Module documentation¶

Available classes¶

GenericDomain

represents the feasible domain of a(n abstract) generic optimisation problem.

AssignmentDomain

represents the feasible domain of an assignment problem.

CubeDomain

represents the feasible domain given by the vertices of a standard cube.

ExplicitDomain

represents the feasible domain given by an explicitly given set of feasible solutions.

Objectives

represents the objectives of a multi-criteria optimisation problem.

PolyNondom

enumerates and visualises different sets of (non-dominated) points.

class polynondom.AssignmentDomain(agents)[source]¶

Bases: polynondom.GenericDomain

Feasible domain of an assignment problem.

The assignment problem has a number of agents and a(n equal) number of tasks. Any agent can be assigned to perform any task. A feasible solution is given by an assignment of agents to tasks in such a way that each agent is one task and all tasks are assigned by exactly by one agent.

Variables:	num_agents (int) – Number of agents of corresponding assignment problem
Example:	ad = AssignmentDomain(4)

class polynondom.CubeDomain(dim)[source]¶

Bases: polynondom.GenericDomain

Feasible domain given by the vertices of an n-dimensional standard cube.

Example:	cd = CubeDomain(3)

exception polynondom.Error[source]¶

Bases: Exception

Base class for exceptions.

with_traceback()¶

Exception.with_traceback(tb) – set self.__traceback__ to tb and return self.

class polynondom.ExplicitDomain(dim, domain)[source]¶

Bases: polynondom.GenericDomain

Explicitely given feasible domain.

Variables:	domain (Iterable) – Feasible domain
Example:	ed = ExplicitDomain(3, some_iterable)

class polynondom.GenericDomain(dim)[source]¶

Bases: object

Feasible domain of a generic optimisation problem.

Variables:	dim (int) – Dimension of feasible domain

Note

Do not use this class directly.

exception polynondom.InfeasibleBoxError[source]¶

Bases: polynondom.Error

Rectangular box is infeasible.

with_traceback()¶

Exception.with_traceback(tb) – set self.__traceback__ to tb and return self.

class polynondom.Objectives[source]¶

Bases: object

Represents the objectives of a multi-criteria optimisation problem.

Variables:	objectives (list) – Objective functions

__call__(sol)[source]¶

Point in objective space corresponding to given solution.

Parameters:	sol (Iterable) – Feasible solution
Returns:	Image in objective space
Return type:	tuple

obj¶

Objective functions

Getter:	Returns objectives as list of tuples
Setter:	Appends objective (given by an Iterable) to list
Example:	mult_crit.obj = [3, 2, -1] where mult_crit = Objectives()

classmethod read(file, *, delimiter=' ')[source]¶

Read objectives given via file.

Parameters:	file (str) – File(name) containing objectives delimiter (str) – Delimiter (Defaults to ‘ ‘)
Return type:	Objectives
Raises:	FileNotFoundError – if file cannot be found PermissionError – if file cannot be opened
Example:	obj = Objectives.read(filename, delimiter=’,’) where filename corresponds to the location of the input file

class polynondom.Points(identifier, color)[source]¶

Bases: object

Represents certain set of points in objective space.

Variables:	_id (str) – Identifier for points _color (str) – Color used for visualisation of points _visualised_items (list) – Container for visualised items points (set) – Container for points

add(item)[source]¶

Add item to points.

Parameters:	item (tuple) – Point belonging to point set

add_visualised_items(items)[source]¶

Add items to container storing visualised objects.

Parameters:	items (matplotlib.collections.PathCollection) – Visualised items

remove_visualised_items()[source]¶

Remove all visualised items from matplotlib figure.

update(items)[source]¶

Add items to points.

