List of algorithms#
Algorithms implemented in Python#
- class pygmo.scipy_optimize(args=(), method: typing.Optional[str] = None, tol: typing.Optional[float] = None, callback: typing.Optional[typing.Callable[[typing.Any], typing.Any]] = None, options: typing.Optional[typing.MutableMapping[str, typing.Any]] = None, selection: pygmo.core.s_policy = Selection policy name: Select best C++ class name: pagmo::select_best Extra info: Absolute migration rate: 1 )#
This class is a user defined algorithm (UDA) providing a wrapper around the function
scipy.optimize.minimize()
.This wraps several well-known local optimization algorithms:
Nelder-Mead
Powell
CG
BFGS
Newton-CG
L-BFGS-B
TNC
COBYLA
SLSQP
trust-constr
dogleg
trust-ncg
trust-exact
trust-krylov
These methods are mostly variants of gradient descent. Some of them require a gradient and will throw an error if invoked on a problem that does not offer one. Constraints are only supported by methods COBYLA, SLSQP and trust-constr.
Example:
>>> import pygmo as pg >>> prob = pg.problem(pg.rosenbrock(10)) >>> pop = pg.population(prob=prob, size=1, seed=0) >>> pop.champion_f[0] 929975.7994682974 >>> scp = pg.algorithm(pg.scipy_optimize(method="L-BFGS-B")) >>> result = scp.evolve(pop).champion_f >>> result[0] 1.13770... >>> pop.problem.get_fevals() 55 >>> pop.problem.get_gevals() 54
The constructor initializes a wrapper instance for a specific algorithm. Construction arguments are those options of
scipy.optimize.minimize()
that are not problem-specific. Problem-specific options, for example the bounds, constraints and the existence of a gradient and hessian, are deduced from the problem in the population given to the evolve function.- Parameters
args – optional - extra arguments for fitness callable
method – optional - string specifying the method to be used by scipy. From scipy docs: “If not given, chosen to be one of BFGS, L-BFGS-B, SLSQP, depending if the problem has constraints or bounds.”
tol – optional - tolerance for termination
callback – optional - callable that is called in each iteration, independent from the fitness function
options – optional - dict of solver-specific options
selection – optional - s_policy to select candidate for local optimization
- Raises
ValueError – If method is not one of Nelder-Mead Powell, CG, BFGS, Newton-CG, L-BFGS-B, TNC, COBYLA, SLSQP, trust-constr, dogleg, trust-ncg, trust-exact, trust-krylov or None.
- evolve(population)#
Call scipy.optimize.minimize with a random member of the population as start value.
The problem is extracted from the population and its fitness function gives the objective value for the optimization process.
- Parameters
population – The population containing the problem and a set of initial solutions.
- Returns
The changed population.
- Raises
ValueError – If the problem has constraints, but during construction a method was selected that cannot deal with them.
ValueError – If the problem contains multiple objectives
ValueError – If the problem is stochastic
unspecified – any exception thrown by the member functions of the problem
- set_verbosity(level: int) None #
Modifies the ‘disp’ parameter in the options dict, which prints out a final convergence message.
- Parameters
level – Every verbosity level above zero prints out a convergence message.
- Raises
ValueError – If options dict was given in instance constructor and has options conflicting with verbosity level
Algorithms exposed from C++#
- class pygmo.null_algorithm#
The null algorithm.
An algorithm used in the default-initialization of
pygmo.algorithm
and of the meta-algorithms.
- class pygmo.gaco(gen = 1, ker = 63, q = 1.0, oracle = 0., acc = 0.01, threshold = 1u, n_gen_mark = 7u, impstop = 100000u, evalstop = 100000u, focus = 0., memory = false, seed = random)#
Extended Ant Colony Optimization algorithm (gaco).
Ant colony optimization is a class of optimization algorithms modeled on the actions of an ant colony. Artificial ‘ants’ (e.g. simulation agents) locate optimal solutions by moving through a parameter space representing all possible solutions. Real ants lay down pheromones directing each other to resources while exploring their environment. The simulated ‘ants’ similarly record their positions and the quality of their solutions, so that in later simulation iterations more ants locate better solutions.
In pygmo we propose a version of this algorithm called extended ACO and originally described by Schlueter et al. Extended ACO generates future generations of ants by using the a multi-kernel gaussian distribution based on three parameters (i.e., pheromone values) which are computed depending on the quality of each previous solution. The solutions are ranked through an oracle penalty method.
This algorithm can be applied to box-bounded single-objective, constrained and unconstrained optimization, with both continuous and integer variables.
Note
The ACO version implemented in PaGMO is an extension of Schlueter’s originally proposed extended ACO algorithm. The main difference between the implemented version and the original one lies in how two of the three pheromone values are computed (in particular, the weights and the standard deviations).
See also
Schlueter, et al. (2009). Extended ant colony optimization for non-convex mixed integer non-linear programming. Computers & Operations Research.
- Parameters
gen (
int
) – number of generationsker (
int
) – kernel sizeq (
float
) – convergence speed parameteroracle (
float
) – oracle parameteracc (
float
) – accuracy parameterthreshold (
int
) – threshold parametern_gen_mark (
int
) – std convergence speed parameterimpstop (
int
) – improvement stopping criterionevalstop (
int
) – evaluation stopping criterionfocus (
float
) – focus parametermemory (
bool
) – memory parameterseed (
int
) – seed used by the internal random number generator (default is random)
- Raises
OverflowError – if gen or seed are negative or greater than an implementation-defined value
ValueError – if either acc is not >=0, focus is not >=0 or q is not >=0, threshold is not in [1,gen] when gen!=0 and memory==false, or threshold is not in >=1 when gen!=0 and memory==true
See also the docs of the C++ class
pagmo::gaco
.- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
and printed to screen. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with agaco
. A verbosity ofN
implies a log line eachN
generations.- Returns
at each logged epoch, the values
Gen
,Fevals
,Best
,Kernel
,Oracle
,dx
,dp
, where:Gen
(int
), generation numberFevals
(int
), number of functions evaluation madeBest
(float
), best fitness function valueKernel
(int
), kernel sizeOracle
(float
), oracle parameterdx
(float
), sum of the absolute value of the difference between the variables’ values of the best and worst solutionsdp
(float
), absolute value of the difference between the worst and best solutions’ penalty values
- Return type
Examples
>>> import pygmo as pg >>> prob = pg.problem(pg.rosenbrock(dim = 2)) >>> pop = pg.population(prob, size=13, seed=23) >>> algo = pg.algorithm(pg.gaco(10, 13, 1.0, 1e9, 0.0, 1, 7, 100000, 100000, 0.0, False, 23)) >>> algo.set_verbosity(1) >>> pop = algo.evolve(pop) Gen: Fevals: Best: Kernel: Oracle: dx: dp: 1 0 179.464 13 1e+09 13.1007 649155 2 13 166.317 13 179.464 5.11695 15654.1 3 26 3.81781 13 166.317 5.40633 2299.95 4 39 3.81781 13 3.81781 2.11767 385.781 5 52 2.32543 13 3.81781 1.30415 174.982 6 65 2.32543 13 2.32543 4.58441 43.808 7 78 1.17205 13 2.32543 1.18585 21.6315 8 91 1.17205 13 1.17205 0.806727 12.0702 9 104 1.17205 13 1.17205 0.806727 12.0702 10 130 0.586187 13 0.586187 0.806727 12.0702 >>> uda = algo.extract(pg.gaco) >>> uda.get_log() [(1, 0, 179.464, 13, 1e+09, 13.1007, 649155), (2, 15, 166.317, 13, 179.464, ...
See also the docs of the relevant C++ method
pagmo::gaco::get_log()
.
- get_seed()#
This method will return the random seed used internally by this uda.
- Returns
the random seed of the population
- Return type
- class pygmo.maco(gen=1, ker=63, q=1.0, threshold=1, n_gen_mark=7, evalstop=100000, focus=0., memory=False, seed=random)#
Multi-objective Ant Colony Optimizer (MACO).
- Parameters
gen (
int
) – number of generationsker (
int
) – kernel sizeq (
float
) – convergence speed parameterthreshold (
int
) – threshold parametern_gen_mark (
int
) – std convergence speed parameterevalstop (
int
) – evaluation stopping criterionfocus (
float
) – focus parametermemory (
bool
) – memory parameterseed (
int
) – seed used by the internal random number generator (default is random)
- Raises
OverflowError – if gen or seed are negative or greater than an implementation-defined value
ValueError – if either focus is < 0, threshold is not in [0,*gen*] when gen is > 0 and memory is False, or if threshold is not >=1 when gen is > 0 and memory is True
See also the docs of the C++ class
pagmo::maco
.- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
and printed to screen. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with amaco
. A verbosity ofN
implies a log line eachN
generations.- Returns
at each logged epoch, the values
Gen
,Fevals
,ideal_point
, where:- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(maco(gen=100)) >>> algo.set_verbosity(20) >>> pop = population(zdt(1), 63) >>> pop = algo.evolve(pop) Gen: Fevals: ideal1: ideal2: 1 0 0.0422249 2.72416 21 1260 0.000622664 1.27304 41 2520 0.000100557 0.542994 61 3780 8.06766e-06 0.290677 81 5040 8.06766e-06 0.290677 >>> uda = algo.extract(maco) >>> uda.get_log() [(1, 0, array([0.04222492, 2.72415949])), (21, 1260, array([6.22663991e-04, ...
See also the docs of the relevant C++ method
pagmo::maco::get_log()
.
- get_seed()#
This method will return the random seed used internally by this uda.
- Returns
the random seed of the population
- Return type
- class pygmo.gwo(gen=1, seed=random)#
Grey Wolf Optimizer (gwo).
Grey Wolf Optimizer is an optimization algorithm based on the leadership hierarchy and hunting mechanism of greywolves, proposed by Seyedali Mirjalilia, Seyed Mohammad Mirjalilib, Andrew Lewis in 2014.
This algorithm is a classic example of a highly criticizable line of search that led in the first decades of our millenia to the development of an entire zoo of metaphors inspiring optimzation heuristics. In our opinion they, as is the case for the grey wolf optimizer, are often but small variations of already existing heuristics rebranded with unnecessray and convoluted biological metaphors. In the case of GWO this is particularly evident as the position update rule is shokingly trivial and can also be easily seen as a product of an evolutionary metaphor or a particle swarm one. Such an update rule is also not particulary effective and results in a rather poor performance most of times. Reading the original peer-reviewed paper, where the poor algorithmic perfromance is hidden by the methodological flaws of the benchmark presented, one is left with a bitter opinion of the whole peer-review system.
This algorithm can be applied to box-bounded single-objective, constrained and unconstrained optimization, with continuous value.
- Parameters
- Raises
OverflowError – if gen or seed are negative or greater than an implementation-defined value
ValueError – if gen is not >=3
See also the docs of the C++ class
pagmo::gwo
.- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
and printed to screen. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with agwo
. A verbosity ofN
implies a log line eachN
generations.- Returns
at each logged epoch, the values
Gen
,Fevals
,ideal_point
, where:- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(gwo(gen=10)) >>> algo.set_verbosity(2) >>> prob = problem(rosenbrock(dim=2)) >>> pop = population(prob, size=13, seed=23) >>> pop = algo.evolve(pop) Gen: Alpha: Beta: Delta: 1 179.464 3502.82 3964.75 3 6.82024 30.2149 61.1906 5 0.321879 2.39373 3.46188 7 0.134441 0.342357 0.439651 9 0.100281 0.211849 0.297448 >>> uda = algo.extract(gwo) >>> uda.get_log() [(1, 179.46420983829944, 3502.8158822203472, 3964.7542658046486), ...
See also the docs of the relevant C++ method
pagmo::gwo::get_log()
.
- class pygmo.bee_colony(gen=1, limit=1, seed=random)#
Artificial Bee Colony.
- Parameters
- Raises
OverflowError – if gen, limit or seed is negative or greater than an implementation-defined value
ValueError – if limit is not greater than 0
See also the docs of the C++ class
pagmo::bee_colony
.- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with abee_colony
. A verbosity ofN
implies a log line eachN
generations.- Returns
at each logged epoch, the values
Gen
,Fevals
,Current best
,Best
, where:- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(bee_colony(gen = 500, limit = 20)) >>> algo.set_verbosity(100) >>> prob = problem(rosenbrock(10)) >>> pop = population(prob, 20) >>> pop = algo.evolve(pop) Gen: Fevals: Best: Current Best: 1 40 261363 261363 101 4040 112.237 267.969 201 8040 20.8885 265.122 301 12040 20.6076 20.6076 401 16040 18.252 140.079 >>> uda = algo.extract(bee_colony) >>> uda.get_log() [(1, 40, 183727.83934515435, 183727.83934515435), ...
