Pagmo¶

class Pagmo(*args)¶

Pagmo algorithms.

This class exposes bio-inspired and evolutionary global optimization algorithms from the Pagmo library. These algorithms start from an initial population and make it evolve to obtain a final population after a defined number of generations (by setMaximumIterationNumber()). A few of these algorithms allow for multi-objective optimization, and in that case the result is not the best point among the final population but a set of dominant points: a pareto front.

Parameters:

problemOptimizationProblem: Optimization problem to solve
algoNamestr, default=’gaco’: Identifier of the optimization method to use.
startingSample2-d sequence of float, optional: Initial population

Notes

The total number of evaluations is the size of the initial population multiplied by the iteration number plus one. Starting points provided through the startingSample parameter should be within the bounds of the OptimizationProblem, but this is not enforced.

Pagmo provides the following global heuristics:

Algorithm	Description	Multi-objective	MINLP	Batch
gaco	Extended Ant Colony Optimization	no	yes	yes
de	Differential Evolution	no	no	no
sade	Self-adaptive DE (jDE and iDE)	no	no	no
de1220	Self-adaptive DE (de_1220 aka pDE)	no	no	no
gwo	Grey wolf optimizer	no	no	no
ihs	Improved Harmony Search	no	yes	no
pso	Particle Swarm Optimization	no	no	no
pso_gen	Particle Swarm Optimization Generational	no	no	yes
sea	(N+1)-ES Simple Evolutionary Algorithm	no	no	no
sga	Simple Genetic Algorithm	no	yes	no
simulated_annealing	Corana’s Simulated Annealing	no	no	no
bee_colony	Artificial Bee Colony	no	no	no
cmaes	Covariance Matrix Adaptation Evo. Strategy	no	no	yes
xnes	Exponential Evolution Strategies	no	no	no
nsga2	Non-dominated Sorting GA	yes	yes	yes
moead	Multi-objective EA with Decomposition	yes	no	no
moead_gen	Multi-objective EA with Decomposition Gen.	yes	no	yes
mhaco	Multi-objective Hypervolume-based ACO	yes	yes	yes
nspso	Non-dominated Sorting PSO	yes	no	yes

Only gaco and ihs natively support constraints, but for the other algorithms constraints are emulated through penalization. For mhaco, the initial population must satisfy constraints, else it is built by boostrap on valid points with the same population size as the one provided. Some algorithms support batch evaluation, see setBlockSize(). Default parameters are available in the ResourceMap for each algorithm, refer to the correspondings keys in the Pagmo documentation.

Examples

Define an optimization problem to find the minimum of the Rosenbrock function:

>>> import openturns as ot
>>> dim = 2
>>> rosenbrock = ot.SymbolicFunction(['x1', 'x2'], ['(1-x1)^2+100*(x2-x1^2)^2'])
>>> bounds = ot.Interval([-5.0] * dim, [5.0] * dim)
>>> problem = ot.OptimizationProblem(rosenbrock)
>>> problem.setBounds(bounds)

Sample the initial population inside a box:

>>> uniform = ot.JointDistribution([ot.Uniform(-2.0, 2.0)] * dim)
>>> ot.RandomGenerator.SetSeed(0)
>>> init_pop = uniform.getSample(5)

Run GACO on our problem:

>>> algo = ot.Pagmo(problem, 'gaco', init_pop) 
>>> algo.setMaximumIterationNumber(5) 
>>> algo.run() 
>>> result = algo.getResult() 
>>> x_star = result.getOptimalPoint() 
>>> y_star = result.getOptimalValue() 

Get the final population:

>>> final_pop_x = result.getFinalPoints() 
>>> final_pop_y = result.getFinalValues() 

Define a multi-objective problem:

>>> dim = 2
>>> model = ot.SymbolicFunction(['x', 'y'], ['x^2+y^2*(1-x)^3', '-x^2'])
>>> bounds = ot.Interval([-2.0] * dim, [3.0] * dim)
>>> problem = ot.OptimizationProblem(model)
>>> problem.setBounds(bounds)

Sample the initial population inside a box:

