Selfadaptive Differential Evolution (jDE and iDE)

class pagmo::sade
Selfadaptive Differential Evolution Algorithm.
.
Two different variants of the Differential Evolution algorithm exploiting the idea of selfadaptation.
The original Differential Evolution algorithm (pagmo::de) can be significantly improved introducing the idea of parameter selfadaptation. Many different proposals have been made to selfadapt both the CR and the F parameters of the original differential evolution algorithm. In PaGMO we implement two different mechanisms we found effective. The first one, proposed by Brest et al., does not make use of the DE operators to produce new values for F and CR and, strictly speaking, is thus not selfadaptation, rather parameter control. The resulting DE variant is often referred to as jDE. The second variant here implemented is inspired by the ideas introduced by Elsayed et al. and uses a variaton of the selected DE operator to produce new CR anf F parameters for each individual. We refer to this variant as to iDE.
Warning
A movedfrom pagmo::sade is destructible and assignable. Any other operation will result in undefined behaviour.
Warning
The algorithm referred to as SaDE in the literature is not the algorithm implemented in pagmo. We use the name sade to indicate, generically, selfadaptation in a differential evolution algorithm
Note
The feasibility correction, that is the correction applied to an allele when some mutation puts it outside the allowed boxbounds, is here done by creating a random number in the bounds.
See also
(jDE)  Brest, J., Greiner, S., Bošković, B., Mernik, M., & Zumer, V. (2006). Selfadapting control parameters in differential evolution: a comparative study on numerical benchmark problems. Evolutionary Computation, IEEE Transactions on, 10(6), 646657. Chicago
See also
(iDE)  Elsayed, S. M., Sarker, R. A., & Essam, D. L. (2011, June). Differential evolution with multiple strategies for solving CEC2011 realworld numerical optimization problems. In Evolutionary Computation (CEC), 2011 IEEE Congress on (pp. 10411048). IEEE.
Public Types

typedef std::tuple<unsigned, unsigned long long, double, double, double, double, double> log_line_type
Single entry of the log (gen, fevals, best, F, CR, dx, df)

typedef std::vector<log_line_type> log_type
The log.
Public Functions

sade(unsigned gen = 1u, unsigned variant = 2u, unsigned variant_adptv = 1u, double ftol = 1e6, double xtol = 1e6, bool memory = false, unsigned seed = pagmo::random_device::next())
Constructor.
Constructs selfadaptive differential evolution
Two selfadaptation variants are available to control the F and CR parameters:
1  jDE (Brest et al.) 2  iDE (Elsayed at al.)
The following variants are available to produce a mutant vector:
1  best/1/exp 2.  rand/1/exp 3  randtobest/1/exp 4.  best/2/exp 5  rand/2/exp 6.  best/1/bin 7  rand/1/bin 8.  randtobest/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.  randtocurrent/2/exp 16.  randtocurrent/2/bin 17.  randtobestandcurrent/2/exp 18.  randtobestandcurrent/2/bin
The first ten are the classical mutation variants introduced in the orginal DE algorithm, the remaining ones are, instead, considered in the work by Elsayed et al.
 Parameters
gen – number of generations.
variant – mutation variant (dafault variant is 2: /rand/1/exp)
variant_adptv – F and CR parameter adaptation scheme to be used (one of 1..2)
ftol – stopping criteria on the x tolerance (default is 1e6)
xtol – stopping criteria on the f tolerance (default is 1e6)
memory – when true the adapted parameters CR anf F are not reset between successive calls to the evolve method
seed – seed used by the internal random number generator (default is random)
 Throws
std::invalid_argument – if
variant_adptv
is not one of 0,1std::invalid_argument – if variant is not one of 1, .., 18

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 or stochastic
std::invalid_argument – if the population size is not at least 7
 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, F is the F used to create the best so far, CR the CR used to create the best so far, dx is the population flatness evaluated as the distance between the decisions vector of the best and of the worst individual and df is the population flatness evaluated as the distance between the fitness of the best and of the worst individual.Gen: Fevals: Best: F: CR: dx: df: 301 4515 0.668472 0.374983 0.502932 0.000276682 0.000388866 302 4530 0.668472 0.374983 0.502932 0.000213271 0.00020986 303 4545 0.668426 0.598243 0.234825 0.000167061 0.000186339 304 4560 0.668426 0.598243 0.234825 0.000217549 0.000144896 305 4575 0.668339 0.807236 0.863048 0.000192539 0.000232005 306 4590 0.668339 0.807236 0.863048 0.000143711 0.000229041 307 4605 0.668307 0.374983 0.820731 0.000163919 0.000245393
 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 sade::log_line_type containing: Gen, Fevals, Best, F, CR, dx, df as described in sade::set_verbosity Returns
an
std::vector
of sade::log_line_type containing the logged values Gen, Fevals, Best, F, CR, dx, df

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