See also the docs of the relevant C++ method
pagmo::bee_colony::get_log()
.
- class pygmo.de(gen=1, F=0.8, CR=0.9, variant=2, ftol=1e-6, xtol=1e-6, seed=random)#
Differential Evolution
- Parameters
gen (
int
) – number of generationsF (
float
) – weight coefficient (dafault value is 0.8)CR (
float
) – crossover probability (dafault value is 0.9)variant (
int
) – mutation variant (dafault variant is 2: /rand/1/exp)ftol (
float
) – stopping criteria on the f tolerance (default is 1e-6)xtol (
float
) – stopping criteria on the x tolerance (default is 1e-6)seed (
int
) – seed used by the internal random number generator (default is random)
- Raises
OverflowError – if gen, variant or seed is negative or greater than an implementation-defined value
ValueError – if F, CR are not in [0,1] or variant is not in [1, 10]
The following variants (mutation variants) are available to create a new candidate individual:
1 - best/1/exp
2 - rand/1/exp
3 - rand-to-best/1/exp
4 - best/2/exp
5 - rand/2/exp
6 - best/1/bin
7 - rand/1/bin
8 - rand-to-best/1/bin
9 - best/2/bin
10 - rand/2/bin
See also the docs of the C++ class
pagmo::de
.- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with ade
. A verbosity ofN
implies a log line eachN
generations.- Returns
at each logged epoch, the values
Gen
,Fevals
,Best
,dx
,df
, where:Gen
(int
), generation numberFevals
(int
), number of functions evaluation madeBest
(float
), the best fitness function currently in the populationdx
(float
), the norm of the distance to the population mean of the mutant vectorsdf
(float
), the population flatness evaluated as the distance between the fitness of the best and of the worst individual
- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(de(gen = 500)) >>> algo.set_verbosity(100) >>> prob = problem(rosenbrock(10)) >>> pop = population(prob, 20) >>> pop = algo.evolve(pop) Gen: Fevals: Best: dx: df: 1 20 162446 65.2891 1.78686e+06 101 2020 198.402 8.4454 572.161 201 4020 21.1155 2.60629 24.5152 301 6020 6.67069 0.51811 1.99744 401 8020 3.60022 0.583444 0.554511 Exit condition -- generations = 500 >>> uda = algo.extract(de) >>> uda.get_log() [(1, 20, 162446.0185265718, 65.28911664703388, 1786857.8926660626), ...
See also the docs of the relevant C++ method
pagmo::de::get_log()
.
- class pygmo.sea(gen=1, seed=random)#
(N+1)-ES simple evolutionary algorithm.
- Parameters
- Raises
OverflowError – if gen or seed are negative or greater than an implementation-defined value
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
See also the docs of the C++ class
pagmo::sea
.- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
and printed to screen. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with asea
. A verbosity larger than 1 will produce a log with one entry each verbosity fitness evaluations. A verbosity equal to 1 will produce a log with one entry at each improvement of the fitness.- Returns
at each logged epoch, the values
Gen
,Fevals
,Best
,Improvement
,Mutations
- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(sea(500)) >>> algo.set_verbosity(50) >>> prob = problem(schwefel(dim = 20)) >>> pop = population(prob, 20) >>> pop = algo.evolve(pop) Gen: Fevals: Best: Improvement: Mutations: 1 1 6363.44 2890.49 2 1001 1001 1039.92 -562.407 3 2001 2001 358.966 -632.6 2 3001 3001 106.08 -995.927 3 4001 4001 83.391 -266.8 1 5001 5001 62.4994 -1018.38 3 6001 6001 39.2851 -732.695 2 7001 7001 37.2185 -518.847 1 8001 8001 20.9452 -450.75 1 9001 9001 17.9193 -270.679 1 >>> uda = algo.extract(sea) >>> uda.get_log() [(1, 1, 6363.442036625835, 2890.4854414320716, 2), (1001, 1001, ...
See also the docs of the relevant C++ method
pagmo::sea::get_log()
.
- class pygmo.sga(gen=1, cr=.90, eta_c=1., m=0.02, param_m=1., param_s=2, crossover='exponential', mutation='polynomial', selection='tournament', seed=random)#
A Simple Genetic Algorithm
New in version 2.2.
Approximately during the same decades as Evolutionary Strategies (see
sea
) were studied, a different group led by John Holland, and later by his student David Goldberg, introduced and studied an algorithmic framework called “genetic algorithms” that were, essentially, leveraging on the same idea but introducing also crossover as a genetic operator. This led to a few decades of confusion and discussions on what was an evolutionary startegy and what a genetic algorithm and on whether the crossover was a useful operator or mutation only algorithms were to be preferred.In pygmo we provide a rather classical implementation of a genetic algorithm, letting the user choose between selected crossover types, selection schemes and mutation types.
The pseudo code of our version is:
> Start from a population (pop) of dimension N > while i < gen > > Selection: create a new population (pop2) with N individuals selected from pop (with repetition allowed) > > Crossover: create a new population (pop3) with N individuals obtained applying crossover to pop2 > > Mutation: create a new population (pop4) with N individuals obtained applying mutation to pop3 > > Evaluate all new chromosomes in pop4 > > Reinsertion: set pop to contain the best N individuals taken from pop and pop4
The various blocks of pygmo genetic algorithm are listed below:
Selection: two selection methods are provided:
tournament
andtruncated
.Tournament
selection works by selecting each offspring as the one having the minimal fitness in a random group of size param_s. Thetruncated
selection, instead, works selecting the best param_s chromosomes in the entire population over and over. We have deliberately not implemented the popular roulette wheel selection as we are of the opinion that such a system does not generalize much being highly sensitive to the fitness scaling.Crossover: four different crossover schemes are provided:
single
,exponential
,binomial
,sbx
. Thesingle
point crossover, works selecting a random point in the parent chromosome and, with probability cr, inserting the partner chromosome thereafter. Theexponential
crossover is taken from the algorithm differential evolution, implemented, in pygmo, asde
. It essentially selects a random point in the parent chromosome and inserts, in each successive gene, the partner values with probability cr up to when it stops. The binomial crossover inserts each gene from the partner with probability cr. The simulated binary crossover (calledsbx
), is taken from the NSGA-II algorithm, implemented in pygmo asnsga2
, and makes use of an additional parameter called distribution index eta_c.Mutation: three different mutations schemes are provided:
uniform
,gaussian
andpolynomial
. Uniform mutation simply randomly samples from the bounds. Gaussian muattion samples around each gene using a normal distribution with standard deviation proportional to the param_m and the bounds width. The last scheme is thepolynomial
mutation from Deb.Reinsertion: the only reinsertion strategy provided is what we call pure elitism. After each generation all parents and children are put in the same pool and only the best are passed to the next generation.
- Parameters
gen (
int
) – number of generations.cr (
float
) – crossover probability.eta_c (
float
) – distribution index forsbx
crossover. This parameter is inactive if other types of crossover are selected.m (
float
) – mutation probability.param_m (
float
) – distribution index (polynomial
mutation), gaussian width (gaussian
mutation) or inactive (uniform
mutation)param_s (
float
) – the number of best individuals to use in “truncated” selection or the size of the tournament intournament
selection.crossover (
str
) – the crossover strategy. One ofexponential
,binomial
,single
orsbx
mutation (
str
) – the mutation strategy. One ofgaussian
,polynomial
oruniform
.selection (
str
) – the selection strategy. One oftournament
, “truncated”.seed (
int
) – seed used by the internal random number generator
- Raises
OverflowError – if gen or seed are negative or greater than an implementation-defined value
ValueError – if cr is not in [0,1], if eta_c is not in [1,100], if m is not in [0,1], input_f mutation is not one of
gaussian
,uniform
orpolynomial
, if selection not one of “roulette”, “truncated” or crossover is not one ofexponential
,binomial
,sbx
,single
, if param_m is not in [0,1] and mutation is notpolynomial
, if mutation is not in [1,100] and mutation ispolynomial
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
See also the docs of the C++ class
pagmo::sga
.- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
and printed to screen. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with asga
. A verbosity larger than 1 will produce a log with one entry each verbosity fitness evaluations. A verbosity equal to 1 will produce a log with one entry at each improvement of the fitness.- Returns
at each logged epoch, the values
Gen
,Fevals
,Best
,Improvement
Gen
(int
), generation.Fevals
(int
), number of functions evaluation made.Best
(float
), the best fitness function found so far.Improvement
(float
), improvement made by the last generation.- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(sga(gen = 500)) >>> algo.set_verbosity(50) >>> prob = problem(schwefel(dim = 20)) >>> pop = population(prob, 20) >>> pop = algo.evolve(pop) Gen: Fevals: Best: Improvement: Mutations: 1 1 6363.44 2890.49 2 1001 1001 1039.92 -562.407 3 2001 2001 358.966 -632.6 2 3001 3001 106.08 -995.927 3 4001 4001 83.391 -266.8 1 5001 5001 62.4994 -1018.38 3 6001 6001 39.2851 -732.695 2 7001 7001 37.2185 -518.847 1 8001 8001 20.9452 -450.75 1 9001 9001 17.9193 -270.679 1 >>> uda = algo.extract(sea) >>> uda.get_log() [(1, 1, 6363.442036625835, 2890.4854414320716, 2), (1001, 1001, ...
See also the docs of the relevant C++ method
pagmo::sga::get_log()
.
- class pygmo.sade(gen=1, variant=2, variant_adptv=1, ftol=1e-6, xtol=1e-6, memory=False, seed=random)#
Self-adaptive Differential Evolution.
- Parameters
gen (
int
) – number of generationsvariant (
int
) – mutation variant (dafault variant is 2: /rand/1/exp)variant_adptv (
int
) – F and CR parameter adaptation scheme to be used (one of 1..2)ftol (
float
) – stopping criteria on the x tolerance (default is 1e-6)xtol (
float
) – stopping criteria on the f tolerance (default is 1e-6)memory (
bool
) – when true the adapted parameters CR anf F are not reset between successive calls to the evolve methodseed (
int
) – seed used by the internal random number generator (default is random)
- Raises
OverflowError – if gen, variant, variant_adptv or seed is negative or greater than an implementation-defined value
ValueError – if variant is not in [1,18] or variant_adptv is not in [0,1]
The following variants (mutation variants) are available to create a new candidate individual:
1 - best/1/exp
2 - rand/1/exp
3 - rand-to-best/1/exp
4 - best/2/exp
5 - rand/2/exp
6 - best/1/bin
7 - rand/1/bin
8 - rand-to-best/1/bin
9 - best/2/bin
10 - rand/2/bin
11 - rand/3/exp
12 - rand/3/bin
13 - best/3/exp
14 - best/3/bin
15 - rand-to-current/2/exp
16 - rand-to-current/2/bin
17 - rand-to-best-and-current/2/exp
18 - rand-to-best-and-current/2/bin
The following adaptation schemes are available:
1 - jDE
2 - iDE
See also the docs of the C++ class
pagmo::sade
.- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with asade
. A verbosity ofN
implies a log line eachN
generations.- Returns
at each logged epoch, the values
Gen
,Fevals
,Best
,F
,CR
,dx
,df
, where:Gen
(int
), generation numberFevals
(int
), number of functions evaluation madeBest
(float
), the best fitness function currently in the populationF
(float
), the value of the adapted paramter F used to create the best so farCR
(float
), the value of the adapted paramter CR used to create the best so fardx
(float
), the norm of the distance to the population mean of the mutant vectorsdf
(float
), the population flatness evaluated as the distance between the fitness of the best and of the worst individual
- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(sade(gen = 500)) >>> algo.set_verbosity(100) >>> prob = problems.rosenbrock(10) >>> pop = population(prob, 20) >>> pop = algo.evolve(pop) Gen: Fevals: Best: F: CR: dx: df: 1 20 297060 0.690031 0.294769 44.1494 2.30584e+06 101 2020 97.4258 0.58354 0.591527 13.3115 441.545 201 4020 8.79247 0.6678 0.53148 17.8822 121.676 301 6020 6.84774 0.494549 0.98105 12.2781 40.9626 401 8020 4.7861 0.428741 0.743813 12.2938 39.7791 Exit condition -- generations = 500 >>> uda = algo.extract(sade) >>> uda.get_log() [(1, 20, 297059.6296130389, 0.690031071850855, 0.29476914701127666, 44.14940516578547, 2305836.7422693395), ...