>>> uniform = ot.JointDistribution([ot.Uniform(-2.0, 3.0)] * dim)
>>> ot.RandomGenerator.SetSeed(0)
>>> init_pop = uniform.getSample(5)

Run NSGA2 on our problem:

>>> algo = ot.Pagmo(problem, 'nsga2', init_pop) 
>>> algo.setMaximumIterationNumber(5) 
>>> algo.run() 
>>> result = algo.getResult() 
>>> final_pop_x = result.getFinalPoints() 
>>> final_pop_y = result.getFinalValues() 

Get the best front points and values:

>>> front0 = result.getParetoFrontsIndices()[0] 
>>> front0_x = final_pop_x.select(front0) 
>>> front0_y = final_pop_y.select(front0) 

Methods

`GetAlgorithmNames`()	Accessor to the list of algorithm names provided.
`getAlgorithmName`()	Accessor to the algorithm name.
`getBlockSize`()	Block size accessor.
`getCheckStatus`()	Accessor to check status flag.
`getClassName`()	Accessor to the object's name.
`getMaximumAbsoluteError`()	Accessor to maximum allowed absolute error.
`getMaximumCallsNumber`()	Accessor to maximum allowed number of calls.
`getMaximumConstraintError`()	Accessor to maximum allowed constraint error.
`getMaximumIterationNumber`()	Accessor to maximum allowed number of iterations.
`getMaximumRelativeError`()	Accessor to maximum allowed relative error.
`getMaximumResidualError`()	Accessor to maximum allowed residual error.
`getMaximumTimeDuration`()	Accessor to the maximum duration.
`getName`()	Accessor to the object's name.
`getProblem`()	Accessor to optimization problem.
`getResult`()	Accessor to optimization result.
`getSeed`()	Random generator seed accessor.
`getStartingPoint`()	Accessor to starting point.
`getStartingSample`()	Accessor to the sample of starting points.
`hasName`()	Test if the object is named.
`run`()	Launch the optimization.
`setAlgorithmName`(algoName)	Accessor to the algorithm name.
`setBlockSize`(blockSize)	Block size accessor.
`setCheckStatus`(checkStatus)	Accessor to check status flag.
`setMaximumAbsoluteError`(maximumAbsoluteError)	Accessor to maximum allowed absolute error.
`setMaximumCallsNumber`(maximumCallsNumber)	Accessor to maximum allowed number of calls
`setMaximumConstraintError`(maximumConstraintError)	Accessor to maximum allowed constraint error.
`setMaximumIterationNumber`(maximumIterationNumber)	Accessor to maximum allowed number of iterations.
`setMaximumRelativeError`(maximumRelativeError)	Accessor to maximum allowed relative error.
`setMaximumResidualError`(maximumResidualError)	Accessor to maximum allowed residual error.
`setMaximumTimeDuration`(maximumTime)	Accessor to the maximum duration.
`setName`(name)	Accessor to the object's name.
`setProblem`(problem)	Accessor to optimization problem.
`setProgressCallback`(*args)	Set up a progress callback.
`setResult`(result)	Accessor to optimization result.
`setSeed`(seed)	Random generator seed accessor.
`setStartingPoint`(point)	Accessor to starting point.
`setStartingSample`(startingSample)	Accessor to the sample of starting points.
`setStopCallback`(*args)	Set up a stop callback.

getMaximumEvaluationNumber
setMaximumEvaluationNumber

__init__(*args)¶

static GetAlgorithmNames()¶

Accessor to the list of algorithm names provided.

Returns:

namesDescription: List of algorithm names provided, according to its naming convention.

getAlgorithmName()¶

Accessor to the algorithm name.

Returns:

algoNamestr: The identifier of the algorithm.

getBlockSize()¶

Block size accessor.

Returns:

blockSizeint: Batch evaluation granularity.

getCheckStatus()¶

Accessor to check status flag.

Returns:

checkStatusbool: Whether to check the termination status. If set to False, run() will not throw an exception if the algorithm does not fully converge and will allow one to still find a feasible candidate.

getClassName()¶

Accessor to the object’s name.

