Exponential Natural Evolution Strategies (xNES)
Exponential Natural Evolution Strategies (xNES)#

class xnes#
Exponential Natural Evolution Strategies.
Exponential Natural Evolution Strategies is an algorithm closely related to pagmo::cmaes and based on the adaptation of a gaussian sampling distribution via the socalled natural gradient. Like pagmo::cmaes it is based on the idea of sampling new trial vectors from a multivariate distribution and using the new sampled points to update the distribution parameters. Naively this could be done following the gradient of the expected fitness as approximated by a finite number of sampled points. While this idea offers a powerful lead on algorithmic construction it has some major drawbacks that are solved in the socalled Natural Evolution Strategies class of algorithms by adopting, instead, the natural gradient. xNES is one of the most performing variants in this class.
See also
Glasmachers, T., Schaul, T., Yi, S., Wierstra, D., & Schmidhuber, J. (2010, July). Exponential natural evolution strategies. In Proceedings of the 12th annual conference on Genetic and evolutionary computation (pp. 393400). ACM.
Note
This userdefined algorithm is available only if pagmo was compiled with the
PAGMO_WITH_EIGEN3
option enabled (see the installation instructions).Note
We introduced one change to the original algorithm in order to simplify its use for the generic user. The initial covariance matrix depends on the bounds width so that heterogenously scaled variables are not a problem: the width along the ith direction will be w_i = sigma_0 * (ub_i  lb_i)
Note
Since at each generation all newly generated individuals sampled from the adapted distribution are reinserted into the population, xNES may not preserve the best individual (not elitist). As a consequence the plot of the population best fitness may not be perfectly monotonically decreasing.
Warning
A movedfrom pagmo::xnes is destructible and assignable. Any other operation will result in undefined behaviour.
Public Types

typedef std::tuple<unsigned, unsigned long long, double, double, double, double> log_line_type#
Single data line for the algorithm’s log.
A log data line is a tuple consisting of:
the generation number,
the number of function evaluations
the best fitness vector so far,
the population flatness evaluated as the distance between the decisions vector of the best and of the worst individual,
the population flatness evaluated as the distance between the fitness of the best and of the worst individual.

typedef std::vector<log_line_type> log_type#
Log type.
The algorithm log is a collection of xnes::log_line_type data lines, stored in chronological order during the optimisation if the verbosity of the algorithm is set to a nonzero value (see xnes::set_verbosity()).
Public Functions

xnes(unsigned gen = 1, double eta_mu = 1, double eta_sigma = 1, double eta_b = 1, double sigma0 = 1, double ftol = 1e6, double xtol = 1e6, bool memory = false, bool force_bounds = false, unsigned seed = pagmo::random_device::next())#
Constructor.
Constructs xnes
 Parameters
gen – number of generations.
eta_mu – learning rate for mean update (if 1 will be automatically selected to be 1)
eta_sigma – learning rate for stepsize update (if 1 will be automatically selected)
eta_b – learning rate for the covariance matrix update (if 1 will be automatically selected)
sigma0 – the initial search width will be sigma0 * (ub  lb) (if 1 will be selected to be 0.5)
ftol – stopping criteria on the x tolerance (default is 1e6)
xtol – stopping criteria on the f tolerance (default is 1e6)
memory – when true the distribution parameters are not reset between successive calls to the evolve method
force_bounds – when true the box bounds are enforced. The fitness will never be called outside the bounds but the covariance matrix adaptation mechanism will worsen
seed – seed used by the internal random number generator (default is random)
 Throws
std::invalid_argument – if eta_mu, eta_sigma, eta_b and sigma0 are not in ]0, 1] or 1

population evolve(population) const#
Algorithm evolve method.
Evolves the population for a maximum number of generations, until one of tolerances set on the population flatness (x_tol, f_tol) are met.
 Parameters
pop – population to be evolved
 Throws
std::invalid_argument – if the problem is multiobjective or constrained
std::invalid_argument – if the problem is unbounded
std::invalid_argument – if the population size is not at least 4
 Returns
evolved population

void set_seed(unsigned)#
Sets the seed.
 Parameters
seed – the seed controlling the algorithm stochastic behaviour

inline unsigned get_seed() const#
Gets the seed.
 Returns
the seed controlling the algorithm stochastic behaviour

inline void set_verbosity(unsigned level)#
Sets the algorithm verbosity.
Sets the verbosity level of the screen output and of the log returned by get_log().
level
can be:0: no verbosity
>0: will print and log one line each
level
generations.
Example (verbosity 1):
Gen, is the generation number, Fevals the number of function evaluation used, Best is the best fitness function currently in the population, dx is the norm of the distance to the population mean of the mutant vectors, df is the population flatness evaluated as the distance between the fitness of the best and of the worst individual and sigma is the current stepsizeGen: Fevals: Best: dx: df: sigma: 51 1000 1.15409e06 0.00205151 3.38618e05 0.138801 52 1020 3.6735e07 0.00423372 2.91669e05 0.13002 53 1040 3.7195e07 0.000655583 1.04182e05 0.107739 54 1060 6.26405e08 0.00181163 3.86002e06 0.0907474 55 1080 4.09783e09 0.000714699 3.57819e06 0.0802022 56 1100 1.77896e08 4.91136e05 9.14752e07 0.075623 57 1120 7.63914e09 0.000355162 1.10134e06 0.0750457 58 1140 1.35199e09 0.000356034 2.65614e07 0.0622128 59 1160 8.24796e09 0.000695454 1.14508e07 0.04993
 Parameters
level – verbosity level

inline unsigned get_verbosity() const#
Gets the verbosity level.
 Returns
the verbosity level

inline unsigned get_gen() const#
Gets the generations.
 Returns
the number of generations to evolve for

inline std::string get_name() const#
Algorithm name.
One of the optional methods of any userdefined algorithm (UDA).
 Returns
a string containing the algorithm name

std::string get_extra_info() const#
Extra info.
One of the optional methods of any userdefined algorithm (UDA).
 Returns
a string containing extra info on the algorithm

inline const log_type &get_log() const#
Get log.
A log containing relevant quantities monitoring the last call to evolve. Each element of the returned
std::vector
is a xnes::log_line_type containing: Gen, Fevals, Best, dx, df, sigma as described in xnes::set_verbosity Returns
an
std::vector
of xnes::log_line_type containing the logged values Gen, Fevals, Best, dx, df, sigma

typedef std::tuple<unsigned, unsigned long long, double, double, double, double> log_line_type#