See also the docs of the relevant C++ method
pagmo::sade::get_log()
.
- class pygmo.de1220(gen=1, allowed_variants=[2, 3, 7, 10, 13, 14, 15, 16], variant_adptv=1, ftol=1e-6, xtol=1e-6, memory=False, seed=random)#
Self-adaptive Differential Evolution, pygmo flavour (pDE). The adaptation of the mutation variant is added to
sade
- Parameters
gen (
int
) – number of generationsallowed_variants (array-like object) – allowed mutation variants, each one being a number in [1, 18]
variant_adptv (
int
) – F and CR parameter adaptation scheme to be used (one of 1..2)ftol (
float
) – stopping criteria on the x tolerance (default is 1e-6)xtol (
float
) – stopping criteria on the f tolerance (default is 1e-6)memory (
bool
) – when true the adapted parameters CR anf F are not reset between successive calls to the evolve methodseed (
int
) – seed used by the internal random number generator (default is random)
- Raises
OverflowError – if gen, variant, variant_adptv or seed is negative or greater than an implementation-defined value
ValueError – if each id in variant_adptv is not in [1,18] or variant_adptv is not in [0,1]
The following variants (mutation variants) can be put into allowed_variants:
1 - best/1/exp
2 - rand/1/exp
3 - rand-to-best/1/exp
4 - best/2/exp
5 - rand/2/exp
6 - best/1/bin
7 - rand/1/bin
8 - rand-to-best/1/bin
9 - best/2/bin
10 - rand/2/bin
11 - rand/3/exp
12 - rand/3/bin
13 - best/3/exp
14 - best/3/bin
15 - rand-to-current/2/exp
16 - rand-to-current/2/bin
17 - rand-to-best-and-current/2/exp
18 - rand-to-best-and-current/2/bin
The following adaptation schemes for the parameters F and CR are available:
1 - jDE
2 - iDE
See also the docs of the C++ class
pagmo::de1220
.- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with ade1220
. A verbosity of N implies a log line each N generations.- Returns
at each logged epoch, the values
Gen
,Fevals
,Best
,F
,CR
,Variant
,dx
,df
, where:Gen
(int
), generation numberFevals
(int
), number of functions evaluation madeBest
(float
), the best fitness function currently in the populationF
(float
), the value of the adapted paramter F used to create the best so farCR
(float
), the value of the adapted paramter CR used to create the best so farVariant
(int
), the mutation variant used to create the best so fardx
(float
), the norm of the distance to the population mean of the mutant vectorsdf
(float
), the population flatness evaluated as the distance between the fitness of the best and of the worst individual
- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(de1220(gen = 500)) >>> algo.set_verbosity(100) >>> prob = problem(rosenbrock(10)) >>> pop = population(prob, 20) >>> pop = algo.evolve(pop) Gen: Fevals: Best: F: CR: Variant: dx: df: 1 20 285653 0.55135 0.441551 16 43.9719 2.02379e+06 101 2020 12.2721 0.127285 0.0792493 14 3.22986 106.764 201 4020 5.72927 0.148337 0.777806 14 2.72177 4.10793 301 6020 4.85084 0.12193 0.996191 3 2.95555 3.85027 401 8020 4.20638 0.235997 0.996259 3 3.60338 4.49432 Exit condition -- generations = 500 >>> uda = algo.extract(de1220) >>> uda.get_log() [(1, 20, 285652.7928977573, 0.551350234239449, 0.4415510963067054, 16, 43.97185788345982, 2023791.5123259544), ...
See also the docs of the relevant C++ method
pagmo::de1220::get_log()
.
- class pygmo.cmaes(gen=1, cc=- 1, cs=- 1, c1=- 1, cmu=- 1, sigma0=0.5, ftol=1e-6, xtol=1e-6, memory=False, force_bounds=False, seed=random)#
Covariance Matrix Evolutionary Strategy (CMA-ES).
- Parameters
gen (
int
) – number of generationscc (
float
) – backward time horizon for the evolution path (by default is automatically assigned)cs (
float
) – makes partly up for the small variance loss in case the indicator is zero (by default is automatically assigned)c1 (
float
) – learning rate for the rank-one update of the covariance matrix (by default is automatically assigned)cmu (
float
) – learning rate for the rank-mu update of the covariance matrix (by default is automatically assigned)sigma0 (
float
) – initial step-sizeftol (
float
) – stopping criteria on the x tolerancextol (
float
) – stopping criteria on the f tolerancememory (
bool
) – when true the adapted parameters are not reset between successive calls to the evolve methodforce_bounds (
bool
) – when true the box bounds are enforced. The fitness will never be called outside the bounds but the covariance matrix adaptation mechanism will worsenseed (
int
) – seed used by the internal random number generator (default is random)
- Raises
OverflowError – if gen is negative or greater than an implementation-defined value
ValueError – if cc, cs, c1, cmu are not in [0,1] or -1
See also the docs of the C++ class
pagmo::cmaes
.- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with acmaes
. A verbosity ofN
implies a log line eachN
generations.- Returns
at each logged epoch, the values
Gen
,Fevals
,Best
,dx
,df
,sigma
, where:Gen
(int
), generation numberFevals
(int
), number of functions evaluation madeBest
(float
), the best fitness function currently in the populationdx
(float
), the norm of the distance to the population mean of the mutant vectorsdf
(float
), the population flatness evaluated as the distance between the fitness of the best and of the worst individualsigma
(float
), the current step-size
- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(cmaes(gen = 500)) >>> algo.set_verbosity(100) >>> prob = problem(rosenbrock(10)) >>> pop = population(prob, 20) >>> pop = algo.evolve(pop) Gen: Fevals: Best: dx: df: sigma: 1 0 173924 33.6872 3.06519e+06 0.5 101 2000 92.9612 0.583942 156.921 0.0382078 201 4000 8.79819 0.117574 5.101 0.0228353 301 6000 4.81377 0.0698366 1.34637 0.0297664 401 8000 1.04445 0.0568541 0.514459 0.0649836 Exit condition -- generations = 500 >>> uda = algo.extract(cmaes) >>> uda.get_log() [(1, 0, 173924.2840042722, 33.68717961390855, 3065192.3843070837, 0.5), ...
See also the docs of the relevant C++ method
pagmo::cmaes::get_log()
.
- class pygmo.moead(gen=1, weight_generation='grid', decomposition='tchebycheff', neighbours=20, CR=1, F=0.5, eta_m=20, realb=0.9, limit=2, preserve_diversity=true, seed=random)#
Multi Objective Evolutionary Algorithms by Decomposition (the DE variant)
- Parameters
gen (
int
) – number of generationsweight_generation (
str
) – method used to generate the weights, one of “grid”, “low discrepancy” or “random”decomposition (
str
) – method used to decompose the objectives, one of “tchebycheff”, “weighted” or “bi”neighbours (
int
) – size of the weight’s neighborhoodCR (
float
) – crossover parameter in the Differential Evolution operatorF (
float
) – parameter for the Differential Evolution operatoreta_m (
float
) – distribution index used by the polynomial mutationrealb (
float
) – chance that the neighbourhood is considered at each generation, rather than the whole population (only if preserve_diversity is true)limit (
int
) – maximum number of copies reinserted in the population (only if m_preserve_diversity is true)preserve_diversity (
bool
) – when true activates diversity preservation mechanismsseed (
int
) – seed used by the internal random number generator (default is random)
- Raises
OverflowError – if gen, neighbours, seed or limit are negative or greater than an implementation-defined value
ValueError – if either decomposition is not one of ‘tchebycheff’, ‘weighted’ or ‘bi’, weight_generation is not one of ‘random’, ‘low discrepancy’ or ‘grid’, CR or F or realb are not in [0.,1.] or eta_m is negative, if neighbours is not >=2
See also the docs of the C++ class
pagmo::moead
.- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with amoead
. A verbosity ofN
implies a log line eachN
generations.- Returns
at each logged epoch, the values
Gen
,Fevals
,ADR
,ideal_point
, where:Gen
(int
), generation numberFevals
(int
), number of functions evaluation madeADF
(float
), Average Decomposed Fitness, that is the average across all decomposed problem of the single objective decomposed fitness along the corresponding directionideal_point
(array
), the ideal point of the current population (cropped to max 5 dimensions only in the screen output)
- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(moead(gen=500)) >>> algo.set_verbosity(100) >>> prob = problem(zdt()) >>> pop = population(prob, 40) >>> pop = algo.evolve(pop) Gen: Fevals: ADF: ideal1: ideal2: 1 0 32.5747 0.00190532 2.65685 101 4000 5.67751 2.56736e-09 0.468789 201 8000 5.38297 2.56736e-09 0.0855025 301 12000 5.05509 9.76581e-10 0.0574796 401 16000 5.13126 9.76581e-10 0.0242256 >>> uda = algo.extract(moead) >>> uda.get_log() [(1, 0, 32.574745630075874, array([ 1.90532430e-03, 2.65684834e+00])), ...
See also the docs of the relevant C++ method
pagmo::moead::get_log()
.
- class pygmo.moead_gen(gen=1, weight_generation='grid', decomposition='tchebycheff', neighbours=20, CR=1, F=0.5, eta_m=20, realb=0.9, limit=2, preserve_diversity=true, seed=random)#
Multi Objective Evolutionary Algorithms by Decomposition (the DE variant)
- Parameters
gen (
int
) – number of generationsweight_generation (
str
) – method used to generate the weights, one of “grid”, “low discrepancy” or “random”decomposition (
str
) – method used to decompose the objectives, one of “tchebycheff”, “weighted” or “bi”neighbours (
int
) – size of the weight’s neighborhoodCR (
float
) – crossover parameter in the Differential Evolution operatorF (
float
) – parameter for the Differential Evolution operatoreta_m (
float
) – distribution index used by the polynomial mutationrealb (
float
) – chance that the neighbourhood is considered at each generation, rather than the whole population (only if preserve_diversity is true)limit (
int
) – maximum number of copies reinserted in the population (only if m_preserve_diversity is true)preserve_diversity (
bool
) – when true activates diversity preservation mechanismsseed (
int
) – seed used by the internal random number generator (default is random)
- Raises
OverflowError – if gen, neighbours, seed or limit are negative or greater than an implementation-defined value
ValueError – if either decomposition is not one of ‘tchebycheff’, ‘weighted’ or ‘bi’, weight_generation is not one of ‘random’, ‘low discrepancy’ or ‘grid’, CR or F or realb are not in [0.,1.] or eta_m is negative, if neighbours is not >=2
See also the docs of the C++ class
pagmo::moead_gen
.- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with amoead_gen
. A verbosity ofN
implies a log line eachN
generations.- Returns
at each logged epoch, the values
Gen
,Fevals
,ADR
,ideal_point
, where:Gen
(int
), generation numberFevals
(int
), number of functions evaluation madeADF
(float
), Average Decomposed Fitness, that is the average across all decomposed problem of the single objective decomposed fitness along the corresponding directionideal_point
(array
), the ideal point of the current population (cropped to max 5 dimensions only in the screen output)
- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(moead_gen(gen=500)) >>> algo.set_verbosity(100) >>> prob = problem(zdt()) >>> pop = population(prob, 40) >>> pop = algo.evolve(pop) Gen: Fevals: ADF: ideal1: ideal2: 1 0 32.5747 0.00190532 2.65685 101 4000 5.67751 2.56736e-09 0.468789 201 8000 5.38297 2.56736e-09 0.0855025 301 12000 5.05509 9.76581e-10 0.0574796 401 16000 5.13126 9.76581e-10 0.0242256 >>> uda = algo.extract(moead_gen) >>> uda.get_log() [(1, 0, 32.574745630075874, array([ 1.90532430e-03, 2.65684834e+00])), ...
See also the docs of the relevant C++ method
pagmo::moead_gen::get_log()
.