Returns:

class_namestr: The object class name (object.__class__.__name__).

getMaximumAbsoluteError()¶

Accessor to maximum allowed absolute error.

Returns:

maximumAbsoluteErrorfloat: Maximum allowed absolute error, where the absolute error is defined by $\epsilon^a_n=\|\vect{x}_{n+1}-\vect{x}_n\|_{\infty}$ where $\vect{x}_{n+1}$ and $\vect{x}_n$ are two consecutive approximations of the optimum.

getMaximumCallsNumber()¶

Accessor to maximum allowed number of calls.

Returns:

maximumEvaluationNumberint: Maximum allowed number of direct objective function calls through the () operator. Does not take into account eventual indirect calls through finite difference gradient calls.

getMaximumConstraintError()¶

Accessor to maximum allowed constraint error.

Returns:

maximumConstraintErrorfloat: Maximum allowed constraint error, where the constraint error is defined by $\gamma_n=\|g(\vect{x}_n)\|_{\infty}$ where $\vect{x}_n$ is the current approximation of the optimum and $g$ is the function that gathers all the equality and inequality constraints (violated values only)

getMaximumIterationNumber()¶

Accessor to maximum allowed number of iterations.

Returns:

maximumIterationNumberint: Maximum allowed number of iterations.

getMaximumRelativeError()¶

Accessor to maximum allowed relative error.

Returns:

maximumRelativeErrorfloat: Maximum allowed relative error, where the relative error is defined by $\epsilon^r_n=\epsilon^a_n/\|\vect{x}_{n+1}\|_{\infty}$ if $\|\vect{x}_{n+1}\|_{\infty}\neq 0$ , else $\epsilon^r_n=-1$ .

getMaximumResidualError()¶

Accessor to maximum allowed residual error.

Returns:

maximumResidualErrorfloat: Maximum allowed residual error, where the residual error is defined by $\epsilon^r_n=\frac{\|f(\vect{x}_{n+1})-f(\vect{x}_{n})\|}{\|f(\vect{x}_{n+1})\|}$ if $\|f(\vect{x}_{n+1})\|\neq 0$ , else $\epsilon^r_n=-1$ .

getMaximumTimeDuration()¶

Accessor to the maximum duration.

Returns:

maximumTimefloat: Maximum optimization duration in seconds.

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getProblem()¶

Accessor to optimization problem.

Returns:

problemOptimizationProblem: Optimization problem.

getResult()¶

Accessor to optimization result.

Returns:

resultOptimizationResult: Result class.

getSeed()¶

Random generator seed accessor.

Returns:

seedint: Seed.

getStartingPoint()¶

Accessor to starting point.

Returns:

startingPointPoint: Starting point.

getStartingSample()¶

Accessor to the sample of starting points.

Returns:

startingSampleSample: The initial population.

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

run()¶: Launch the optimization.

setAlgorithmName(algoName)¶

Accessor to the algorithm name.

Parameters:

algoNamestr: The identifier of the algorithm.

setBlockSize(blockSize)¶

Block size accessor.

Parameters:

blockSizeint: Batch evaluation granularity.

setCheckStatus(checkStatus)¶

Accessor to check status flag.

Parameters:

checkStatusbool: Whether to check the termination status. If set to False, run() will not throw an exception if the algorithm does not fully converge and will allow one to still find a feasible candidate.

setMaximumAbsoluteError(maximumAbsoluteError)¶

Accessor to maximum allowed absolute error.

Parameters:

maximumAbsoluteErrorfloat: Maximum allowed absolute error, where the absolute error is defined by $\epsilon^a_n=\|\vect{x}_{n+1}-\vect{x}_n\|_{\infty}$ where $\vect{x}_{n+1}$ and $\vect{x}_n$ are two consecutive approximations of the optimum.

setMaximumCallsNumber(maximumCallsNumber)¶

Accessor to maximum allowed number of calls

Parameters:

maximumEvaluationNumberint: Maximum allowed number of direct objective function calls through the () operator. Does not take into account eventual indirect calls through finite difference gradient calls.

setMaximumConstraintError(maximumConstraintError)¶

Accessor to maximum allowed constraint error.

