OMADS package

Submodules

OMADS.POLL module

This is a python implementation of the orothognal mesh adaptive direct search method (OMADS)

class OMADS.POLL.DType(_prec: str = 'medium', _dtype: numpy.dtype = <class 'numpy.float64'>, _itype: numpy.dtype = <class 'numpy.int64'>, _zero: float = 1e-15, _warned: bool = False)

Bases: object

A numpy data type delegator for decimal precision control

Parameters

• prec (str, optional) – Default precision option can be set to “high”, “medium” or “low” precision resolution, defaults to “medium”

• dtype (np.dtype, optional) – Numpy double data type precision, defaults to np.float64

• itype (np.dtype, optional) – Numpy integer data type precision, defaults to np.int

• zero (float, optional) – Zero value resolution, defaults to np.finfo(np.float64).resolution

property zero: float

This is the mantissa value of the machine zero

Returns

machine precision zero resolution

Return type

float

property precision

Set/get precision resolution level

Returns

float precision value

Return type

numpy float

Note

MS Windows does not support precision with the {1e-18} high resolution of the python numerical library (numpy) so high precision will be changed to medium precision which supports {1e-15} resolution check: https://numpy.org/doc/stable/user/basics.types.html

property dtype

Set/get the double formate type

Returns

float precision value

Return type

numpy float

property itype

Set/Get for the integer formate type

Returns

integer precision value

Return type

numpy float

__init__(_prec: str = 'medium', _dtype: numpy.dtype = <class 'numpy.float64'>, _itype: numpy.dtype = <class 'numpy.int64'>, _zero: float = 1e-15, _warned: bool = False) → None

class OMADS.POLL.Options(seed: int = 0, budget: int = 1000, tol: float = 1e-09, psize_init: float = 1.0, display: bool = False, opportunistic: bool = False, check_cache: bool = False, store_cache: bool = False, collect_y: bool = False, rich_direction: bool = False, precision: str = 'high', save_results: bool = False, save_coordinates: bool = False, save_all_best: bool = False, parallel_mode: bool = False, np: int = 1)

Bases: object

The running study and algorithmic options of OMADS

Parameters

• seed – Random generator seed

• budget – The evaluation budget

• tol – The threshold of the minimum poll size at which the run will be terminated

• psize_init – Initial poll size

• dispaly – Print the study progress during the run

• opportunistic – Loop on the points populated in the poll set until a better minimum found, then stop the evaluation loop

• check_cache – Check the hash table before points evaluation to avoid duplicates

• store_cache – Enable storing evaluated points into the hash table

• collect_y – Collect dependent design variables (required for DMDO)

• rich_direction – Go with the rich direction (Impact the mesh size update)

• precision – Define the precision level

• save_results – A boolean flag that indicates saving results in a csv file

• save_coordinates – A boolean flag that indicates saving coordinates of the poll set in a JSON file (required to generate animations of the spinner)

• save_all_best – A boolean used to check whether saving best points only in the MADS.out file

• parallel_mode – A boolean to check whether evaluating the poll set in parallel multiprocessing

• np – The number of CPUs

seed: int = 0

budget: int = 1000

tol: float = 1e-09

psize_init: float = 1.0

display: bool = False

opportunistic: bool = False

check_cache: bool = False

store_cache: bool = False

collect_y: bool = False

rich_direction: bool = False

precision: str = 'high'

save_results: bool = False

save_coordinates: bool = False

save_all_best: bool = False

parallel_mode: bool = False

np: int = 1

__init__(seed: int = 0, budget: int = 1000, tol: float = 1e-09, psize_init: float = 1.0, display: bool = False, opportunistic: bool = False, check_cache: bool = False, store_cache: bool = False, collect_y: bool = False, rich_direction: bool = False, precision: str = 'high', save_results: bool = False, save_coordinates: bool = False, save_all_best: bool = False, parallel_mode: bool = False, np: int = 1) → None

class OMADS.POLL.VAR_TYPE(value)

Bases: enum.Enum

An enumeration.

CONTINUOUS = 1

INTEGER = 2

DISCRETE = 3

BINARY = 4

CATEGORICAL = 5

ORDINAL = 6

class OMADS.POLL.Parameters(baseline: typing.List[float] = <factory>, lb: typing.List[float] = <factory>, ub: typing.List[float] = <factory>, var_names: typing.List[str] = <factory>, scaling: float = 10.0, post_dir: str = '/Users/ahmedb/apps/code/Bay_dev/OMADS/docs-dev/.\\', var_type: typing.Optional[typing.List[str]] = None, var_sets: typing.Optional[typing.Dict] = None, constants: typing.Optional[typing.List] = None, constants_name: typing.Optional[typing.List] = None)