- get_seed()#
This method will return the random seed used internally by this uda.
- Returns
the random seed of the population
- Return type
- class pygmo.compass_search(max_fevals=1, start_range=.1, stop_range=.01, reduction_coeff=.5)#
Compass Search
- Parameters
- Raises
OverflowError – if max_fevals is negative or greater than an implementation-defined value
ValueError – if start_range is not in (0, 1], if stop_range is not in (start_range, 1] or if reduction_coeff is not in (0,1)
See also the docs of the C++ class
pagmo::compass_search
.- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
and printed to screen. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with acompass_search
. A verbosity larger than 0 implies one log line at each improvment of the fitness or change in the search range.- Returns
at each logged epoch, the values``Fevals``,
Best
,Range
, where:- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(compass_search(max_fevals = 500)) >>> algo.set_verbosity(1) >>> prob = problem(hock_schittkowski_71()) >>> pop = population(prob, 1) >>> pop = algo.evolve(pop) Fevals: Best: Violated: Viol. Norm: Range: 4 110.785 1 2.40583 0.5 12 110.785 1 2.40583 0.25 20 110.785 1 2.40583 0.125 22 91.0454 1 1.01855 0.125 25 96.2795 1 0.229446 0.125 33 96.2795 1 0.229446 0.0625 41 96.2795 1 0.229446 0.03125 45 94.971 1 0.127929 0.03125 53 94.971 1 0.127929 0.015625 56 95.6252 1 0.0458521 0.015625 64 95.6252 1 0.0458521 0.0078125 68 95.2981 1 0.0410151 0.0078125 76 95.2981 1 0.0410151 0.00390625 79 95.4617 1 0.00117433 0.00390625 87 95.4617 1 0.00117433 0.00195312 95 95.4617 1 0.00117433 0.000976562 103 95.4617 1 0.00117433 0.000488281 111 95.4617 1 0.00117433 0.000244141 115 95.4515 0 0 0.000244141 123 95.4515 0 0 0.00012207 131 95.4515 0 0 6.10352e-05 139 95.4515 0 0 3.05176e-05 143 95.4502 0 0 3.05176e-05 151 95.4502 0 0 1.52588e-05 159 95.4502 0 0 7.62939e-06 Exit condition -- range: 7.62939e-06 <= 1e-05 >>> uda = algo.extract(compass_search) >>> uda.get_log() [(4, 110.785345345, 1, 2.405833534534, 0.5), (12, 110.785345345, 1, 2.405833534534, 0.25) ...
See also the docs of the relevant C++ method
pagmo::compass_search::get_log()
.
- property replacement#
Individual replacement policy.
This attribute represents the policy that is used in the
evolve()
method to select the individual that will be replaced by the optimised individual. The attribute can be either a string or an integral.If the attribute is a string, it must be one of
"best"
,"worst"
and"random"
:"best"
will select the best individual in the population,"worst"
will select the worst individual in the population,"random"
will randomly choose one individual in the population.
set_random_sr_seed()
can be used to seed the random number generator used by the"random"
policy.If the attribute is an integer, it represents the index (in the population) of the individual that will be replaced by the optimised individual.
- Returns
the individual replacement policy or index
- Return type
- Raises
OverflowError – if the attribute is set to an integer which is negative or too large
ValueError – if the attribute is set to an invalid string
TypeError – if the attribute is set to a value of an invalid type
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- property selection#
Individual selection policy.
This attribute represents the policy that is used in the
evolve()
method to select the individual that will be optimised. The attribute can be either a string or an integral.If the attribute is a string, it must be one of
"best"
,"worst"
and"random"
:"best"
will select the best individual in the population,"worst"
will select the worst individual in the population,"random"
will randomly choose one individual in the population.
set_random_sr_seed()
can be used to seed the random number generator used by the"random"
policy.If the attribute is an integer, it represents the index (in the population) of the individual that is selected for optimisation.
- Returns
the individual selection policy or index
- Return type
- Raises
OverflowError – if the attribute is set to an integer which is negative or too large
ValueError – if the attribute is set to an invalid string
TypeError – if the attribute is set to a value of an invalid type
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- set_random_sr_seed(seed)#
Set the seed for the
"random"
selection/replacement policies.- Parameters
seed (
int
) – the value that will be used to seed the random number generator used by the"random"
election/replacement policies (seeselection
andreplacement
)- Raises
OverflowError – if the attribute is set to an integer which is negative or too large
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- class pygmo.simulated_annealing(Ts=10., Tf=.1, n_T_adj=10, n_range_adj=10, bin_size=10, start_range=1., seed=random)#
Simulated Annealing (Corana’s version)
- Parameters
Ts (
float
) – starting temperatureTf (
float
) – final temperaturen_T_adj (
int
) – number of temperature adjustments in the annealing schedulen_range_adj (
int
) – number of adjustments of the search range performed at a constant temperaturebin_size (
int
) – number of mutations that are used to compute the acceptance ratestart_range (
float
) – starting range for mutating the decision vectorseed (
int
) – seed used by the internal random number generator (default is random)
- Raises
OverflowError – if n_T_adj, n_range_adj or bin_size are negative or greater than an implementation-defined value
ValueError – if Ts is not in (0, inf), if Tf is not in (0, inf), if Tf > Ts or if start_range is not in (0,1]
ValueError – if n_T_adj is not strictly positive or if n_range_adj is not strictly positive
See also the docs of the C++ class
pagmo::simulated_annealing
.- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
and printed to screen. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with asimulated_annealing
. A verbosity larger than 0 will produce a log with one entry each verbosity fitness evaluations.- Returns
at each logged epoch, the values
Fevals
,Best
,Current
,Mean range
,Temperature
, where:Fevals
(int
), number of functions evaluation madeBest
(float
), the best fitness function found so farCurrent
(float
), last fitness sampledMean range
(float
), the mean search range across the decision vector components (relative to the box bounds width)Temperature
(float
), the current temperature
- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(simulated_annealing(Ts=10., Tf=1e-5, n_T_adj = 100)) >>> algo.set_verbosity(5000) >>> prob = problem(rosenbrock(dim = 10)) >>> pop = population(prob, 1) >>> pop = algo.evolve(pop) Fevals: Best: Current: Mean range: Temperature: 57 5937 5937 0.48 10 10033 9.50937 28.6775 0.0325519 2.51189 15033 7.87389 14.3951 0.0131132 1.25893 20033 7.87389 8.68616 0.0120491 0.630957 25033 2.90084 4.43344 0.00676893 0.316228 30033 0.963616 1.36471 0.00355931 0.158489 35033 0.265868 0.63457 0.00202753 0.0794328 40033 0.13894 0.383283 0.00172611 0.0398107 45033 0.108051 0.169876 0.000870499 0.0199526 50033 0.0391731 0.0895308 0.00084195 0.01 55033 0.0217027 0.0303561 0.000596116 0.00501187 60033 0.00670073 0.00914824 0.000342754 0.00251189 65033 0.0012298 0.00791511 0.000275182 0.00125893 70033 0.00112816 0.00396297 0.000192117 0.000630957 75033 0.000183055 0.00139717 0.000135137 0.000316228 80033 0.000174868 0.00192479 0.000109781 0.000158489 85033 7.83e-05 0.000494225 8.20723e-05 7.94328e-05 90033 5.35153e-05 0.000120148 5.76009e-05 3.98107e-05 95033 5.35153e-05 9.10958e-05 3.18624e-05 1.99526e-05 99933 2.34849e-05 8.72206e-05 2.59215e-05 1.14815e-05 >>> uda = algo.extract(simulated_annealing) >>> uda.get_log() [(57, 5936.999957947842, 5936.999957947842, 0.47999999999999987, 10.0), (10033, ...
See also the docs of the relevant C++ method
pagmo::simulated_annealing::get_log()
.
- get_seed()#
This method will return the random seed used internally by this uda.
- Returns
the random seed of the population
- Return type
- property replacement#
Individual replacement policy.
This attribute represents the policy that is used in the
evolve()
method to select the individual that will be replaced by the optimised individual. The attribute can be either a string or an integral.If the attribute is a string, it must be one of
"best"
,"worst"
and"random"
:"best"
will select the best individual in the population,"worst"
will select the worst individual in the population,"random"
will randomly choose one individual in the population.
set_random_sr_seed()
can be used to seed the random number generator used by the"random"
policy.If the attribute is an integer, it represents the index (in the population) of the individual that will be replaced by the optimised individual.
- Returns
the individual replacement policy or index
- Return type
- Raises
OverflowError – if the attribute is set to an integer which is negative or too large
ValueError – if the attribute is set to an invalid string
TypeError – if the attribute is set to a value of an invalid type
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- property selection#
Individual selection policy.
This attribute represents the policy that is used in the
evolve()
method to select the individual that will be optimised. The attribute can be either a string or an integral.If the attribute is a string, it must be one of
"best"
,"worst"
and"random"
:"best"
will select the best individual in the population,"worst"
will select the worst individual in the population,"random"
will randomly choose one individual in the population.
set_random_sr_seed()
can be used to seed the random number generator used by the"random"
policy.If the attribute is an integer, it represents the index (in the population) of the individual that is selected for optimisation.
- Returns
the individual selection policy or index
- Return type
- Raises
OverflowError – if the attribute is set to an integer which is negative or too large
ValueError – if the attribute is set to an invalid string
TypeError – if the attribute is set to a value of an invalid type
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- set_random_sr_seed(seed)#
Set the seed for the
"random"
selection/replacement policies.- Parameters
seed (
int
) – the value that will be used to seed the random number generator used by the"random"
election/replacement policies (seeselection
andreplacement
)- Raises
OverflowError – if the attribute is set to an integer which is negative or too large
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- class pygmo.pso(gen=1, omega=0.7298, eta1=2.05, eta2=2.05, max_vel=0.5, variant=5, neighb_type=2, neighb_param=4, memory=False, seed=random)#
Particle Swarm Optimization
- Parameters
gen (
int
) – number of generationsomega (
float
) – inertia weight (or constriction factor)eta1 (
float
) – social componenteta2 (
float
) – cognitive componentmax_vel (
float
) – maximum allowed particle velocities (normalized with respect to the bounds width)variant (
int
) – algorithmic variantneighb_type (
int
) – swarm topology (defining each particle’s neighbours)neighb_param (
int
) – topology parameter (defines how many neighbours to consider)memory (
bool
) – when true the velocities are not reset between successive calls to the evolve methodseed (
int
) – seed used by the internal random number generator (default is random)
- Raises
OverflowError – if gen or seed is negative or greater than an implementation-defined value
ValueError – if omega is not in the [0,1] interval, if eta1, eta2 are not in the [0,4] interval, if max_vel is not in ]0,1]
ValueError – variant is not one of 1 .. 6, if neighb_type is not one of 1 .. 4 or if neighb_param is zero
The following variants can be selected via the variant parameter:
1 - Canonical (with inertia weight)
2 - Same social and cognitive rand.
3 - Same rand. for all components
4 - Only one rand.
5 - Canonical (with constriction fact.)
6 - Fully Informed (FIPS)
The following topologies are selected by neighb_type:
1 - gbest
2 - lbest
3 - Von Neumann
4 - Adaptive random
The topology determines (together with the topology parameter) which particles need to be considered when computing the social component of the velocity update.
- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
and printed to screen. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with apso
. A verbosity ofN
implies a log line eachN
generations.- Returns
at each logged epoch, the values
Gen
,Fevals
,gbest
,Mean Vel.
,Mean lbest
,Avg. Dist.
, where:Gen
(int
), generation numberFevals
(int
), number of functions evaluation madegbest
(float
), the best fitness function found so far by the the swarmMean Vel.
(float
), the average particle velocity (normalized)Mean lbest
(float
), the average fitness of the current particle locationsAvg. Dist.
