Differential Evolution¶

class
de
¶ Differential Evolution Algorithm.
Differential Evolution is an heuristic optimizer developed by Rainer Storn and Kenneth Price.
‘’A breakthrough happened, when Ken came up with the idea of using vector differences for perturbing the vector population. Since this seminal idea a lively discussion between Ken and Rainer and endless ruminations and computer simulations on both parts yielded many substantial improvements which make DE the versatile and robust tool it is today’’ (from the official web pages….)
The implementation provided for PaGMO is based on the code provided in the official DE web site. pagmo::de is suitable for boxconstrained singleobjective continuous optimization.
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
The official DE web site: http://www1.icsi.berkeley.edu/~storn/code.html
The paper that introduces Differential Evolution https://link.springer.com/article/10.1023%2FA%3A1008202821328
Public Types

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

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

de
(unsigned gen = 1u, double F = 0.8, double CR = 0.9, unsigned variant = 2u, double ftol = 1e6, double xtol = 1e6, unsigned seed = pagmo::random_device::next())¶ Constructor.
Constructs de
The following variants (mutation variants) are available to create a new candidate individual:
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
 Parameters
gen
: number of generations.F
: weight coefficient (dafault value is 0.8)CR
: crossover probability (dafault value is 0.9)variant
: mutation variant (dafault variant is 2: /rand/1/exp)ftol
: stopping criteria on the f tolerance (default is 1e6)xtol
: stopping criteria on the x tolerance (default is 1e6)seed
: seed used by the internal random number generator (default is random)
 Exceptions
std::invalid_argument
: if F, CR are not in [0,1]std::invalid_argument
: if variant is not one of 1 .. 10

population
evolve
(population pop) 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.
 Return
evolved population
 Parameters
pop
: population to be evolved
 Exceptions
std::invalid_argument
: if the problem is multiobjective or constrained or stochasticstd::invalid_argument
: if the population size is not at least 5

void
set_seed
(unsigned seed)¶ Sets the seed.
 Parameters
seed
: the seed controlling the algorithm stochastic behaviour

unsigned
get_seed
() const¶ Get the seed.
 Return
the seed controlling the algorithm stochastic behaviour

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 100):
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 population flatness evaluated as the distance between the decisions vector of the best and of the worst individual, df is the population flatness evaluated as the distance between the fitness of the best and of the worst individual.Gen: Fevals: Best: dx: df: 5001 100020 3.62028e05 0.0396687 0.0002866 5101 102020 1.16784e05 0.0473027 0.000249057 5201 104020 1.07883e05 0.0455471 0.000243651 5301 106020 6.05099e06 0.0268876 0.000103512 5401 108020 3.60664e06 0.0230468 5.78161e05 5501 110020 1.7188e06 0.0141655 2.25688e05
 Parameters
level
: verbosity level

unsigned
get_verbosity
() const¶ Gets the verbosity level.
 Return
the verbosity level

unsigned
get_gen
() const¶ Gets the generations.
 Return
the number of generations to evolve for

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

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

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 de::log_line_type containing: Gen, Fevals, Best, dx, df as described in de::set_verbosity Return
an
std::vector
of de::log_line_type containing the logged values Gen, Fevals, Best, dx, df

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