Bases: object

Variables and algorithmic parameters

Parameters

• baseline – Baseline design point (initial point x0)

• lb – The variables lower bound

• ub – The variables upper bound

• var_names – The variables name

• scaling – Scaling factor (can be defined as a list (assigning a factor for each variable) or a scalar value that will be applied on all variables)

• post_dir – The location and name of the post directory where the output results file will live in (if any)

baseline: List[float]

lb: List[float]

ub: List[float]

var_names: List[str]

scaling: float = 10.0

post_dir: str = '/Users/ahmedb/apps/code/Bay_dev/OMADS/docs-dev/.\\'

var_type: List[str] = None

var_sets: Dict = None

constants: List = None

constants_name: List = None

__init__(baseline: typing.List[float] = <factory>, lb: typing.List[float] = <factory>, ub: typing.List[float] = <factory>, var_names: typing.List[str] = <factory>, scaling: float = 10.0, post_dir: str = '/Users/ahmedb/apps/code/Bay_dev/OMADS/docs-dev/.\\', var_type: typing.Optional[typing.List[str]] = None, var_sets: typing.Optional[typing.Dict] = None, constants: typing.Optional[typing.List] = None, constants_name: typing.Optional[typing.List] = None) → None

class OMADS.POLL.Evaluator(blackbox: typing.Any = 'rosenbrock', commandOptions: typing.Optional[typing.Any] = None, internal: typing.Optional[str] = None, path: str = '..\\tests\\Rosen', input: str = 'input.inp', output: str = 'output.out', constants: typing.Optional[typing.List] = None, bb_eval: int = 0, _dtype: OMADS.POLL.DType = DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False), timeout: float = 1000000.0)

Bases: object

Define the evaluator attributes and settings

Parameters

• blackbox – The blackbox name (it can be a callable function or an executable file)

• commandOptions – Define options that will be added to the execution command of the executable file. Command options should be defined as a string in one line

• internal – If the blackbox callable function is part of the internal benchmarking library

• path – The path of the executable file (if any)

• input – The input file name – should include the file extension

• output – The output file name – should include the file extension

• constants – Define constant parameters list, see the documentation in Tutorials->Blackbox evaluation->User parameters

• _dtype – The precision delegator of the numpy library

• timeout – The time out of the evaluation process

blackbox: Any = 'rosenbrock'

commandOptions: Any = None

internal: Optional[str] = None

path: str = '..\\tests\\Rosen'

input: str = 'input.inp'

output: str = 'output.out'

constants: List = None

bb_eval: int = 0

timeout: float = 1000000.0

property dtype

eval(values: List[float])

Evaluate the poll point

Parameters

values (List[float]) – Poll point coordinates (design vector)

Raises

• IOError – Incorrect number of input arguments introduced to the callable function

• IOError – Incorrect number of input arguments introduced to the callable function

• IOError – The blackbox file is not an executable file (if not a callable function)

• IOError – Incorrect benchmarking keyword category

Returns

Evaluated optimization functions

Return type

List[float, List[float]]

write_input(values: List[float])

_summary_

Parameters

values (List[float]) – Write the variables in the input file

read_output() → List[float]

_summary_

Returns

Read the output values from the output file

Return type

List[float]

__init__(blackbox: typing.Any = 'rosenbrock', commandOptions: typing.Optional[typing.Any] = None, internal: typing.Optional[str] = None, path: str = '..\\tests\\Rosen', input: str = 'input.inp', output: str = 'output.out', constants: typing.Optional[typing.List] = None, bb_eval: int = 0, _dtype: OMADS.POLL.DType = DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False), timeout: float = 1000000.0) → None

class OMADS.POLL.Point(_n: int = 0, _coords: typing.List[float] = <factory>, _defined: typing.List[bool] = <factory>, _evaluated: bool = False, _f: float = inf, _freal: float = inf, _c_ineq: typing.List[float] = <factory>, _c_eq: typing.List[float] = <factory>, _h: float = inf, _signature: int = 0, _dtype: OMADS.POLL.DType = DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False), _var_type: typing.Optional[typing.List[int]] = None, _sets: typing.Optional[typing.Dict] = None, _var_link: typing.Optional[typing.List[str]] = None)

Bases: object

A class for the poll point

Parameters

• _n – # Dimension of the point

• _coords – Coordinates of the point

• _defined – Coordinates definition boolean

• _evaluated – Evaluation boolean

• _f – Objective function

• _freal – Realistic target value of the objective function

• _c_ineq – Inequality constraints

• _c_eq – Equality constraints

• _h – Aggregated constraints; active set

• _signature – hash signature; facilitate looking for duplicates and storing coordinates, hash signature, in the cache memory

• _dtype – numpy double data type precision

property var_link

property var_type: List[int]

property sets

property dtype

property evaluated

property signature

property n_dimensions

property coordinates

Get the coordinates of the point.

property defined: List[bool]

is_any_defined() → bool

Check if at least one coordinate is defined.

property f

property freal

property c_ineq

property c_eq

property h

reset(n: int = 0, d: Optional[float] = None)

Sets all coordinates to d.