(float
), the average distance between particles (normalized)
- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(pso(gen = 500)) >>> algo.set_verbosity(50) >>> prob = problem(rosenbrock(10)) >>> pop = population(prob, 20) >>> pop = algo.evolve(pop) Gen: Fevals: gbest: Mean Vel.: Mean lbest: Avg. Dist.: 1 40 72473.3 0.173892 677427 0.281744 51 1040 135.867 0.0183806 748.001 0.065826 101 2040 12.6726 0.00291046 84.9531 0.0339452 151 3040 8.4405 0.000852588 33.5161 0.0191379 201 4040 7.56943 0.000778264 28.213 0.00789202 251 5040 6.8089 0.00435521 22.7988 0.00107112 301 6040 6.3692 0.000289725 17.3763 0.00325571 351 7040 6.09414 0.000187343 16.8875 0.00172307 401 8040 5.78415 0.000524536 16.5073 0.00234197 451 9040 5.4662 0.00018305 16.2339 0.000958182 >>> uda = algo.extract(pso) >>> uda.get_log() [(1,40,72473.32713790605,0.1738915144248373,677427.3504996448,0.2817443174278134), (51,1040,...
See also the docs of the relevant C++ method
pagmo::pso::get_log()
.
- class pygmo.pso_gen(gen=1, omega=0.7298, eta1=2.05, eta2=2.05, max_vel=0.5, variant=5, neighb_type=2, neighb_param=4, memory=False, seed=random)#
Particle Swarm Optimization (generational) is identical to
pso
, but does update the velocities of each particle before new particle positions are computed (taking into consideration all updated particle velocities). Each particle is thus evaluated on the same seed within a generation as opposed to the standard PSO which evaluates single particle at a time. Consequently, the generational PSO algorithm is suited for stochastic optimization problems.- Parameters
gen (
int
) – number of generationsomega (
float
) – inertia weight (or constriction factor)eta1 (
float
) – social componenteta2 (
float
) – cognitive componentmax_vel (
float
) – maximum allowed particle velocities (normalized with respect to the bounds width)variant (
int
) – algorithmic variantneighb_type (
int
) – swarm topology (defining each particle’s neighbours)neighb_param (
int
) – topology parameter (defines how many neighbours to consider)memory (
bool
) – when true the velocities are not reset between successive calls to the evolve methodseed (
int
) – seed used by the internal random number generator (default is random)
- Raises
OverflowError – if gen or seed is negative or greater than an implementation-defined value
ValueError – if omega is not in the [0,1] interval, if eta1, eta2 are not in the [0,1] interval, if max_vel is not in ]0,1]
ValueError – variant is not one of 1 .. 6, if neighb_type is not one of 1 .. 4 or if neighb_param is zero
The following variants can be selected via the variant parameter:
1 - Canonical (with inertia weight)
2 - Same social and cognitive rand.
3 - Same rand. for all components
4 - Only one rand.
5 - Canonical (with constriction fact.)
6 - Fully Informed (FIPS)
The following topologies are selected by neighb_type:
1 - gbest
2 - lbest
3 - Von Neumann
4 - Adaptive random
The topology determines (together with the topology parameter) which particles need to be considered when computing the social component of the velocity update.
- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
and printed to screen. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with apso
. A verbosity ofN
implies a log line eachN
generations.- Returns
at each logged epoch, the values
Gen
,Fevals
,gbest
,Mean Vel.
,Mean lbest
,Avg. Dist.
, where:Gen
(int
), generation numberFevals
(int
), number of functions evaluation madegbest
(float
), the best fitness function found so far by the the swarmMean Vel.
(float
), the average particle velocity (normalized)Mean lbest
(float
), the average fitness of the current particle locationsAvg. Dist.
(float
), the average distance between particles (normalized)
- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(pso(gen = 500)) >>> algo.set_verbosity(50) >>> prob = problem(rosenbrock(10)) >>> pop = population(prob, 20) >>> pop = algo.evolve(pop) Gen: Fevals: gbest: Mean Vel.: Mean lbest: Avg. Dist.: 1 40 72473.3 0.173892 677427 0.281744 51 1040 135.867 0.0183806 748.001 0.065826 101 2040 12.6726 0.00291046 84.9531 0.0339452 151 3040 8.4405 0.000852588 33.5161 0.0191379 201 4040 7.56943 0.000778264 28.213 0.00789202 251 5040 6.8089 0.00435521 22.7988 0.00107112 301 6040 6.3692 0.000289725 17.3763 0.00325571 351 7040 6.09414 0.000187343 16.8875 0.00172307 401 8040 5.78415 0.000524536 16.5073 0.00234197 451 9040 5.4662 0.00018305 16.2339 0.000958182 >>> uda = algo.extract(pso) >>> uda.get_log() [(1,40,72473.32713790605,0.1738915144248373,677427.3504996448,0.2817443174278134), (51,1040,...
See also the docs of the relevant C++ method
pagmo::pso::get_log()
.
- get_seed()#
This method will return the random seed used internally by this uda.
- Returns
the random seed of the population
- Return type
- class pygmo.nsga2(gen=1, cr=0.95, eta_c=10., m=0.01, eta_m=50., seed=random)#
Non dominated Sorting Genetic Algorithm (NSGA-II).
- Parameters
- Raises
OverflowError – if gen or seed are negative or greater than an implementation-defined value
ValueError – if either cr is not in [0,1[, eta_c is not in [0,100[, m is not in [0,1], or eta_m is not in [0,100[
See also the docs of the C++ class
pagmo::nsga2
.- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
and printed to screen. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with ansga2
. A verbosity ofN
implies a log line eachN
generations.- Returns
at each logged epoch, the values
Gen
,Fevals
,ideal_point
, where:- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(nsga2(gen=100)) >>> algo.set_verbosity(20) >>> pop = population(zdt(1), 40) >>> pop = algo.evolve(pop) Gen: Fevals: ideal1: ideal2: 1 0 0.0033062 2.44966 21 800 0.000275601 0.893137 41 1600 3.15834e-05 0.44117 61 2400 2.3664e-05 0.206365 81 3200 2.3664e-05 0.133305 >>> uda = algo.extract(nsga2) >>> uda.get_log() [(1, 0, array([ 0.0033062 , 2.44965599])), (21, 800, array([ 2.75601086e-04 ...
See also the docs of the relevant C++ method
pagmo::nsga2::get_log()
.
- get_seed()#
This method will return the random seed used internally by this uda.
- Returns
the random seed of the population
- Return type
- class pygmo.nspso(gen=1, omega=0.6, c1=0.01, c2=0.5, chi=0.5, v_coeff=0.5, leader_selection_range=2, diversity_mechanism='crowding distance', memory=false, seed=random)#
Non dominated Sorting Particle Swarm Optimization (NSPSO).
- Parameters
gen (
int
) – number of generations to evolveomega (
float
) – particles’ inertia weightc1 (
float
) – magnitude of the force, applied to the particle’s velocity, in the direction of its previous best position.c2 (
float
) – magnitude of the force, applied to the particle’s velocity, in the direction of its global best position.chi (
float
) – velocity scaling factor.v_coeff (
float
) – velocity coefficient.leader_selection_range (
int
) – leader selection range.diversity_mechanism (str) – leader selection range.
memory (
bool
) – memory parameter.
- Raises
OverflowError – if gen or seed are negative or greater than an implementation-defined value
ValueError – if either omega < 0 or c1 <= 0 or c2 <= 0 or chi <= 0, if omega > 1,
if v_coeff <= 0 or v_coeff > 1, if leader_selection_range > 100, if diversity_mechanism != "crowding distance", or != "niche count", or != "max min" –
See also the docs of the C++ class
pagmo::nspso
.- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
and printed to screen. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with anspso
. A verbosity ofN
implies a log line eachN
generations.- Returns
at each logged epoch, the values
Gen
,Fevals
,ideal_point
, where:- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(nspso(gen=100)) >>> algo.set_verbosity(20) >>> pop = population(zdt(1), 40) >>> pop = algo.evolve(pop) Gen: Fevals: ideal1: ideal2: 1 40 0.019376 2.75209 21 840 0 1.97882 41 1640 0 1.88428 61 2440 0 1.88428 81 3240 0 1.88428 >>> uda = algo.extract(nspso) >>> uda.get_log() [(1, 40, array([0.04843319, 2.98129814])), (21, 840, array([0., 1.68331679])) ...
See also the docs of the relevant C++ method
pagmo::nspso::get_log()
.
- get_seed()#
This method will return the random seed used internally by this uda.
- Returns
the random seed of the population
- Return type
- class pygmo.mbh(algo=None, stop=5, perturb=0.01, seed=None)#
Monotonic Basin Hopping (generalized).
Monotonic basin hopping, or simply, basin hopping, is an algorithm rooted in the idea of mapping the objective function \(f(\mathbf x_0)\) into the local minima found starting from \(\mathbf x_0\). This simple idea allows a substantial increase of efficiency in solving problems, such as the Lennard-Jones cluster or the MGA-1DSM interplanetary trajectory problem that are conjectured to have a so-called funnel structure.
In pygmo we provide an original generalization of this concept resulting in a meta-algorithm that operates on any
pygmo.population
using any suitable user-defined algorithm (UDA). When a population containing a single individual is used and coupled with a local optimizer, the original method is recovered. The pseudo code of our generalized version is:> Select a pygmo population > Select a UDA > Store best individual > while i < stop_criteria > > Perturb the population in a selected neighbourhood > > Evolve the population using the algorithm > > if the best individual is improved > > > increment i > > > update best individual > > else > > > i = 0
pygmo.mbh
is a user-defined algorithm (UDA) that can be used to constructpygmo.algorithm
objects.See: https://arxiv.org/pdf/cond-mat/9803344.pdf for the paper introducing the basin hopping idea for a Lennard-Jones cluster optimization.
See also the docs of the C++ class
pagmo::mbh
.- Parameters
algo – an
algorithm
or a user-defined algorithm, either C++ or Python (if algo isNone
, acompass_search
algorithm will be used in its stead)stop (int) – consecutive runs of the inner algorithm that need to result in no improvement for
mbh
to stopperturb (float or array-like object) – the perturbation to be applied to each component
seed (int) – seed used by the internal random number generator (if seed is
None
, a randomly-generated value will be used in its stead)
- Raises
ValueError – if perturb (or one of its components, if perturb is an array) is not in the (0,1] range
unspecified – any exception thrown by the constructor of
pygmo.algorithm
, or by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set callingset_verbosity()
on analgorithm
constructed with anmbh
. A verbosity levelN > 0
will log one line at the end of each call to the inner algorithm.- Returns
at each call of the inner algorithm, the values
Fevals
,Best
,Violated
,Viol. Norm
andTrial
, where:Fevals
(int
), the number of fitness evaluations madeBest
(float
), the objective function of the best fitness currently in the populationViolated
(int
), the number of constraints currently violated by the best solutionViol. Norm
(float
), the norm of the violation (discounted already by the constraints tolerance)Trial
(int
), the trial number (which will determine the algorithm stop)
- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(mbh(algorithm(de(gen = 10)))) >>> algo.set_verbosity(3) >>> prob = problem(cec2013(prob_id = 1, dim = 20)) >>> pop = population(prob, 20) >>> pop = algo.evolve(pop) Fevals: Best: Violated: Viol. Norm: Trial: 440 25162.3 0 0 0 880 14318 0 0 0 1320 11178.2 0 0 0 1760 6613.71 0 0 0 2200 6613.71 0 0 1 2640 6124.62 0 0 0 3080 6124.62 0 0 1
See also the docs of the relevant C++ method
pagmo::mbh::get_log()
.
- get_perturb()#
Get the perturbation vector.
- Returns
the perturbation vector
- Return type
1D NumPy float array
- get_seed()#
Get the seed value that was used for the construction of this
mbh
.- Returns
the seed value
- Return type
- get_verbosity()#
Get the verbosity level value that was used for the construction of this
mbh
.- Returns
the verbosity level
- Return type
- property inner_algorithm#
Inner algorithm of the meta-algorithm.
This read-only property gives direct access to the
algorithm
stored within this meta-algorithm.- Returns
a reference to the inner algorithm
- Return type
- set_perturb(perturb)#
Set the perturbation vector.
- Parameters
perturb (array-like object) – perturb the perturbation to be applied to each component
- Raises
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- class pygmo.cstrs_self_adaptive(iters=1, algo=None, seed=None)#
This meta-algorithm implements a constraint handling technique that allows the use of any user-defined algorithm (UDA) able to deal with single-objective unconstrained problems, on single-objective constrained problems. The technique self-adapts its parameters during each successive call to the inner UDA basing its decisions on the entire underlying population. The resulting approach is an alternative to using the meta-problem
unconstrain
to transform the constrained fitness into an unconstrained fitness.The self-adaptive constraints handling meta-algorithm is largely based on the ideas of Faramani and Wright but it extends their use to any-algorithm, in particular to non generational, population based, evolutionary approaches where a steady-state reinsertion is used (i.e. as soon as an individual is found fit it is immediately reinserted into the population and will influence the next offspring genetic material).
