Python API Reference Manual

Octeract Engine v1.06.10
Copyright (c) Octeract Ltd, 2017-2020
June 12, 2020

Table Of Contents

1. Overview

The Octeract Python API is a package that allows the Octeract Engine library functions to be accessed from within the Python programming language. When first familiarising yourself with the API, we recommend using the library interactively with a command shell like IPython3, as the tab completion functionality provided is extremely useful when browsing through the available API calls. The API can also be utilised for writing either small stand-alone scripts or Python libraries within larger scale applications.

This manual assumes that you are familiar with the Python programming language, and that you have the appropriate version of the Python distribution installed on your system.
The API itself explicitly requires Python 3.7.

The standard workflow for solving a global optimization problem using the API involves working with the Octeract Model object. An optimization problem can be built by using Model functions to add/remove variables, set the objective, and add/remove constraints. Once the Model has been built, the global_solve() function can be invoked, which sends the problem to the Octeract engine. As soon as the problem is solved to global optimality, a solution file is written, automatically read by the API and stored as an object in memory. The properties of the solution object (e.g. the optimal objective value and values of the decision variables) can then be accessed by the user and manipulated or fed in as data as part of a larger program.

2. A Simple Example

In this section, we will go through building a simple optimization problem based on the Haverly Pooling problem (a quadratically constrained problem). The current version of the API primarily uses a string-based interface, meaning the majority of the set() and add() methods will take strings as arguments. Future versions will have operator overloaded expression type objects that the user can manipulate directly without having to use quotation marks.

\begin{equation}
\label{MINLP}
\begin{aligned}
\text{minimise} &&&\ x_1 + x_2 \\
\text{subject to} &&&\ x_1 – 6x_3 -16x_4 – 10x_5 = 0 \\
&&&\ x_2 −9x_6 −15x_7 = 0 \\
&&&\ x_6 −x_8 −x_1 0 = 0 \\
&&&\ x_7 −x_9 −x_1 1 = 0 \\
&&&\ x_3 +x_4 −x_1 0−x_1 1 = 0 \\
&&&\ x_5 −x_8 −x_9 = 0 \\
&&&\ x_{12}(x_{10} +x_{11})−3x_2 −x_4 = 0 \\
&&&\ x_{12}x_{10} −2.5x_{10} −0.5x_8 \leq 0 \\
&&&\ x_{12}x_{11} −1.5x_{11} +0.5x_9 \leq 0
\end{aligned} \end{equation}

from octeract import *

# Instantiate model
m = Model()

# Set the objective and add the constraints
m.set_objective("x1-x2")
m.add_constraint("x1 - 6*x3 - 16*x4 - 10*x5 = 0")
m.add_constraint("x2 - 9*x6 - 15*x7 = 0")
m.add_constraint("x6 - x8 - x10 = 0")
m.add_constraint("x7 - x9 - x11 = 0")
m.add_constraint("x3 + x4 - x10 - x11 = 0")
m.add_constraint("x5 - x8 - x9 = 0")
m.add_constraint("x12*(x10 + x11) - 3*x3 - x4 = 0")
m.add_constraint("x12*x10 - 2.5*x10 - 0.5*x8 <= 0")
m.add_constraint("x12*x11 - 1.5*x11 + 0.5*x9 <= 0")

# Set the variable bounds
m.set_variable_lb("x1", 0)
m.set_variable_lb("x2", 0)
m.set_variable_lb("x3", 0)
m.set_variable_lb("x4", 0)
m.set_variable_lb("x5", 0)
m.set_variable_bounds("x6", 0, 100)
m.set_variable_bounds("x7", 0, 200)
m.set_variable_lb("x8", 0)
m.set_variable_lb("x9", 0)
m.set_variable_lb("x10", 0)
m.set_variable_lb("x11", 0)
m.set_variable_lb("x12", 0)

# Solve to model to global optimality using 4 cores
m.global_solve(4)

The solver will produce it’s own real-time output so you will know when the solving process is done and the global solution is found which in this case is −400. The majority of the available methods have intuitive names, and you can use the tab completion functionality of your IDE or command shell, to see a list of the available methods. Since Python is a very flexible language, users will easily be able to integrate their code as part of a larger overall project.