__init__(_n: int = 0, _coords: typing.List[float] = <factory>, _defined: typing.List[bool] = <factory>, _evaluated: bool = False, _f: float = inf, _freal: float = inf, _c_ineq: typing.List[float] = <factory>, _c_eq: typing.List[float] = <factory>, _h: float = inf, _signature: int = 0, _dtype: OMADS.POLL.DType = DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False), _var_type: typing.Optional[typing.List[int]] = None, _sets: typing.Optional[typing.Dict] = None, _var_link: typing.Optional[typing.List[str]] = None) → None

class OMADS.POLL.OrthoMesh(_delta: float = -1.0, _Delta: float = -1.0, _rho: float = -1.0, _exp: int = 0, _mantissa: int = 1, psize_max: float = 0.0, psize_success: float = 0.0, _dtype: OMADS.POLL.DType = DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False))

Bases: object

Mesh coarsness update class

Parameters

• _delta – mesh size

• _Delta – poll size

• _rho – poll size to mesh size ratio

• _exp – manage the poll size granularity for discrete variables. See Audet et. al, The mesh adaptive direct search algorithm for granular and discrete variable

• _mantissa – Same as _exp

• psize_max – Maximum poll size

• psize_success – Poll size at successful evaluation

• _dtype – numpy double data type precision

psize_max: float = 0.0

psize_success: float = 0.0

property dtype

property msize

property psize

property rho

update()

__init__(_delta: float = -1.0, _Delta: float = -1.0, _rho: float = -1.0, _exp: int = 0, _mantissa: int = 1, psize_max: float = 0.0, psize_success: float = 0.0, _dtype: OMADS.POLL.DType = DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False)) → None

class OMADS.POLL.Cache(_hash_ID: typing.List[int] = <factory>, _cache_dict: typing.Dict[typing.Any, typing.Any] = <factory>)

Bases: object

In computing, a hash table (hash map) is a data structure that implements an associative array abstract data type, a structure that can map keys to values. A hash table uses a hash function to compute an index, also called a hash code, into an array of buckets or slots, from which the desired value can be found. During lookup, the key is hashed and the resulting hash indicates where the corresponding value is stored.

property cache_dict: Dict

A getter of the cache memory dictionary

Return type

Dict

property hash_id: List[int]

A getter to return the list of hash IDs

Return type

List[int]

property size: int

A getter of the size of the hash ID list

Return type

int

is_duplicate(x: OMADS.POLL.Point) → bool

Check if the point is in the cache memory

Parameters

x (Point) – Design point

Returns

A boolean flag indicate whether the point exist in the cache memory

Return type

bool

get_index(x: OMADS.POLL.Point) → int

Get the index of hash value, associated with the point x, if that point was saved in the cach memory

Parameters

x (Point) – Input point

Returns

The index of the point in the hash ID list

Return type

int

add_to_cache(x: OMADS.POLL.Point)

Save the point x to the cache memory

Parameters

x (Point) – Evaluated point to be saved in the cache memory

__init__(_hash_ID: typing.List[int] = <factory>, _cache_dict: typing.Dict[typing.Any, typing.Any] = <factory>) → None

class OMADS.POLL.Dirs2n(_poll_dirs: typing.List[OMADS.POLL.Point] = <factory>, _point_index: typing.List[int] = <factory>, _n: int = 0, _defined: typing.List[bool] = <factory>, scaling: typing.List[typing.List[float]] = <factory>, _xmin: OMADS.POLL.Point = Point(_n=0, _coords=[], _defined=[False], _evaluated=False, _f=inf, _freal=inf, _c_ineq=[], _c_eq=[], _h=inf, _signature=0, _dtype=DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False), _var_type=None, _sets=None, _var_link=None), _nb_success: int = 0, _bb_eval: int = <factory>, _psize: float = <factory>, _iter: int = <factory>, hashtable: OMADS.POLL.Cache = <factory>, _check_cache: bool = True, _display: bool = True, _store_cache: bool = True, mesh: OMADS.POLL.OrthoMesh = <factory>, _opportunistic: bool = False, _eval_budget: int = 100, _dtype: OMADS.POLL.DType = DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False), bb_handle: OMADS.POLL.Evaluator = <factory>, _success: bool = False, _seed: int = 0, _terminate: bool = False, _bb_output: typing.List[float] = <factory>)

