Differential Evolution

class pagmo::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 box-constrained single-objective continuous optimization.


The feasibility correction, that is the correction applied to an allele when some mutation puts it outside the allowed box-bounds, is here done by creating a random number in the bounds.

See also

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 = 1e-6, double xtol = 1e-6, unsigned seed = pagmo::random_device::next())


Constructs de

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

  • 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 1e-6)

  • xtol – stopping criteria on the x tolerance (default is 1e-6)

  • seed – seed used by the internal random number generator (default is random)

  • 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) 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.


pop – population to be evolved

  • std::invalid_argument – if the problem is multi-objective or constrained or stochastic

  • std::invalid_argument – if the population size is not at least 5


evolved population

void set_seed(unsigned)

Sets the seed.


seed – the seed controlling the algorithm stochastic behaviour

inline unsigned get_seed() const

Get the seed.


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 100):

Gen:        Fevals:          Best:            dx:            df:
5001         100020    3.62028e-05      0.0396687      0.0002866
5101         102020    1.16784e-05      0.0473027    0.000249057
5201         104020    1.07883e-05      0.0455471    0.000243651
5301         106020    6.05099e-06      0.0268876    0.000103512
5401         108020    3.60664e-06      0.0230468    5.78161e-05
5501         110020     1.7188e-06      0.0141655    2.25688e-05
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.


level – verbosity level

inline unsigned get_verbosity() const

Gets the verbosity level.


the verbosity level

inline unsigned get_gen() const

Gets the generations.


the number of generations to evolve for

inline std::string get_name() const

Algorithm name.

One of the optional methods of any user-defined algorithm (UDA).


a string containing the algorithm name

std::string get_extra_info() const

Extra info.

One of the optional methods of any user-defined algorithm (UDA).


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 de::log_line_type containing: Gen, Fevals, Best, dx, df as described in de::set_verbosity


an std::vector of de::log_line_type containing the logged values Gen, Fevals, Best, dx, df