3. API Reference

This section provides a comprehensive list of all the API methods. Each subsection contains a brief description of the method, the arguments the function takes as input, the Return type, and example usages.

3.1 Model

3.1.1 Model

Model()

Description:
Instantiates an empty model.
Arguments:
None
Return type:
None
Example usage:
m = Model()

3.1.2 Model.add constraint()

Model.add_constraint()

add_constraint(constraint_string)
Description:
Adds a constraint to the model.
Arguments:
constraint string: the function string of the constraint to be added
Return type:
None
Example usage:
model.add_constraint("x1 + sin(x2*x3) = 2")

3.1.3 Model.add variable() .

Model.add_variable()

add_variable(variable_name, lb=-OCT INFTY, ub=OCT INFTY, variable_type=CONT)
Description:
Adds a variable to the model
Arguments:
variable_name: the name of the variable to be added
lb: the lower bound of the variable
ub: the upper bound of the variable
variable_type: the variable type (CONT or BIN)
Return type:
None
Example usage:
model.add_variable("x1")
model.add_variable("x1", -1)
model.add_variable("x1", -10, 10)
model.add_variable("x1", 0, 1, BIN)

3.1.4 Model.classify problem()

Model.classify problem()

classify_problem()
Description:
Detects the problem structure (MINLP, NLP, MIQCQP, QCQP, MIQP, QP, MILP, LP) of the current model.
Arguments:
None
Return type:
String
Example usage:
model.classify_problem()

3.1.5 Model.clear()

Model.clear()

clear()
Description:
Clears the model - removes the objective, all variables, all constraints and any settings the user might have
specified.
Arguments:
None
Return type:
None
Example usage:
model.clear()

3.1.6 Model.detect bounds()

Model.detect_bounds()

detect_bounds()
Description:
Tries to detect valid variable bounds based on the constraints present in the model.
Arguments:
None
Return type:
None
Example usage:
model.detect_bounds()

3.1.7 Model.detect problem convexity()

Model.detect problem_convexity()

detect problem_convexity()
Description:
Tries to determine whether the current model is convex using various techniques. If the problem is proven to
be convex, the function returns True, otherwise it returns False.
Arguments:
None
Return type:
Boolean
Example usage:
model.detect problem_convexity()

3.1.8 Model.get binary constraint names()

Model.get_binary_constraint_names()

get_binary_constraint_names()
Description:
Returns a list of constraint names which only contain binary variables.
Arguments:
None
Return type:
A list of constraint names
Example usage:
model.get_binary_constraint_names()

3.1.9 Model.get binary variable names()

Model.get_binary_variable_names()

get_binary_variable_names()
Description:
Returns the binary variables of the model.
Arguments:
None
Return type:
A list of variable names
Example usage:
model.get_binary_variable_names()

3.1.10 Model.get bound multipliers()

Model.get_bound_multipliers()

get_bound_multipliers()
Description:
Returns a map of the decision variable names to their bound multipliers at the optimal solution.
Arguments:
None
Return type:
Dictionary from String to Double
Example usage:
model.get_bound_multipliers()

3.1.11 Model.get constraint lb()

Model.get_constraint_lb()

get_constraint_lb(constraint name)
Description:
Returns the lower bound of a constraint.
Arguments:
constraint name: the name of the constraint
Return type:
Double
Example usage:
model.get_constraint_lb("c1")

3.1.12 Model.get constraint lhs()

Model.get_constraint_lhs()

get_constraint_lhs(constraint name)
Description:
Returns the function string (left hand side) of a constraint.
Arguments:
constraint name: the name of the constraint
Return type:
String
Example usage:
model.get_constraint_lhs("c1")

3.1.13 Model.get constraint multipliers()

Model.get_constraint_multipliers()

get_constraint_multipliers()
Description:
Returns a map of the constraint names to their Lagrange multipliers at the optimal solution.
Arguments:
None
Return type:
Dictionary from String to Double
Example usage:
model.get_constraint_multipliers()

3.1.14 Model.get constraint names()

Model.get_constraint_names()

get_constraint_names()
Description:
Returns all the constraints of the model.
Arguments:
None
Return type:
A list of constraint names
Example usage:
model.get_constraint_names()

3.1.15 Model.get constraint ub()

Model.get_constraint_ub()

get_constraint_ub(constraint name)
Description:
Returns the upper bound of a constraint.
Arguments:
constraint name: the name of the constraint
Return type:
Double
Example usage:
model.get_constraint_ub("c1")