Each decision vector is assigned an infeasibility measure \(\iota\) which accounts for the normalized violation of all the constraints (discounted by the constraints tolerance as returned by
pygmo.problem.c_tol
). The normalization factor used \(c_{j_{max}}\) is the maximum violation of the \(j\) constraint.As in the original paper, three individuals in the evolving population are then used to penalize the single objective.
\[\begin{split}\begin{array}{rl} \check X & \mbox{: the best decision vector} \\ \hat X & \mbox{: the worst decision vector} \\ \breve X & \mbox{: the decision vector with the highest objective} \end{array}\end{split}\]The best and worst decision vectors are defined accounting for their infeasibilities and for the value of the objective function. Using the above definitions the overall pseudo code can be summarized as follows:
> Select a pygmo.population (related to a single-objective constrained problem) > Select a UDA (able to solve single-objective unconstrained problems) > while i < iter > > Compute the normalization factors (will depend on the current population) > > Compute the best, worst, highest (will depend on the current population) > > Evolve the population using the UDA and a penalized objective > > Reinsert the best decision vector from the previous evolution
pygmo.cstrs_self_adaptive
is a user-defined algorithm (UDA) that can be used to constructpygmo.algorithm
objects.Note
Self-adaptive constraints handling implements an internal cache to avoid the re-evaluation of the fitness for decision vectors already evaluated. This makes the final counter of fitness evaluations somewhat unpredictable. The number of function evaluation will be bounded to iters times the fevals made by one call to the inner UDA. The internal cache is reset at each iteration, but its size will grow unlimited during each call to the inner UDA evolve method.
Note
Several modification were made to the original Faramani and Wright ideas to allow their approach to work on corner cases and with any UDAs. Most notably, a violation to the \(j\)-th constraint is ignored if all the decision vectors in the population satisfy that particular constraint (i.e. if \(c_{j_{max}} = 0\)).
Note
The performances of
cstrs_self_adaptive
are highly dependent on the particular inner algorithm employed and in particular to its parameters (generations / iterations).See also
Farmani, Raziyeh, and Jonathan A. Wright. “Self-adaptive fitness formulation for constrained optimization.” IEEE Transactions on Evolutionary Computation 7.5 (2003): 445-455.
See also the docs of the C++ class
pagmo::cstrs_self_adaptive
.- Parameters
iter (int) – number of iterations (i.e., calls to the inner algorithm evolve)
algo – an
algorithm
or a user-defined algorithm, either C++ or Python (if algo isNone
, ade
algorithm will be used in its stead)seed (int) – seed used by the internal random number generator (if seed is
None
, a randomly-generated value will be used in its stead)
- Raises
ValueError – if iters is negative or greater than an implementation-defined value
unspecified – any exception thrown by the constructor of
pygmo.algorithm
, or by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set callingset_verbosity()
on analgorithm
constructed with ancstrs_self_adaptive
. A verbosity level ofN > 0
will log one line eachN
iters
.- Returns
at each call of the inner algorithm, the values
Iters
,Fevals
,Best
,Infeasibility
,Violated
,Viol. Norm
andN. Feasible
, where:Iters
(int
), the number of iterations made (i.e. calls to the evolve method of the inner algorithm)Fevals
(int
), the number of fitness evaluations madeBest
(float
), the objective function of the best fitness currently in the populationInfeasibility
(float
), the aggregated (and normalized) infeasibility value ofBest
Violated
(int
), the number of constraints currently violated by the best solutionViol. Norm
(float
), the norm of the violation (discounted already by the constraints tolerance)N. Feasible
(int
), the number of feasible individuals currently in the population.
- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(cstrs_self_adaptive(iters = 20, algo = de(10))) >>> algo.set_verbosity(3) >>> prob = problem(cec2006(prob_id = 1)) >>> pop = population(prob, 20) >>> pop = algo.evolve(pop) Iter: Fevals: Best: Infeasibility: Violated: Viol. Norm: N. Feasible: 1 0 -96.5435 0.34607 4 177.705 0 i 4 600 -96.5435 0.360913 4 177.705 0 i 7 1200 -96.5435 0.36434 4 177.705 0 i 10 1800 -96.5435 0.362307 4 177.705 0 i 13 2400 -23.2502 0.098049 4 37.1092 0 i 16 3000 -23.2502 0.071571 4 37.1092 0 i 19 3600 -23.2502 0.257604 4 37.1092 0 i >>> uda = algo.extract(moead) >>> uda.get_log() [(1, 0, -96.54346700540063, 0.34606950943401493, 4, 177.70482046341274, 0), (4, 600, ...
See also the docs of the relevant C++ method
pagmo::cstrs_self_adaptive::get_log()
.
- class pygmo.nlopt(solver='cobyla')#
NLopt algorithms.
This user-defined algorithm wraps a selection of solvers from the NLopt library, focusing on local optimisation (both gradient-based and derivative-free). The complete list of supported NLopt algorithms is:
COBYLA,
BOBYQA,
NEWUOA + bound constraints,
PRAXIS,
Nelder-Mead simplex,
sbplx,
MMA (Method of Moving Asymptotes),
CCSA,
SLSQP,
low-storage BFGS,
preconditioned truncated Newton,
shifted limited-memory variable-metric,
augmented Lagrangian algorithm.
The desired NLopt solver is selected upon construction of an
nlopt
algorithm. Various properties of the solver (e.g., the stopping criteria) can be configured via class attributes. Multiple stopping criteria can be active at the same time: the optimisation will stop as soon as at least one stopping criterion is satisfied. By default, only thextol_rel
stopping criterion is active (seextol_rel
).All NLopt solvers support only single-objective optimisation, and, as usual in pygmo, minimisation is always assumed. The gradient-based algorithms require the optimisation problem to provide a gradient. Some solvers support equality and/or inequality constraints. The constraints’ tolerances will be set to those specified in the
problem
being optimised (seepygmo.problem.c_tol
).In order to support pygmo’s population-based optimisation model, the
evolve()
method will select a single individual from the inputpopulation
to be optimised by the NLopt solver. If the optimisation produces a better individual (as established bycompare_fc()
), the optimised individual will be inserted back into the population. The selection and replacement strategies can be configured via theselection
andreplacement
attributes.Note
This user-defined algorithm is available only if pygmo was compiled with the
PAGMO_WITH_NLOPT
option enabled (see the installation instructions).See also
The NLopt website contains a detailed description of each supported solver.
This constructor will initialise an
nlopt
object which will use the NLopt algorithm specified by the input string solver, the"best"
individual selection strategy and the"best"
individual replacement strategy. solver is translated to an NLopt algorithm type according to the following translation table:solver string
NLopt algorithm
"cobyla"
NLOPT_LN_COBYLA
"bobyqa"
NLOPT_LN_BOBYQA
"newuoa"
NLOPT_LN_NEWUOA
"newuoa_bound"
NLOPT_LN_NEWUOA_BOUND
"praxis"
NLOPT_LN_PRAXIS
"neldermead"
NLOPT_LN_NELDERMEAD
"sbplx"
NLOPT_LN_SBPLX
"mma"
NLOPT_LD_MMA
"ccsaq"
NLOPT_LD_CCSAQ
"slsqp"
NLOPT_LD_SLSQP
"lbfgs"
NLOPT_LD_LBFGS
"tnewton_precond_restart"
NLOPT_LD_TNEWTON_PRECOND_RESTART
"tnewton_precond"
NLOPT_LD_TNEWTON_PRECOND
"tnewton_restart"
NLOPT_LD_TNEWTON_RESTART
"tnewton"
NLOPT_LD_TNEWTON
"var2"
NLOPT_LD_VAR2
"var1"
NLOPT_LD_VAR1
"auglag"
NLOPT_AUGLAG
"auglag_eq"
NLOPT_AUGLAG_EQ
The parameters of the selected solver can be configured via the attributes of this class.
See also the docs of the C++ class
pagmo::nlopt
.See also
The NLopt website contains a detailed description of each supported solver.
- Parameters
solver (
str
) – the name of the NLopt algorithm that will be used by thisnlopt
object- Raises
RuntimeError – if the NLopt version is not at least 2
ValueError – if solver is not one of the allowed algorithm names
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
Examples
>>> from pygmo import * >>> nl = nlopt('slsqp') >>> nl.xtol_rel = 1E-6 # Change the default value of the xtol_rel stopping criterion >>> nl.xtol_rel 1E-6 >>> algo = algorithm(nl) >>> algo.set_verbosity(1) >>> prob = problem(luksan_vlcek1(20)) >>> prob.c_tol = [1E-6] * 18 # Set constraints tolerance to 1E-6 >>> pop = population(prob, 20) >>> pop = algo.evolve(pop) objevals: objval: violated: viol. norm: 1 95959.4 18 538.227 i 2 89282.7 18 5177.42 i 3 75580 18 464.206 i 4 75580 18 464.206 i 5 77737.6 18 1095.94 i 6 41162 18 350.446 i 7 41162 18 350.446 i 8 67881 18 362.454 i 9 30502.2 18 249.762 i 10 30502.2 18 249.762 i 11 7266.73 18 95.5946 i 12 4510.3 18 42.2385 i 13 2400.66 18 35.2507 i 14 34051.9 18 749.355 i 15 1657.41 18 32.1575 i 16 1657.41 18 32.1575 i 17 1564.44 18 12.5042 i 18 275.987 14 6.22676 i 19 232.765 12 12.442 i 20 161.892 15 4.00744 i 21 161.892 15 4.00744 i 22 17.6821 11 1.78909 i 23 7.71103 5 0.130386 i 24 6.24758 4 0.00736759 i 25 6.23325 1 5.12547e-05 i 26 6.2325 0 0 27 6.23246 0 0 28 6.23246 0 0 29 6.23246 0 0 30 6.23246 0 0 Optimisation return status: NLOPT_XTOL_REACHED (value = 4, Optimization stopped because xtol_rel or xtol_abs was reached)
- property ftol_abs#
ftol_abs
stopping criterion.The
ftol_abs
stopping criterion instructs the solver to stop when an optimization step (or an estimate of the optimum) changes the function value by less thanftol_abs
. Defaults to 0 (that is, this stopping criterion is disabled by default).- Returns
the value of the
ftol_abs
stopping criterion- Return type
- Raises
ValueError – if, when setting this property, a
NaN
is passedunspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- property ftol_rel#
ftol_rel
stopping criterion.The
ftol_rel
stopping criterion instructs the solver to stop when an optimization step (or an estimate of the optimum) changes the objective function value by less thanftol_rel
multiplied by the absolute value of the function value. Defaults to 0 (that is, this stopping criterion is disabled by default).- Returns
the value of the
ftol_rel
stopping criterion- Return type
- Raises
ValueError – if, when setting this property, a
NaN
is passedunspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- get_last_opt_result()#
Get the result of the last optimisation.
- Returns
the NLopt return code for the last optimisation run, or
NLOPT_SUCCESS
if no optimisations have been run yet- Return type
- Raises
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- get_log()#
Optimisation log.
The optimisation log is a collection of log data lines. A log data line is a tuple consisting of:
the number of objective function evaluations made so far,
the objective function value for the current decision vector,
the number of constraints violated by the current decision vector,
the constraints violation norm for the current decision vector,
a boolean flag signalling the feasibility of the current decision vector.
- Returns
the optimisation log
- Return type
- Raises
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- get_solver_name()#
Get the name of the NLopt solver used during construction.
- Returns
the name of the NLopt solver used during construction
- Return type
- Raises
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- property local_optimizer#
Local optimizer.
Some NLopt algorithms rely on other NLopt algorithms as local/subsidiary optimizers. This property, of type
nlopt
, allows to set such local optimizer. By default, no local optimizer is specified, and the property is set toNone
.Note
At the present time, only the
"auglag"
and"auglag_eq"
solvers make use of a local optimizer. Setting a local optimizer on any other solver will have no effect.Note
The objective function, bounds, and nonlinear-constraint parameters of the local optimizer are ignored (as they are provided by the parent optimizer). Conversely, the stopping criteria should be specified in the local optimizer.The verbosity of the local optimizer is also forcibly set to zero during the optimisation.