Bases: object

This is the orthognal 2n-directions class used for the poll step

Parameters

• _poll_dirs – Poll set (list of points)

• _point_index – List of point indices

• _n – Number of directions

• _defined – A boolean that indicate if the poll points are defined

scaling: List[List[float]]

hashtable: OMADS.POLL.Cache

mesh: OMADS.POLL.OrthoMesh

bb_handle: OMADS.POLL.Evaluator

property bb_output: List[float]

property dtype

property point_index

property terminate

property seed

property success

property eval_budget

property opportunistic

property save_results

property store_cache

property check_cache

property display

__init__(_poll_dirs: typing.List[OMADS.POLL.Point] = <factory>, _point_index: typing.List[int] = <factory>, _n: int = 0, _defined: typing.List[bool] = <factory>, scaling: typing.List[typing.List[float]] = <factory>, _xmin: OMADS.POLL.Point = Point(_n=0, _coords=[], _defined=[False], _evaluated=False, _f=inf, _freal=inf, _c_ineq=[], _c_eq=[], _h=inf, _signature=0, _dtype=DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False), _var_type=None, _sets=None, _var_link=None), _nb_success: int = 0, _bb_eval: int = <factory>, _psize: float = <factory>, _iter: int = <factory>, hashtable: OMADS.POLL.Cache = <factory>, _check_cache: bool = True, _display: bool = True, _store_cache: bool = True, mesh: OMADS.POLL.OrthoMesh = <factory>, _opportunistic: bool = False, _eval_budget: int = 100, _dtype: OMADS.POLL.DType = DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False), bb_handle: OMADS.POLL.Evaluator = <factory>, _success: bool = False, _seed: int = 0, _terminate: bool = False, _bb_output: typing.List[float] = <factory>) → None

property bb_eval

property psize

property iter

property poll_dirs

property dim

property defined

property xmin

property nb_success

generate_dir()

ran()

create_housholder(is_rich: bool, domain: Optional[List[int]] = None) → numpy.ndarray

Create householder matrix

Parameters

is_rich (bool) – A flag that indicates if the rich direction option is enabled

Returns

The householder matrix

Return type

np.ndarray

create_poll_set(hhm: numpy.ndarray, ub: List[float], lb: List[float], it: int, var_type: List, var_sets: Dict, var_link: List[str])

Create the poll directions

Parameters

• hhm (np.ndarray) – Householder matrix

• ub (List[float]) – Variables upper bound

• lb (List[float]) – Variables lower bound

• it (int) – iteration

scale(ub: List[float], lb: List[float], factor: float = 10.0)

eval_poll_point(index: int)

Evaluate the point i on the poll set

master_updates(x: List[OMADS.POLL.Point], peval)

class OMADS.POLL.PreMADS(data: Dict[Any, Any])

Bases: object

Preprocessor for setting up optimization settings and parameters

__init__(data: Dict[Any, Any]) → None

data: Dict[Any, Any]

initialize_from_dict()

MADS initialization

class OMADS.POLL.Output(file_path: str, vnames: typing.List[str], field_names: typing.List[str] = <factory>)

Bases: object

Results output file decorator

__init__(file_path: str, vnames: typing.List[str], field_names: typing.List[str] = <factory>) → None

file_path: str

vnames: List[str]

file_writer: Any

field_names: List[str]

add_row(iterno: int, evalno: int, poll_size: float, h: float, f: float, x: List[float])

class OMADS.POLL.PostMADS(x_incumbent: typing.List[OMADS.POLL.Point], xmin: OMADS.POLL.Point, coords: typing.List[typing.List[OMADS.POLL.Point]] = <factory>, poll_dirs: typing.List[OMADS.POLL.Point] = <factory>, iter: typing.List[int] = <factory>, bb_eval: typing.List[int] = <factory>, psize: typing.List[float] = <factory>)

Bases: object

Results postprocessor

__init__(x_incumbent: typing.List[OMADS.POLL.Point], xmin: OMADS.POLL.Point, coords: typing.List[typing.List[OMADS.POLL.Point]] = <factory>, poll_dirs: typing.List[OMADS.POLL.Point] = <factory>, iter: typing.List[int] = <factory>, bb_eval: typing.List[int] = <factory>, psize: typing.List[float] = <factory>) → None

x_incumbent: List[OMADS.POLL.Point]

xmin: OMADS.POLL.Point

coords: List[List[OMADS.POLL.Point]]

poll_dirs: List[OMADS.POLL.Point]

iter: List[int]

bb_eval: List[int]

psize: List[float]

output_results(out: OMADS.POLL.Output)

Create a results file from the saved cache

output_coordinates(out: OMADS.POLL.Output)

Save spinners in a json file

OMADS.POLL.main(*args) → Dict[str, Any]