3.1.16 Model.get constraint variables()

Model.get_constraint_variables()

get_constraint_variables(constraint name)
Description:
Returns all the variables of a constraint.
Arguments:
constraint name: the name of the constraint
Return type:
A list of variable names
Example usage:
model.get_constraint_variables("c1")

3.1.17 Model.get continuous variable names()

Model.get_continuous_variable_names()

get_continuous_variable_names()
Description:
Returns the continuous variables of the model.
Arguments:
None
Return type:
A list of variable names
Example usage:
model.get_continuous_variable_names()

3.1.18 Model.get linear constraint names()

Model.get_linear_constraint_names()

get_linear_constraint_names()
Description:
Returns the linear constraints of the model.
Arguments:
None
Return type:
A list of constraint names
Example usage:
model.get_linear_constraint_names()

3.1.19 Model.get linear equality constraint names()

Model.get_linear_equality_constraint_names()

get_linear_equality_constraint_names()
Description:
Returns the linear equality constraints of the model.
Arguments:
None
Return type:
A list of constraint names
Example usage:
model.get_linear_equality_constraint_names()

3.1.20 Model.get linear variable names()

Model.get_linear_variable_names()

get_linear_variable_names()
Description:
Returns the linear variables of the model.
Arguments:
None
Return type:
A list of variable names
Example usage:
model.get_linear_variable_names()

3.1.21 Model.get nonlinear constraint names()

Model.get_nonlinear_constraint_names()

get_nonlinear_constraint_names()
Description:
Returns the nonlinear constraints of the model.
Arguments:
None
Return type:
A list of constraint names
Example usage:
model.get_nonlinear_constraint_names()

3.1.22 Model.get nonlinear equality constraint names()

Model.get_nonlinear_equality_constraint_names()

get_nonlinear_equality_constraint_names()
Description:
Returns the nonlinear equality constraints of the model.
Arguments:
None
Return type:
A list of constraint names
Example usage:
model.get_nonlinear_equality_constraint_names()

3.1.23 Model.get nonlinear variable names()

Model.get_nonlinear_variable_names()

get_nonlinear_variable_names()
Description:
Returns the nonlinear variables of the model.
Arguments:
None
Return type:
A list of variable names
Example usage:
model.get_continuous_nonlinear_names()

3.1.24 Model.get objective function string()

Model.get_objective_function_string()

get_objective_function_string()
Description:
Returns the function string of objective.
Arguments:
None
Return type:
String
Example usage:
model.get_objective_function_string()

3.1.25 Model.get problem type()

Model.get_problem_type()

get_problem_type()
Description:
Returns the problem structure (MINLP, NLP, MIQCQP, QCQP, MIQP, QP, MILP, LP).
Arguments:
None
Return type:
String
Example usage:
model.get_problem_type()

3.1.26 Model.get solution objective value()

Model.get_solution_objective_value()

get_solution_objective_value()
Description:
Returns the value of the Objective at the optimal solution.
Arguments:
None
Return type:
Double
Example usage:
model.get_solution_objective_value()

3.1.27 Model.get solution path()

Model.get_solution_path()

get_solution_path()
Description:
Returns the path where the solution file will be written to.
Arguments:
None
Return type:
String
Example usage:
model.get_solution_path()

3.1.28 Model.get solution vector()

Model.get_solution_vector()

get_solution_vector()
Description:
Returns a map of the decision variable names to their optimal solution values.
Arguments:
None
Return type:
Dictionary from String to Double
Example usage:
model.get_solution_vector()

3.1.29 Model.get variable lb()

Model.get_variable_lb()

get_variable_lb(variable name)
Description: Returns the lower bound of a variable.
Arguments:
variable name: the name of the variable
Return type:
Double
Example usage:
model.get_variable_lb("x1")

3.1.30 Model.get variable names()

Model.get_variable_names()

get_variable_names()
Description:
Returns all the variables of the model.
Arguments:
None
Return type:
A list of variable names
Example usage:
model.get_variable_names()

3.1.31 Model.get variable ub()

Model.get_variable_ub()

get_variable_ub(variable name)
Description:
Returns the upper bound of a variable.
Arguments:
variable name: the name of the variable
Return type:
Double
Example usage:
model.get_variable_ub("x1")