- Returns
the local optimizer, or
None
if not set- Return type
- Raises
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.), when setting the property
- property maxeval#
maxeval
stopping criterion.The
maxeval
stopping criterion instructs the solver to stop when the number of function evaluations exceedsmaxeval
. Defaults to 0 (that is, this stopping criterion is disabled by default).- Returns
the value of the
maxeval
stopping criterion- Return type
- Raises
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- property maxtime#
maxtime
stopping criterion.The
maxtime
stopping criterion instructs the solver to stop when the optimization time (in seconds) exceedsmaxtime
. Defaults to 0 (that is, this stopping criterion is disabled by default).- Returns
the value of the
maxtime
stopping criterion- Return type
- Raises
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- property replacement#
Individual replacement policy.
This attribute represents the policy that is used in the
evolve()
method to select the individual that will be replaced by the optimised individual. The attribute can be either a string or an integral.If the attribute is a string, it must be one of
"best"
,"worst"
and"random"
:"best"
will select the best individual in the population,"worst"
will select the worst individual in the population,"random"
will randomly choose one individual in the population.
set_random_sr_seed()
can be used to seed the random number generator used by the"random"
policy.If the attribute is an integer, it represents the index (in the population) of the individual that will be replaced by the optimised individual.
- Returns
the individual replacement policy or index
- Return type
- Raises
OverflowError – if the attribute is set to an integer which is negative or too large
ValueError – if the attribute is set to an invalid string
TypeError – if the attribute is set to a value of an invalid type
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- property selection#
Individual selection policy.
This attribute represents the policy that is used in the
evolve()
method to select the individual that will be optimised. The attribute can be either a string or an integral.If the attribute is a string, it must be one of
"best"
,"worst"
and"random"
:"best"
will select the best individual in the population,"worst"
will select the worst individual in the population,"random"
will randomly choose one individual in the population.
set_random_sr_seed()
can be used to seed the random number generator used by the"random"
policy.If the attribute is an integer, it represents the index (in the population) of the individual that is selected for optimisation.
- Returns
the individual selection policy or index
- Return type
- Raises
OverflowError – if the attribute is set to an integer which is negative or too large
ValueError – if the attribute is set to an invalid string
TypeError – if the attribute is set to a value of an invalid type
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- set_random_sr_seed(seed)#
Set the seed for the
"random"
selection/replacement policies.- Parameters
seed (
int
) – the value that will be used to seed the random number generator used by the"random"
election/replacement policies (seeselection
andreplacement
)- Raises
OverflowError – if the attribute is set to an integer which is negative or too large
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- property stopval#
stopval
stopping criterion.The
stopval
stopping criterion instructs the solver to stop when an objective value less than or equal tostopval
is found. Defaults to the C constant-HUGE_VAL
(that is, this stopping criterion is disabled by default).- Returns
the value of the
stopval
stopping criterion- Return type
- Raises
ValueError – if, when setting this property, a
NaN
is passedunspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- property xtol_abs#
xtol_abs
stopping criterion.The
xtol_abs
stopping criterion instructs the solver to stop when an optimization step (or an estimate of the optimum) changes every parameter by less thanxtol_abs
. Defaults to 0 (that is, this stopping criterion is disabled by default).- Returns
the value of the
xtol_abs
stopping criterion- Return type
- Raises
ValueError – if, when setting this property, a
NaN
is passedunspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- property xtol_rel#
xtol_rel
stopping criterion.The
xtol_rel
stopping criterion instructs the solver to stop when an optimization step (or an estimate of the optimum) changes every parameter by less thanxtol_rel
multiplied by the absolute value of the parameter. Defaults to 1E-8.- Returns
the value of the
xtol_rel
stopping criterion- Return type
- Raises
ValueError – if, when setting this property, a
NaN
is passedunspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- class pygmo.ipopt#
Ipopt.
New in version 2.2.
This class is a user-defined algorithm (UDA) that wraps the Ipopt (Interior Point OPTimizer) solver, a software package for large-scale nonlinear optimization. Ipopt is a powerful solver that is able to handle robustly and efficiently constrained nonlinear opimization problems at high dimensionalities.
Ipopt supports only single-objective minimisation, and it requires the availability of the gradient in the optimisation problem. If possible, for best results the Hessians should be provided as well (but Ipopt can estimate numerically the Hessians if needed).
In order to support pygmo’s population-based optimisation model, the
evolve()
method will select a single individual from the inputpopulation
to be optimised. If the optimisation produces a better individual (as established bycompare_fc()
), the optimised individual will be inserted back into the population. The selection and replacement strategies can be configured via theselection
andreplacement
attributes.Ipopt supports a large amount of options for the configuration of the optimisation run. The options are divided into three categories:
string options (i.e., the type of the option is
str
),integer options (i.e., the type of the option is
int
),numeric options (i.e., the type of the option is
float
).
The full list of options is available on the Ipopt website.
pygmo.ipopt
allows to configure any Ipopt option via methods such asset_string_options()
,set_string_option()
,set_integer_options()
, etc., which need to be used before invoking theevolve()
method.If the user does not set any option,
pygmo.ipopt
use Ipopt’s default values for the options (see the documentation), with the following modifications:if the
"print_level"
integer option is not set by the user, it will be set to 0 bypygmo.ipopt
(this will suppress most screen output produced by the solver - note that we support an alternative form of logging via thepygmo.algorithm.set_verbosity()
machinery);if the
"hessian_approximation"
string option is not set by the user and the optimisation problem does not provide the Hessians, then the option will be set to"limited-memory"
bypygmo.ipopt
. This makes it possible to optimise problems without Hessians out-of-the-box (i.e., Ipopt will approximate numerically the Hessians for you);if the
"constr_viol_tol"
numeric option is not set by the user and the optimisation problem is constrained, thenpygmo.ipopt
will compute the minimum valuemin_tol
in the vector returned bypygmo.problem.c_tol
for the optimisation problem at hand. Ifmin_tol
is nonzero, then the"constr_viol_tol"
Ipopt option will be set tomin_tol
, otherwise the default Ipopt value (1E-4) will be used for the option. This ensures that, if the constraint tolerance is not explicitly set by the user, a solution deemed feasible by Ipopt is also deemed feasible by pygmo (but the opposite is not necessarily true).
Note
This user-defined algorithm is available only if pygmo was compiled with the
PAGMO_WITH_IPOPT
option enabled (see the installation instructions).Note
Ipopt is not thread-safe, and thus it cannot be used in a
pygmo.thread_island
.See also
See also the docs of the C++ class
pagmo::ipopt
.Examples
>>> from pygmo import * >>> ip = ipopt() >>> ip.set_numeric_option("tol",1E-9) # Change the relative convergence tolerance >>> ip.get_numeric_options() {'tol': 1e-09} >>> algo = algorithm(ip) >>> algo.set_verbosity(1) >>> prob = problem(luksan_vlcek1(20)) >>> prob.c_tol = [1E-6] * 18 # Set constraints tolerance to 1E-6 >>> pop = population(prob, 20) >>> pop = algo.evolve(pop) ****************************************************************************** This program contains Ipopt, a library for large-scale nonlinear optimization. Ipopt is released as open source code under the Eclipse Public License (EPL). For more information visit https://coin-or.github.io/Ipopt/ ****************************************************************************** objevals: objval: violated: viol. norm: 1 201174 18 1075.3 i 2 209320 18 691.814 i 3 36222.3 18 341.639 i 4 11158.1 18 121.097 i 5 4270.38 18 46.4742 i 6 2054.03 18 20.7306 i 7 705.959 18 5.43118 i 8 37.8304 18 1.52099 i 9 2.89066 12 0.128862 i 10 0.300807 3 0.0165902 i 11 0.00430279 3 0.000496496 i 12 7.54121e-06 2 9.70735e-06 i 13 4.34249e-08 0 0 14 3.71925e-10 0 0 15 3.54406e-13 0 0 16 2.37071e-18 0 0 Optimisation return status: Solve_Succeeded (value = 0)
- get_integer_options()#
Get integer options.
Examples
>>> from pygmo import * >>> ip = ipopt() >>> ip.set_integer_option("print_level",3) >>> ip.get_integer_options() {'print_level': 3}
- get_last_opt_result()#
Get the result of the last optimisation.
- Returns
the Ipopt return code for the last optimisation run, or
Ipopt::Solve_Succeeded
if no optimisations have been run yet- Return type
- Raises
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
Examples
>>> from pygmo import * >>> ip = ipopt() >>> ip.get_last_opt_result() 0
- get_log()#
Optimisation log.
The optimisation log is a collection of log data lines. A log data line is a tuple consisting of:
the number of objective function evaluations made so far,
the objective function value for the current decision vector,
the number of constraints violated by the current decision vector,
the constraints violation norm for the current decision vector,
a boolean flag signalling the feasibility of the current decision vector.
- Returns
the optimisation log
- Return type
- Raises
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
Warning
The number of constraints violated, the constraints violation norm and the feasibility flag stored in the log are all determined via the facilities and the tolerances specified within
pygmo.problem
. That is, they might not necessarily be consistent with Ipopt’s notion of feasibility. See the explanation of how the"constr_viol_tol"
numeric option is handled inpygmo.ipopt
.Note
Ipopt supports its own logging format and protocol, including the ability to print to screen and write to file. Ipopt’s screen logging is disabled by default (i.e., the Ipopt verbosity setting is set to 0 - see
pygmo.ipopt
). On-screen logging can be enabled via the"print_level"
string option.
- get_numeric_options()#
Get numeric options.
Examples
>>> from pygmo import * >>> ip = ipopt() >>> ip.set_numeric_option("tol",1E-4) >>> ip.get_numeric_options() {'tol': 1E-4}
- get_string_options()#
Get string options.
Examples
>>> from pygmo import * >>> ip = ipopt() >>> ip.set_string_option("hessian_approximation","limited-memory") >>> ip.get_string_options() {'hessian_approximation': 'limited-memory'}
- property replacement#
Individual replacement policy.
This attribute represents the policy that is used in the
evolve()
method to select the individual that will be replaced by the optimised individual. The attribute can be either a string or an integral.If the attribute is a string, it must be one of
"best"
,"worst"
and"random"
:"best"
will select the best individual in the population,"worst"
will select the worst individual in the population,"random"
will randomly choose one individual in the population.
set_random_sr_seed()
can be used to seed the random number generator used by the"random"
policy.If the attribute is an integer, it represents the index (in the population) of the individual that will be replaced by the optimised individual.
- Returns
the individual replacement policy or index
- Return type
- Raises
OverflowError – if the attribute is set to an integer which is negative or too large
ValueError – if the attribute is set to an invalid string
TypeError – if the attribute is set to a value of an invalid type
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- reset_integer_options()#
Clear all integer options.
Examples
>>> from pygmo import * >>> ip = ipopt() >>> ip.set_integer_option("print_level",3) >>> ip.get_integer_options() {'print_level': 3} >>> ip.reset_integer_options() >>> ip.get_integer_options() {}
- reset_numeric_options()#
Clear all numeric options.
Examples
>>> from pygmo import * >>> ip = ipopt() >>> ip.set_numeric_option("tol",1E-4) >>> ip.get_numeric_options() {'tol': 1E-4} >>> ip.reset_numeric_options() >>> ip.get_numeric_options() {}
- reset_string_options()#
Clear all string options.
Examples
>>> from pygmo import * >>> ip = ipopt() >>> ip.set_string_option("hessian_approximation","limited-memory") >>> ip.get_string_options() {'hessian_approximation': 'limited-memory'} >>> ip.reset_string_options() >>> ip.get_string_options() {}
- property selection#
Individual selection policy.
This attribute represents the policy that is used in the
evolve()
method to select the individual that will be optimised. The attribute can be either a string or an integral.If the attribute is a string, it must be one of
"best"
,"worst"
and"random"
:"best"
will select the best individual in the population,"worst"
will select the worst individual in the population,"random"
will randomly choose one individual in the population.
set_random_sr_seed()
can be used to seed the random number generator used by the"random"
policy.If the attribute is an integer, it represents the index (in the population) of the individual that is selected for optimisation.