Otho-MADS main algorithm

OMADS.POLL.rosen(x, p, *argv)

OMADS.POLL.alpine(x)

OMADS.POLL.Ackley3(x)

OMADS.POLL.eggHolder(individual)

OMADS.SEARCH module

OMADS.MADS module

Module contents

class OMADS.DType(_prec: str = 'medium', _dtype: numpy.dtype = <class 'numpy.float64'>, _itype: numpy.dtype = <class 'numpy.int64'>, _zero: float = 1e-15, _warned: bool = False)

Bases: object

A numpy data type delegator for decimal precision control

Parameters

• prec (str, optional) – Default precision option can be set to “high”, “medium” or “low” precision resolution, defaults to “medium”

• dtype (np.dtype, optional) – Numpy double data type precision, defaults to np.float64

• itype (np.dtype, optional) – Numpy integer data type precision, defaults to np.int

• zero (float, optional) – Zero value resolution, defaults to np.finfo(np.float64).resolution

property zero: float

This is the mantissa value of the machine zero

Returns

machine precision zero resolution

Return type

float

property precision

Set/get precision resolution level

Returns

float precision value

Return type

numpy float

Note

MS Windows does not support precision with the {1e-18} high resolution of the python numerical library (numpy) so high precision will be changed to medium precision which supports {1e-15} resolution check: https://numpy.org/doc/stable/user/basics.types.html

property dtype

Set/get the double formate type

Returns

float precision value

Return type

numpy float

property itype

Set/Get for the integer formate type

Returns

integer precision value

Return type

numpy float

__init__(_prec: str = 'medium', _dtype: numpy.dtype = <class 'numpy.float64'>, _itype: numpy.dtype = <class 'numpy.int64'>, _zero: float = 1e-15, _warned: bool = False) → None

class OMADS.Options(seed: int = 0, budget: int = 1000, tol: float = 1e-09, psize_init: float = 1.0, display: bool = False, opportunistic: bool = False, check_cache: bool = False, store_cache: bool = False, collect_y: bool = False, rich_direction: bool = False, precision: str = 'high', save_results: bool = False, save_coordinates: bool = False, save_all_best: bool = False, parallel_mode: bool = False, np: int = 1)

Bases: object

The running study and algorithmic options of OMADS

Parameters

• seed – Random generator seed

• budget – The evaluation budget

• tol – The threshold of the minimum poll size at which the run will be terminated

• psize_init – Initial poll size

• dispaly – Print the study progress during the run

• opportunistic – Loop on the points populated in the poll set until a better minimum found, then stop the evaluation loop

• check_cache – Check the hash table before points evaluation to avoid duplicates

• store_cache – Enable storing evaluated points into the hash table

• collect_y – Collect dependent design variables (required for DMDO)

• rich_direction – Go with the rich direction (Impact the mesh size update)

• precision – Define the precision level

• save_results – A boolean flag that indicates saving results in a csv file

• save_coordinates – A boolean flag that indicates saving coordinates of the poll set in a JSON file (required to generate animations of the spinner)

• save_all_best – A boolean used to check whether saving best points only in the MADS.out file

• parallel_mode – A boolean to check whether evaluating the poll set in parallel multiprocessing

• np – The number of CPUs

seed: int = 0

budget: int = 1000

tol: float = 1e-09

psize_init: float = 1.0

display: bool = False

opportunistic: bool = False

check_cache: bool = False

store_cache: bool = False

collect_y: bool = False

rich_direction: bool = False

precision: str = 'high'

save_results: bool = False

save_coordinates: bool = False

save_all_best: bool = False

parallel_mode: bool = False

np: int = 1

__init__(seed: int = 0, budget: int = 1000, tol: float = 1e-09, psize_init: float = 1.0, display: bool = False, opportunistic: bool = False, check_cache: bool = False, store_cache: bool = False, collect_y: bool = False, rich_direction: bool = False, precision: str = 'high', save_results: bool = False, save_coordinates: bool = False, save_all_best: bool = False, parallel_mode: bool = False, np: int = 1) → None

class OMADS.Parameters(baseline: typing.List[float] = <factory>, lb: typing.List[float] = <factory>, ub: typing.List[float] = <factory>, var_names: typing.List[str] = <factory>, scaling: float = 10.0, post_dir: str = '/Users/ahmedb/apps/code/Bay_dev/OMADS/docs-dev/.\\', var_type: typing.Optional[typing.List[str]] = None, var_sets: typing.Optional[typing.Dict] = None, constants: typing.Optional[typing.List] = None, constants_name: typing.Optional[typing.List] = None)

Bases: object

Variables and algorithmic parameters

Parameters

• baseline – Baseline design point (initial point x0)