3.1.32 Model.global solve()

Model.global_solve()

global_solve()
Description:
Solves the model to global optimality.
Arguments:
None
Return type:
None
Example usage:
model.global_solve()

3.1.33 Model.import model file()

Model.import_model_file()

import_model_file(problem file_path)
Description:
Imports a model file, which can be either in ASL format (.nl extension) or AMPL format (.mod extension).
Arguments:
problem file_path: the path to the problem file
Return type:
None
Example usage:
model.import_model_file("myProblem.nl")

3.1.34 Model.import solution file()

Model.import_solution_file()

import_solution_file(solution_file_path)
Description:
Imports an Octeract solution file (.octsol extension) and stores the solution data in memory.
Arguments:
problem_file_path: the path to the problem file
Return type:
None
Example usage:
model.import_solution_file("myProblem.octsol")

3.1.35 Model.is problem convex()

Model.is_problem_convex()

is_problem_convex()
Description:
Returns whether the current model has been detected to be convex.
Arguments:
None
Return type:
Boolean
Example usage:
model.is_problem_convex()

3.1.36 Model.local solve()

Model.local_solve()

local_solve()
Description:
Solves the model to local optimality.
Arguments:
None
Return type:
None
Example usage:
model.local_solve()

3.1.37 Model.num binary constraints()

Model.num_binary_constraints()

num_binary_constraints()
Description:
Returns the number of constraints which only contain binary variables.
Arguments:
None
Return type:
Integer
Example usage:
model.num_binary_constraints()

3.1.38 Model.num binary variables()

Model.num_binary_variables()

num_binary_variables()
Description:
Returns the number of binary variables present in the model.
Arguments:
None
Return type:
Integer
Example usage:
model.num_binary_variables()

3.1.39 Model.num constraints()

Model.num_constraints()

num_constraints()
Description:
Returns the total number of constraints present in the model.
Arguments:
None
Return type:
Integer
Example usage:
model.num_constraints()

3.1.40 Model.num continuous variables()

Model.num_continuous_variables()

num_continuous_variables()
Description:
Returns the number of continuous variables present in the model.
Arguments:
None
Return type:
Integer
Example usage:
model.num_continuous_variables()

3.1.41 Model.num linear constraints()

Model.num_linear_constraints()

num_linear_constraints()
Description:
Returns the number of linear constraints present in the model.
Arguments:
None
Return type:
Integer
Example usage:
model.num_linear_constraints()

3.1.42 Model.num nonlinear constraints()

Model.num_nonlinear_constraints()

num_nonlinear_constraints()
Description:
Returns the number of nonlinear constraints present in the model.
Arguments:
None
Return type:
Integer
Example usage:
model.num_nonlinear_constraints()

3.1.43 Model.num nonlinear equality constraints()

Model.num_nonlinear_equality_constraints()

num_nonlinear_equality_constraints()
Description:
Returns the number of nonlinear equality constraints present in the model.
Arguments:
None
Return type:
Integer
Example usage:
model.num_nonlinear_equality_constraints()

3.1.44 Model.num nonlinear variables()

Model.num_nonlinear_variables()

num_nonlinear_variables()
Description:
Returns the number of nonlinear variables present in the model.
Arguments:
None
Return type:
Integer
Example usage:
model.num_nonlinear_variables()

3.1.45 Model.num variables()

Model.num_variables()

num_variables()
Description:
Returns the total number of variables present in the model.
Arguments:
None
Return type:
Integer
Example usage:
model.num_variables()

3.1.46 Model.print problem summary()

Model.print_problem_summary()

print_problem_summary()
Description:
Prints a summary of the loaded or constructed optimization problem onto the console.
Arguments:
None
Return type:
None
Example usage:
model.print_problem_summary()

3.1.47 Model.print solution summary()

Model.print_solution_summary()

print_solution_summary()
Description:
Prints a summary of the solution obtained from a local solve or global solve call.
Arguments:
None
Return type:
None
Example usage:
model.print_solution_summary()

3.1.48 Model.read options file()

Model.read_options_file()

read_options_file(options_file_path)
Description:
Loads an options file, which will be read by the solver.
Arguments:
options file path: the path to the options file
Return type:
None
Example usage:
model.read_options_file("octeract.opt")

