(SingleReal 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<SingleReal>
 Parameters:
candidate
 The candidate solution to evaluate. Returns:
 The actual optimization value of the candidate solution.