• lb – The variables lower bound

• ub – The variables upper bound

• var_names – The variables name

• scaling – Scaling factor (can be defined as a list (assigning a factor for each variable) or a scalar value that will be applied on all variables)

• post_dir – The location and name of the post directory where the output results file will live in (if any)

baseline: List[float]

lb: List[float]

ub: List[float]

var_names: List[str]

scaling: float = 10.0

post_dir: str = '/Users/ahmedb/apps/code/Bay_dev/OMADS/docs-dev/.\\'

var_type: List[str] = None

var_sets: Dict = None

constants: List = None

constants_name: List = None

__init__(baseline: typing.List[float] = <factory>, lb: typing.List[float] = <factory>, ub: typing.List[float] = <factory>, var_names: typing.List[str] = <factory>, scaling: float = 10.0, post_dir: str = '/Users/ahmedb/apps/code/Bay_dev/OMADS/docs-dev/.\\', var_type: typing.Optional[typing.List[str]] = None, var_sets: typing.Optional[typing.Dict] = None, constants: typing.Optional[typing.List] = None, constants_name: typing.Optional[typing.List] = None) → None

class OMADS.Evaluator(blackbox: typing.Any = 'rosenbrock', commandOptions: typing.Optional[typing.Any] = None, internal: typing.Optional[str] = None, path: str = '..\\tests\\Rosen', input: str = 'input.inp', output: str = 'output.out', constants: typing.Optional[typing.List] = None, bb_eval: int = 0, _dtype: OMADS.POLL.DType = DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False), timeout: float = 1000000.0)

Bases: object

Define the evaluator attributes and settings

Parameters

• blackbox – The blackbox name (it can be a callable function or an executable file)

• commandOptions – Define options that will be added to the execution command of the executable file. Command options should be defined as a string in one line

• internal – If the blackbox callable function is part of the internal benchmarking library

• path – The path of the executable file (if any)

• input – The input file name – should include the file extension

• output – The output file name – should include the file extension

• constants – Define constant parameters list, see the documentation in Tutorials->Blackbox evaluation->User parameters

• _dtype – The precision delegator of the numpy library

• timeout – The time out of the evaluation process

blackbox: Any = 'rosenbrock'

commandOptions: Any = None

internal: Optional[str] = None

path: str = '..\\tests\\Rosen'

input: str = 'input.inp'

output: str = 'output.out'

constants: List = None

bb_eval: int = 0

timeout: float = 1000000.0

property dtype

eval(values: List[float])

Evaluate the poll point

Parameters

values (List[float]) – Poll point coordinates (design vector)

Raises

• IOError – Incorrect number of input arguments introduced to the callable function

• IOError – Incorrect number of input arguments introduced to the callable function

• IOError – The blackbox file is not an executable file (if not a callable function)

• IOError – Incorrect benchmarking keyword category

Returns

Evaluated optimization functions

Return type

List[float, List[float]]

write_input(values: List[float])

_summary_

Parameters

values (List[float]) – Write the variables in the input file

read_output() → List[float]

_summary_

Returns

Read the output values from the output file

Return type

List[float]

__init__(blackbox: typing.Any = 'rosenbrock', commandOptions: typing.Optional[typing.Any] = None, internal: typing.Optional[str] = None, path: str = '..\\tests\\Rosen', input: str = 'input.inp', output: str = 'output.out', constants: typing.Optional[typing.List] = None, bb_eval: int = 0, _dtype: OMADS.POLL.DType = DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False), timeout: float = 1000000.0) → None

class OMADS.Point(_n: int = 0, _coords: typing.List[float] = <factory>, _defined: typing.List[bool] = <factory>, _evaluated: bool = False, _f: float = inf, _freal: float = inf, _c_ineq: typing.List[float] = <factory>, _c_eq: typing.List[float] = <factory>, _h: float = inf, _signature: int = 0, _dtype: OMADS.POLL.DType = DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False), _var_type: typing.Optional[typing.List[int]] = None, _sets: typing.Optional[typing.Dict] = None, _var_link: typing.Optional[typing.List[str]] = None)

Bases: object

A class for the poll point

Parameters

• _n – # Dimension of the point

• _coords – Coordinates of the point

• _defined – Coordinates definition boolean

• _evaluated – Evaluation boolean

• _f – Objective function

• _freal – Realistic target value of the objective function

• _c_ineq – Inequality constraints

• _c_eq – Equality constraints

• _h – Aggregated constraints; active set

• _signature – hash signature; facilitate looking for duplicates and storing coordinates, hash signature, in the cache memory

• _dtype – numpy double data type precision

property var_link

property var_type: List[int]

property sets

property dtype

property evaluated

property signature

property n_dimensions

property coordinates

Get the coordinates of the point.

property defined: List[bool]

is_any_defined() → bool

Check if at least one coordinate is defined.

property f

property freal

property c_ineq

property c_eq

property h

reset(n: int = 0, d: Optional[float] = None)

Sets all coordinates to d.