3.1.49 Model.remove all constraints()

Model.remove_all_constraints()

remove_all_constraints()
Description:
Removes all constraints from the model.
Arguments:
None
Return type:
None
Example usage:
model.remove_all_constraints()

3.1.50 Model.remove all variables()

Model.remove_all_variables()

remove_all_variables()
Description:
Removes all variables from the model. This effectively clears the model, as no objective or constraints can
exist in the model without the presence of variables.
Arguments:
None
Return type:
None
Example usage:
model.remove_all_variables()

3.1.51 Model.remove constraint()

Model.remove_constraint()

remove_constraint(constraint_name)
Description:
Removes a constraint of the model.
Arguments:
constraint name: the name of the constraint to be removed
Return type:
None
Example usage:
model.remove_constraint("c1")

3.1.52 Model.remove objective()

Model.remove_objective()

remove_objective()
Description:
Removes the objective of the model
Arguments:
None
Return type:
None
Example usage:
model.remove_objective()

3.1.53 Model.remove variable()

Model.remove_variable()

remove_variable(variable_name)
Description:
Removes a variable of the model.
Arguments:
variable_name: the name of the variable to be removed
Return type:
None
Example usage:
model.remove_variable("x1")

3.1.54 Model.set objective()

Model.set_objective()

set_objective(objective string, sense=MINIMIZE)
Description:
Sets the objective of the model
Arguments:
objective string: the function string of the objective
sense: the objective sense (MINIMIZE or MAXIMIZE)
Return type:
None
Example usage:
model.set objective("x1log(x1) + x1x2")
model.set objective("x1*x2 + log(x3)", MAXIMIZE)

3.1.55 Model.set solver timeout()

Model.set_solver_timeout()

set_solver_timeout(timeout)
Description:
Sets a timeout for the solver.
Arguments:
timeout: the timeout in seconds
Return type:
None
Example usage:
model.set_solver_timeout(10)

3.1.56 Model.set variable bounds()

Model.set_variable_bounds()

set_variable_bounds(variable name, lb, ub)
Description:
Sets the bounds of a variable.
Arguments:
variable_name: the name of the variable
lb: the lower bound of the variable
ub: the upper bound of the variable
Return type:
None
Example usage:
model.set_variable_bounds("x1", -10, 10)

3.1.57 Model.set variable lb()

Model.set_variable_lb()

set_variable_lb(variable_name, lb)
Description:
Sets the lower bound of a variable.
Arguments:
variable_name: the name of the variable
lb: the lower bound of the variable
Return type:
None
Example usage:
model.set_variable_lb("x1", 2)

3.1.58 Model.set variable type()

Model.set_variable_type()

set_variable_type(variable_name, type)
Description:
Sets the type of a variable.
Arguments:
variable_name: the name of the variable
type: the type of the variable
Return type:
None
Example usage:
model.set_variable type("x1", CONT)
model.set_variable type("x1", BIN)

3.1.59 Model.set variable ub()

Model.set_variable_ub()

set_variable_ub(variable_name, ub)
Description:
Sets the upper bound of a variable.
Arguments:
variable_name: the name of the variable
ub: the upper bound of the variable
Return type:
None
Example usage:
model.set_variable ub("x1", 100)

3.1.60 Model.write current solution to file()

Model.write_current_solution_to_file()

write_current_solution_to_file(file_path)
Description:
Writes the current solution (if any) to a file (Octeract solution format with a .octsol extension).
Arguments:
file_path: the path of the solution file
Return type:
None
Example usage:
model.write_current_solution_to_file("myProblem.octsol")

3.1.61 Model.write problem to mod file()

Model.write_problem_to_mod_file()

write_problem_to_mod_file(file_path)
Description:
Writes the current model to an AMPL (extension .mod) file.
Arguments:
file path: the path of the .mod file
Return type:
None
Example usage:
model.write_problem_to_mod_file("myProblem.mod")

3.1.62 Model.write problem to NL file()

Model.write_problem_to_NL_file()

write_problem_to_NL_file(file_path)
Description:
Writes the current model to an ASL (extension .nl) file.
Arguments:
file path: the path of the .nl file
Return type:
None
Example usage:
model.write_problem_to_NL_file("myProblem.nl")

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