- Returns
the individual selection policy or index
- Return type
- Raises
OverflowError – if the attribute is set to an integer which is negative or too large
ValueError – if the attribute is set to an invalid string
TypeError – if the attribute is set to a value of an invalid type
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- set_integer_option(name, value)#
Set integer option.
This method will set the optimisation integer option name to value. The optimisation options are passed to the Ipopt API when calling the
evolve()
method.- Parameters
- Raises
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
Examples
>>> from pygmo import * >>> ip = ipopt() >>> ip.set_integer_option("print_level",3) >>> algorithm(ip) Algorithm name: Ipopt: Interior Point Optimization [deterministic] C++ class name: ... Thread safety: none Extra info: Last optimisation return code: Solve_Succeeded (value = 0) Verbosity: 0 Individual selection policy: best Individual replacement policy: best Integer options: {print_level : 3}
- set_integer_options(opts)#
Set integer options.
This method will set the optimisation integer options contained in opts. It is equivalent to calling
set_integer_option()
passing all the name-value pairs in opts as arguments.- Parameters
opts (
dict
ofstr
-int
pairs) – the name-value map that will be used to set the options- Raises
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
Examples
>>> from pygmo import * >>> ip = ipopt() >>> ip.set_integer_options({"filter_reset_trigger":4, "print_level":3}) >>> algorithm(ip) Algorithm name: Ipopt: Interior Point Optimization [deterministic] C++ class name: ... Thread safety: none Extra info: Last optimisation return code: Solve_Succeeded (value = 0) Verbosity: 0 Individual selection policy: best Individual replacement policy: best Integer options: {filter_reset_trigger : 4, print_level : 3}
- set_numeric_option(name, value)#
Set numeric option.
This method will set the optimisation numeric option name to value. The optimisation options are passed to the Ipopt API when calling the
evolve()
method.- Parameters
- Raises
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
Examples
>>> from pygmo import * >>> ip = ipopt() >>> ip.set_numeric_option("tol",1E-6) >>> algorithm(ip) Algorithm name: Ipopt: Interior Point Optimization [deterministic] C++ class name: ... Thread safety: none Extra info: Last optimisation return code: Solve_Succeeded (value = 0) Verbosity: 0 Individual selection policy: best Individual replacement policy: best Numeric options: {tol : 1E-6}
- set_numeric_options(opts)#
Set numeric options.
This method will set the optimisation numeric options contained in opts. It is equivalent to calling
set_numeric_option()
passing all the name-value pairs in opts as arguments.- Parameters
opts (
dict
ofstr
-float
pairs) – the name-value map that will be used to set the options- Raises
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
Examples
>>> from pygmo import * >>> ip = ipopt() >>> ip.set_numeric_options({"tol":1E-4, "constr_viol_tol":1E-3}) >>> algorithm(ip) Algorithm name: Ipopt: Interior Point Optimization [deterministic] C++ class name: ... Thread safety: none Extra info: Last optimisation return code: Solve_Succeeded (value = 0) Verbosity: 0 Individual selection policy: best Individual replacement policy: best Numeric options: {constr_viol_tol : 1E-3, tol : 1E-4}
- set_random_sr_seed(seed)#
Set the seed for the
"random"
selection/replacement policies.- Parameters
seed (
int
) – the value that will be used to seed the random number generator used by the"random"
election/replacement policies (seeselection
andreplacement
)- Raises
OverflowError – if the attribute is set to an integer which is negative or too large
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
- set_string_option(name, value)#
Set string option.
This method will set the optimisation string option name to value. The optimisation options are passed to the Ipopt API when calling the
evolve()
method.- Parameters
- Raises
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
Examples
>>> from pygmo import * >>> ip = ipopt() >>> ip.set_string_option("hessian_approximation","limited-memory") >>> algorithm(ip) Algorithm name: Ipopt: Interior Point Optimization [deterministic] C++ class name: ... Thread safety: none Extra info: Last optimisation return code: Solve_Succeeded (value = 0) Verbosity: 0 Individual selection policy: best Individual replacement policy: best String options: {hessian_approximation : limited-memory}
- set_string_options(opts)#
Set string options.
This method will set the optimisation string options contained in opts. It is equivalent to calling
set_string_option()
passing all the name-value pairs in opts as arguments.- Parameters
opts (
dict
ofstr
-str
pairs) – the name-value map that will be used to set the options- Raises
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
Examples
>>> from pygmo import * >>> ip = ipopt() >>> ip.set_string_options({"hessian_approximation":"limited-memory", "limited_memory_initialization":"scalar1"}) >>> algorithm(ip) Algorithm name: Ipopt: Interior Point Optimization [deterministic] C++ class name: ... Thread safety: none Extra info: Last optimisation return code: Solve_Succeeded (value = 0) Verbosity: 0 Individual selection policy: best Individual replacement policy: best String options: {hessian_approximation : limited-memory, limited_memory_initialization : scalar1}
- class pygmo.ihs(gen=1, phmcr=0.85, ppar_min=0.35, ppar_max=0.99, bw_min=1e-5, bw_max=1., seed=random)#
Harmony search (HS) is a metaheuristic algorithm said to mimick the improvisation process of musicians. In the metaphor, each musician (i.e., each variable) plays (i.e., generates) a note (i.e., a value) for finding a best harmony (i.e., the global optimum) all together.
This pygmo UDA implements the so-called improved harmony search algorithm (IHS), in which the probability of picking the variables from the decision vector and the amount of mutation to which they are subject vary (respectively linearly and exponentially) at each call of the
evolve()
method.In this algorithm the number of fitness function evaluations is equal to the number of iterations. All the individuals in the input population participate in the evolution. A new individual is generated at every iteration, substituting the current worst individual of the population if better.
Warning
The HS algorithm can and has been criticized, not for its performances, but for the use of a metaphor that does not add anything to existing ones. The HS algorithm essentially applies mutation and crossover operators to a background population and as such should have been developed in the context of Evolutionary Strategies or Genetic Algorithms and studied in that context. The use of the musicians metaphor only obscures its internal functioning making theoretical results from ES and GA erroneously seem as unapplicable to HS.
Note
The original IHS algorithm was designed to solve unconstrained, deterministic single objective problems. In pygmo, the algorithm was modified to tackle also multi-objective, constrained (box and non linearly). Such extension is original with pygmo.
- Parameters
gen (
int
) – number of generations to consider (each generation will compute the objective function once)phmcr (
float
) – probability of choosing from memory (similar to a crossover probability)ppar_min (
float
) – minimum pitch adjustment rate. (similar to a mutation rate)ppar_max (
float
) – maximum pitch adjustment rate. (similar to a mutation rate)bw_min (
float
) – minimum distance bandwidth. (similar to a mutation width)bw_max (
float
) – maximum distance bandwidth. (similar to a mutation width)seed (
int
) – seed used by the internal random number generator
- Raises
OverflowError – if gen or seed are negative or greater than an implementation-defined value
ValueError – if phmcr is not in the ]0,1[ interval, ppar_min or ppar_max are not in the ]0,1[ interval, min/max quantities are less than/greater than max/min quantities, bw_min is negative.
unspecified – any exception thrown by failures at the intersection between C++ and Python (e.g., type conversion errors, mismatched function signatures, etc.)
See also the docs of the C++ class
pagmo::ihs
.- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
and printed to screen. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with aihs
. A verbosity larger than 1 will produce a log with one entry each verbosity fitness evaluations.- Returns
at each logged epoch, the values
Fevals
,ppar
,bw
,dx
,df
,Violated
,Viol. Norm
,``ideal``Fevals
(int
), number of functions evaluation made.ppar
(float
), the pitch adjustment rate.bw
(float
), the distance bandwidth.dx
(float
), the population flatness evaluated as the distance between the decisions vector of the best and of the worst individual (or -1 in a multiobjective case).df
(float
), the population flatness evaluated as the distance between the fitness of the best and of the worst individual (or -1 in a multiobjective case).Violated
(int
), the number of constraints violated by the current decision vector.Viol. Norm
(float
), the constraints violation norm for the current decision vector.ideal_point
(1D numpy array), the ideal point of the current population (cropped to max 5 dimensions only in the screen output)
- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(ihs(20000)) >>> algo.set_verbosity(2000) >>> prob = problem(hock_schittkowski_71()) >>> prob.c_tol = [1e-1]*2 >>> pop = population(prob, 20) >>> pop = algo.evolve(pop) Fevals: ppar: bw: dx: df: Violated: Viol. Norm: ideal1: 1 0.350032 0.999425 4.88642 14.0397 0 0 43.2982 2001 0.414032 0.316046 5.56101 25.7009 0 0 33.4251 4001 0.478032 0.0999425 5.036 26.9657 0 0 19.0052 6001 0.542032 0.0316046 3.77292 23.9992 0 0 19.0052 8001 0.606032 0.00999425 3.97937 16.0803 0 0 18.1803 10001 0.670032 0.00316046 1.15023 1.57947 0 0 17.8626 12001 0.734032 0.000999425 0.017882 0.0185438 0 0 17.5894 14001 0.798032 0.000316046 0.00531358 0.0074745 0 0 17.5795 16001 0.862032 9.99425e-05 0.00270865 0.00155563 0 0 17.5766 18001 0.926032 3.16046e-05 0.00186637 0.00167523 0 0 17.5748 >>> uda = algo.extract(ihs) >>> uda.get_log() [(1, 0.35003234534534, 0.9994245193792801, 4.886415773459253, 14.0397487316794, ...
See also the docs of the relevant C++ method
pagmo::ihs::get_log()
.
- class pygmo.xnes(gen=1, eta_mu=- 1, eta_sigma=- 1, eta_b=- 1, sigma0=- 1, ftol=1e-6, xtol=1e-6, memory=False, force_bounds=False, seed=random)#
Exponential Evolution Strategies.
- Parameters
gen (
int
) – number of generationseta_mu (
float
) – learning rate for mean update (if -1 will be automatically selected to be 1)eta_sigma (
float
) – learning rate for step-size update (if -1 will be automatically selected)eta_b (
float
) – learning rate for the covariance matrix update (if -1 will be automatically selected)sigma0 (
float
) – the initial search width will be sigma0 * (ub - lb) (if -1 will be automatically selected to be 1)ftol (
float
) – stopping criteria on the x tolerancextol (
float
) – stopping criteria on the f tolerancememory (
bool
) – when true the adapted parameters are not reset between successive calls to the evolve methodforce_bounds (
bool
) – when true the box bounds are enforced. The fitness will never be called outside the bounds but the covariance matrix adaptation mechanism will worsenseed (
int
) – seed used by the internal random number generator (default is random)
- Raises
OverflowError – if gen is negative or greater than an implementation-defined value
ValueError – if eta_mu, eta_sigma, eta_b, sigma0 are not in ]0,1] or -1
See also the docs of the C++ class
pagmo::xnes
.- get_log()#
Returns a log containing relevant parameters recorded during the last call to
evolve()
. The log frequency depends on the verbosity parameter (by default nothing is logged) which can be set calling the methodset_verbosity()
on analgorithm
constructed with axnes
. A verbosity ofN
implies a log line eachN
generations.- Returns
at each logged epoch, the values
Gen
,Fevals
,Best
,dx
,df
,sigma
, where:Gen
(int
), generation numberFevals
(int
), number of functions evaluation madeBest
(float
), the best fitness function currently in the populationdx
(float
), the norm of the distance to the population mean of the mutant vectorsdf
(float
), the population flatness evaluated as the distance between the fitness of the best and of the worst individualsigma
(float
), the current step-size
- Return type
Examples
>>> from pygmo import * >>> algo = algorithm(xnes(gen = 500)) >>> algo.set_verbosity(100) >>> prob = problem(rosenbrock(10)) >>> pop = population(prob, 20) >>> pop = algo.evolve(pop) Gen: Fevals: Best: dx: df: sigma: 1 0 173924 33.6872 3.06519e+06 0.5 101 2000 92.9612 0.583942 156.921 0.0382078 201 4000 8.79819 0.117574 5.101 0.0228353 301 6000 4.81377 0.0698366 1.34637 0.0297664 401 8000 1.04445 0.0568541 0.514459 0.0649836 Exit condition -- generations = 500 >>> uda = algo.extract(xnes) >>> uda.get_log() [(1, 0, 173924.2840042722, 33.68717961390855, 3065192.3843070837, 0.5), ...
See also the docs of the relevant C++ method
pagmo::xnes::get_log()
.