__init__(_n: int = 0, _coords: typing.List[float] = <factory>, _defined: typing.List[bool] = <factory>, _evaluated: bool = False, _f: float = inf, _freal: float = inf, _c_ineq: typing.List[float] = <factory>, _c_eq: typing.List[float] = <factory>, _h: float = inf, _signature: int = 0, _dtype: OMADS.POLL.DType = DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False), _var_type: typing.Optional[typing.List[int]] = None, _sets: typing.Optional[typing.Dict] = None, _var_link: typing.Optional[typing.List[str]] = None) → None

class OMADS.OrthoMesh(_delta: float = -1.0, _Delta: float = -1.0, _rho: float = -1.0, _exp: int = 0, _mantissa: int = 1, psize_max: float = 0.0, psize_success: float = 0.0, _dtype: OMADS.POLL.DType = DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False))

Bases: object

Mesh coarsness update class

Parameters

• _delta – mesh size

• _Delta – poll size

• _rho – poll size to mesh size ratio

• _exp – manage the poll size granularity for discrete variables. See Audet et. al, The mesh adaptive direct search algorithm for granular and discrete variable

• _mantissa – Same as _exp

• psize_max – Maximum poll size

• psize_success – Poll size at successful evaluation

• _dtype – numpy double data type precision

psize_max: float = 0.0

psize_success: float = 0.0

property dtype

property msize

property psize

property rho

update()

__init__(_delta: float = -1.0, _Delta: float = -1.0, _rho: float = -1.0, _exp: int = 0, _mantissa: int = 1, psize_max: float = 0.0, psize_success: float = 0.0, _dtype: OMADS.POLL.DType = DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False)) → None

class OMADS.Cache(_hash_ID: typing.List[int] = <factory>, _cache_dict: typing.Dict[typing.Any, typing.Any] = <factory>)

Bases: object

In computing, a hash table (hash map) is a data structure that implements an associative array abstract data type, a structure that can map keys to values. A hash table uses a hash function to compute an index, also called a hash code, into an array of buckets or slots, from which the desired value can be found. During lookup, the key is hashed and the resulting hash indicates where the corresponding value is stored.

property cache_dict: Dict

A getter of the cache memory dictionary

Return type

Dict

property hash_id: List[int]

A getter to return the list of hash IDs

Return type

List[int]

property size: int

A getter of the size of the hash ID list

Return type

int

is_duplicate(x: OMADS.POLL.Point) → bool

Check if the point is in the cache memory

Parameters

x (Point) – Design point

Returns

A boolean flag indicate whether the point exist in the cache memory

Return type

bool

get_index(x: OMADS.POLL.Point) → int

Get the index of hash value, associated with the point x, if that point was saved in the cach memory

Parameters

x (Point) – Input point

Returns

The index of the point in the hash ID list

Return type

int

add_to_cache(x: OMADS.POLL.Point)

Save the point x to the cache memory

Parameters

x (Point) – Evaluated point to be saved in the cache memory

__init__(_hash_ID: typing.List[int] = <factory>, _cache_dict: typing.Dict[typing.Any, typing.Any] = <factory>) → None

class OMADS.Dirs2n(_poll_dirs: typing.List[OMADS.POLL.Point] = <factory>, _point_index: typing.List[int] = <factory>, _n: int = 0, _defined: typing.List[bool] = <factory>, scaling: typing.List[typing.List[float]] = <factory>, _xmin: OMADS.POLL.Point = Point(_n=0, _coords=[], _defined=[False], _evaluated=False, _f=inf, _freal=inf, _c_ineq=[], _c_eq=[], _h=inf, _signature=0, _dtype=DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False), _var_type=None, _sets=None, _var_link=None), _nb_success: int = 0, _bb_eval: int = <factory>, _psize: float = <factory>, _iter: int = <factory>, hashtable: OMADS.POLL.Cache = <factory>, _check_cache: bool = True, _display: bool = True, _store_cache: bool = True, mesh: OMADS.POLL.OrthoMesh = <factory>, _opportunistic: bool = False, _eval_budget: int = 100, _dtype: OMADS.POLL.DType = DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False), bb_handle: OMADS.POLL.Evaluator = <factory>, _success: bool = False, _seed: int = 0, _terminate: bool = False, _bb_output: typing.List[float] = <factory>)

Bases: object

This is the orthognal 2n-directions class used for the poll step

Parameters

• _poll_dirs – Poll set (list of points)

