Differential Evolution
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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.
See also
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
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typedef std::tuple<unsigned, unsigned long long, double, double, double> log_line_type
Single entry of the log (gen, fevals, best, dx, df)
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typedef std::vector<log_line_type> log_type
The log.
Public Functions
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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 (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)
- Throws
std::invalid_argument – if F, CR are not in [0,1]
std::invalid_argument – if variant is not one of 1 .. 10
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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
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void set_seed(unsigned)
Sets the seed.
- Parameters
seed – the seed controlling the algorithm stochastic behaviour
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inline unsigned get_seed() const
Get the seed.
- Returns
the seed controlling the algorithm stochastic behaviour
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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, 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 3.62028e-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
- Parameters
level – verbosity level
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inline unsigned get_verbosity() const
Gets the verbosity level.
- Returns
the verbosity level
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inline unsigned get_gen() const
Gets the generations.
- Returns
the number of generations to evolve for
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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
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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
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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
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typedef std::tuple<unsigned, unsigned long long, double, double, double> log_line_type