Parameters:	items (iterable) – Points belonging to point set

class polynondom.PolyNondom[source]¶

Bases: object

Enumerates and visualises different sets of (non-dominated) points.

non-dominated point

A point y is non-dominated (in the point set P) if there is no other point z in P such that z_i <= y_i for all i with at least one strict inequality.

dominated point

A point is y is dominated if y is not non-dominated.

polynon-dominated point

A non-dominated point y is polynon-dominated (w.r.t. the underlying multi-objective problem) if the projection of the point is also non-dominated for the given multi-objective problem where one of the objectives was neglected

mononon-dominated point

A non-dominated point y is mononon-dominated if y is not polynon-dominated.

See also the mathematical definitions

Variables:

_dim (int) – Dimension of objective space _fig (Figure) – Figure object of matplotlib _ax (Axes) – Axes object of matplotlib _message (str) – Info message points (dict) – Maps indentifier to Points obj_to_polynd_points (list) – maps objective to polynon-dominated points polynd_boxes (list) – Container for feasible boxes given by polynon-dominated points _ax_limits (dict) – Maps coordinate axes to axes limits used in visualisation _ax_setter (dict) – Maps coordinate axes to matplotlib functions used for setting axes limits

clear_visualisation()[source]¶

Clear current visualisation.

classmethod compute_points(domain, objectives)[source]¶

Computes points sets based on given feasible domain and objectives.

Computes dominated, non-dominated, polynon-dominated and mononon-dominated points in objective space based on given domain and objectives.

Parameters:	domain (GenericDomain) – Feasible domain objectives (Objectives) – Objective functions
Return type:	PolyNondom
Example:	ins = PolyNondom.compute_points(feas_dom, mult_crit) where feas_dom corresponds to GenericDomain and mult_crit corresponds to Objectives

classmethod read_points(file, *, delimiter=' ', all_nondom=False)[source]¶

Read points given via file.

Reads all points given via file, computes dominated, non-dominated, polynon-dominated and mononon-dominated points and returns corresponding instance.

Parameters:	file (str) – File(name) containing points in objective space delimiter (str) – Delimiter for point coordinates (Defaults to ‘ ‘) all_nondom (bool) – Specifier for all given points are non-dominated (Defaults to False)
Return type:	PolyNondom
Raises:	FileNotFoundError – if file cannot be found PermissionError – if file cannot be opened
Example:	ins = PolyNondom.read_points(filename, delimiter=’,’) where filename corresponds to the location of the input file

visualise(id, *, my_color=None, my_width=0.8, my_style='--', my_marker='o', my_marker_size=40, with_lines=True)[source]¶

Visualises point sets corresponding to id.

Parameters:

id (str) – identifier corresponding to (combinations of) ‘d’ominated, ‘n’on-dominated, ‘p’olynon-dominated, ‘m’ononon-dominated points my_color (str) – color to use for visualisation (Defaults are dominated points - black, non-domintated points - blue, polynon-dominated points - green, mononon-dominated points - brown my_width (float) – width of lines (Default is 0.8) my_style (str) – style used for lines (Default is ‘–’) my_marker (str) – marker used for points (Default is ‘o’) my_marker_size (int) – size used for marker (Default is 40) with_lines (bool) – Specifier if lines should be visualised in the 3d case (Default is True)

Example:

ins.visualise(‘dp’, my_color=’blue’)

visualise_box(interval1, interval2, interval3=None, *, my_face_color='blue', my_alpha=0.2)[source]¶

Visualises given rectangular box.

Parameters:	interval1 (tuple) – first interval in Cartesian product corresponding to box interval2 (tuple) – second interval in Cartesian product corresponding to box interval3 (tuple) – (in 3d case) third interval in Cartesian product corresponding to box my_face_color (str) – color used to visualise faces of box (Default is blue) my_alpha (float) – alpha value used for coloring faces
Example:	ins.visualise_box((3, 4), (5, 7), (3, 5), my_face_color=’red’)

Todo

Adjust size of figure to include box in any case.

visualise_polynd_boxes()[source]¶

Visualises all feasible boxes given by polynon-dominated points.

polynondom.get_cmd_line_parser()[source]¶

Command line interface.