• _point_index – List of point indices

• _n – Number of directions

• _defined – A boolean that indicate if the poll points are defined

scaling: List[List[float]]

hashtable: OMADS.POLL.Cache

mesh: OMADS.POLL.OrthoMesh

bb_handle: OMADS.POLL.Evaluator

property bb_output: List[float]

property dtype

property point_index

property terminate

property seed

property success

property eval_budget

property opportunistic

property save_results

property store_cache

property check_cache

property display

__init__(_poll_dirs: typing.List[OMADS.POLL.Point] = <factory>, _point_index: typing.List[int] = <factory>, _n: int = 0, _defined: typing.List[bool] = <factory>, scaling: typing.List[typing.List[float]] = <factory>, _xmin: OMADS.POLL.Point = Point(_n=0, _coords=[], _defined=[False], _evaluated=False, _f=inf, _freal=inf, _c_ineq=[], _c_eq=[], _h=inf, _signature=0, _dtype=DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False), _var_type=None, _sets=None, _var_link=None), _nb_success: int = 0, _bb_eval: int = <factory>, _psize: float = <factory>, _iter: int = <factory>, hashtable: OMADS.POLL.Cache = <factory>, _check_cache: bool = True, _display: bool = True, _store_cache: bool = True, mesh: OMADS.POLL.OrthoMesh = <factory>, _opportunistic: bool = False, _eval_budget: int = 100, _dtype: OMADS.POLL.DType = DType(_prec='medium', _dtype=<class 'numpy.float64'>, _itype=<class 'numpy.int64'>, _zero=1e-15, _warned=False), bb_handle: OMADS.POLL.Evaluator = <factory>, _success: bool = False, _seed: int = 0, _terminate: bool = False, _bb_output: typing.List[float] = <factory>) → None

property bb_eval

property psize

property iter

property poll_dirs

property dim

property defined

property xmin

property nb_success

generate_dir()

ran()

create_housholder(is_rich: bool, domain: Optional[List[int]] = None) → numpy.ndarray

Create householder matrix

Parameters

is_rich (bool) – A flag that indicates if the rich direction option is enabled

Returns

The householder matrix

Return type

np.ndarray

create_poll_set(hhm: numpy.ndarray, ub: List[float], lb: List[float], it: int, var_type: List, var_sets: Dict, var_link: List[str])

Create the poll directions

Parameters

• hhm (np.ndarray) – Householder matrix

• ub (List[float]) – Variables upper bound

• lb (List[float]) – Variables lower bound

• it (int) – iteration

scale(ub: List[float], lb: List[float], factor: float = 10.0)

eval_poll_point(index: int)

Evaluate the point i on the poll set

master_updates(x: List[OMADS.POLL.Point], peval)

class OMADS.PreMADS(data: Dict[Any, Any])

Bases: object

Preprocessor for setting up optimization settings and parameters

__init__(data: Dict[Any, Any]) → None

data: Dict[Any, Any]

initialize_from_dict()

MADS initialization

class OMADS.Output(file_path: str, vnames: typing.List[str], field_names: typing.List[str] = <factory>)

Bases: object

Results output file decorator

__init__(file_path: str, vnames: typing.List[str], field_names: typing.List[str] = <factory>) → None

file_path: str

vnames: List[str]

file_writer: Any

field_names: List[str]

add_row(iterno: int, evalno: int, poll_size: float, h: float, f: float, x: List[float])

class OMADS.PostMADS(x_incumbent: typing.List[OMADS.POLL.Point], xmin: OMADS.POLL.Point, coords: typing.List[typing.List[OMADS.POLL.Point]] = <factory>, poll_dirs: typing.List[OMADS.POLL.Point] = <factory>, iter: typing.List[int] = <factory>, bb_eval: typing.List[int] = <factory>, psize: typing.List[float] = <factory>)

Bases: object

Results postprocessor

__init__(x_incumbent: typing.List[OMADS.POLL.Point], xmin: OMADS.POLL.Point, coords: typing.List[typing.List[OMADS.POLL.Point]] = <factory>, poll_dirs: typing.List[OMADS.POLL.Point] = <factory>, iter: typing.List[int] = <factory>, bb_eval: typing.List[int] = <factory>, psize: typing.List[float] = <factory>) → None

x_incumbent: List[OMADS.POLL.Point]

xmin: OMADS.POLL.Point

coords: List[List[OMADS.POLL.Point]]

poll_dirs: List[OMADS.POLL.Point]

iter: List[int]

bb_eval: List[int]

psize: List[float]

output_results(out: OMADS.POLL.Output)

Create a results file from the saved cache

output_coordinates(out: OMADS.POLL.Output)

Save spinners in a json file

OMADS.main(*args) → Dict[str, Any]

Otho-MADS main algorithm