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 box-constrained single-objective continuous optimization.

The paper that introduces Differential Evolution https://link.springer.com/article/10.1023%2FA%3A1008202821328

Note

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.

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())#

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 - 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
```

Parameters
• gen – number of generations.

• F – weight coefficient (default value is 0.8)

• CR – crossover probability (default value is 0.9)

• variant – mutation variant (default 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)

Throws
• 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.

Parameters

pop – population to be evolved

Throws
• 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

Returns

evolved population

void set_seed(unsigned)#

Sets the seed.

Parameters

seed – the seed controlling the algorithm stochastic behaviour

inline unsigned get_seed() const#

Get 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 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.

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 user-defined algorithm (UDA).

Returns

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).

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

Returns

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