Multi-Objective Memetic Evolutionary Strategy (UDA)

class momes4cgp

Multi-Objective, Memetic Evolutionary Strategy for a Cartesian Genetic Program.

../../_images/multiple_objectives.png../../_images/neo-darwinism.jpg

Symbolic regression tasks seek for good mathematical models to represent input data. By increasing the model complexity it is always (theoretically) possible to find almost perfect fits of any input data. As a consequence, the model complexity must be traded off with its accuracy so that symbolic regression is, ultimately, a two-objectives optimization problem.

In this C++ class we offer an UDA (User Defined Algorithm for the pagmo optimization suite) which extends :class:dcgp::mes4cgp for a multiobjective problem. The resulting algorithm, is outlined by the following pseudo-algorithm:

> Start from a population (pop) of dimension N
> while i < gen
> > Mutation: create a new population pop2 mutating N times the best individual (only the integer part is affected)
> > Life long learning: apply a one step of a second order Newton method to each individual (only the continuous part
    is affected)
> > Reinsertion: set pop to contain the best N individuals taken from pop and pop2 according to non dominated
sorting.

Public Types

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

Single entry of the log (gen, fevals, best loss, ndf size, max. complexity)

typedef std::vector<log_line_type> log_type

The log.

Public Functions

inline momes4cgp(unsigned gen = 1u, unsigned max_mut = 4u, double ftol = 0., unsigned seed = random_device::next())

Constructor.

Constructs a multi-objective memetic evolutionary strategy algorithm for use with a :class:dcgp::symbolic_regression UDP.

Parameters

  • gen – number of generations.

  • max_mut – maximum number of active genes to be mutated. The minimum is 0 as to allow multiple steps of Newton descent.

  • ftol – a stopping criterion on the achieved loss.

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

Throws

std::invalid_argument – if mut_n is 0

inline pagmo::population evolve(pagmo::population pop) const

Algorithm evolve method.

Evolves the population for a maximum number of generations

Parameters

pop – population to be evolved

Throws

  • std::invalid_argument – if a :class:dcgp::symbolic_regression cannot be extracted from the problem

  • std::invalid_argument – if the population size is smaller than 2.

  • std::invalid_argument – if the number of objectives is smaller than 2.

Returns

evolved population

inline void set_seed(unsigned seed)

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 10): 

Gen:        Fevals:     Best loss: Ndf size:   Compl.:
   0              0        6.07319         3        92
  10           1000        2.15419         5        10
  20           2000        1.92403         8        33
  30           3000       0.373663        12        72
  40           4000        0.36954        13        72
  50           5000       0.235749        16        73
  60           6000       0.235749        12        73
  70           7000       0.235749        13        73
  80           8000       0.217968        12        75
  90           9000       0.217968        12        75
 100          10000       0.217968        12        75
 110          11000       0.217968        14        75
 120          12000       0.217968        14        75
 130          13000       0.217968        13        75
 140          14000       0.162293        12        52
Gen is the generation number, Fevals the number of function evaluation used, Best loss is the best loss in the population, Ndf size is the size of the non dominated front (i.e. the number of models that are optimal) and compl. is the complexity of the lowest loss model.

Parameters

level – verbosity level

inline unsigned get_verbosity() const

Gets the verbosity level.

Returns

the verbosity level

inline std::string get_name() const

Algorithm name.

Returns

a string containing the algorithm name

inline std::string get_extra_info() const

Extra info.

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 momes4cgp::log_line_type containing: Gen, Fevals, Best loss, Ndf size and Complexity described in momes4cgp::set_verbosity().

Returns

an std::vector of momes4cgp::log_line_type containing the logged values Gen, Fevals, Best loss, Ndf size * * and Complexity

template<typename Archive>
inline void serialize(Archive &ar, unsigned)

Object serialization.

This method will save/load this into the archive ar.

Parameters

ar – target archive.

Throws

unspecified – any exception thrown by the serialization of the expression and of primitive types.