Parameters:

maximumConstraintErrorfloat: Maximum allowed constraint error, where the constraint error is defined by $\gamma_n=\|g(\vect{x}_n)\|_{\infty}$ where $\vect{x}_n$ is the current approximation of the optimum and $g$ is the function that gathers all the equality and inequality constraints (violated values only)

setMaximumIterationNumber(maximumIterationNumber)¶

Accessor to maximum allowed number of iterations.

Parameters:

maximumIterationNumberint: Maximum allowed number of iterations.

setMaximumRelativeError(maximumRelativeError)¶

Accessor to maximum allowed relative error.

Parameters:

maximumRelativeErrorfloat: Maximum allowed relative error, where the relative error is defined by $\epsilon^r_n=\epsilon^a_n/\|\vect{x}_{n+1}\|_{\infty}$ if $\|\vect{x}_{n+1}\|_{\infty}\neq 0$ , else $\epsilon^r_n=-1$ .

setMaximumResidualError(maximumResidualError)¶

Accessor to maximum allowed residual error.

Parameters:

maximumResidualErrorfloat: Maximum allowed residual error, where the residual error is defined by $\epsilon^r_n=\frac{\|f(\vect{x}_{n+1})-f(\vect{x}_{n})\|}{\|f(\vect{x}_{n+1})\|}$ if $\|f(\vect{x}_{n+1})\|\neq 0$ , else $\epsilon^r_n=-1$ .

setMaximumTimeDuration(maximumTime)¶

Accessor to the maximum duration.

Parameters:

maximumTimefloat: Maximum optimization duration in seconds.

setName(name)¶

Accessor to the object’s name.

Parameters:

namestr: The name of the object.

setProblem(problem)¶

Accessor to optimization problem.

Parameters:

problemOptimizationProblem: Optimization problem.

setProgressCallback(*args)¶

Set up a progress callback.

Can be used to programmatically report the progress of an optimization.

Parameters:

callbackcallable: Takes a float as argument as percentage of progress.

Examples

>>> import sys
>>> import openturns as ot
>>> rosenbrock = ot.SymbolicFunction(['x1', 'x2'], ['(1-x1)^2+100*(x2-x1^2)^2'])
>>> problem = ot.OptimizationProblem(rosenbrock)
>>> solver = ot.OptimizationAlgorithm(problem)
>>> solver.setStartingPoint([0, 0])
>>> solver.setMaximumResidualError(1.e-3)
>>> solver.setMaximumCallsNumber(10000)
>>> def report_progress(progress):
...     sys.stderr.write('-- progress=' + str(progress) + '%\n')
>>> solver.setProgressCallback(report_progress)
>>> solver.run()

setResult(result)¶

Accessor to optimization result.

Parameters:

resultOptimizationResult: Result class.

setSeed(seed)¶

Random generator seed accessor.

Parameters:

seedint: Seed.

Notes

The default is set by the Pagmo-InitialSeed ResourceMap entry.

setStartingPoint(point)¶

Accessor to starting point.

Parameters:

startingPointPoint: Starting point.

setStartingSample(startingSample)¶

Accessor to the sample of starting points.

Parameters:

startingSample2-d sequence of float: The initial population.

setStopCallback(*args)¶

Set up a stop callback.

Can be used to programmatically stop an optimization.

Parameters:

callbackcallable: Returns an int deciding whether to stop or continue.

Examples

>>> import openturns as ot
>>> rosenbrock = ot.SymbolicFunction(['x1', 'x2'], ['(1-x1)^2+100*(x2-x1^2)^2'])
>>> problem = ot.OptimizationProblem(rosenbrock)
>>> solver = ot.OptimizationAlgorithm(problem)
>>> solver.setStartingPoint([0, 0])
>>> solver.setMaximumResidualError(1.e-3)
>>> solver.setMaximumCallsNumber(10000)
>>> def ask_stop():
...     return True
>>> solver.setStopCallback(ask_stop)
>>> solver.run()

Examples using the class¶

Multi-objective optimization using Pagmo

OpenTURNS

An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

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Examples using the class¶