JijMINLPSolver

Mixed Integer Non-Linear Programming (MINLP) is a problem with a non-linear objective function and non-linear constraints containing integer variables. JijMINLPSolver can solve various problems that involve MINLP. JijMINLPSolver supports binary variables BinaryVar, integer variables IntegerVar, continuous variables ContinuousVar from jijmodeling and allows both linear and nonlinear problems.

Usage

The solution can be obtained by using sample_model of JijMINLPSolver as follows.

import jijzept as jz

solver = jz.JijMINLPSolver(config="config.toml")
response = solver.sample_model(problem, instance_data)
sampleset = response.get_sampleset()

Relax to continuous variables

The argument relaxed_variables can be used to solve problems where the specified variables are relaxed to continuous variables. For example, let consider the following problem:

import jijmodeling as jm
import jijzept as jz

x = jm.IntegerVar("x", lower_bound=-2, upper_bound=2)

problem = jm.Problem("Relax")
problem += (x-0.5)**2

problem

$\begin{array}{cccc}\text{Problem:} & \text{Relax} & & \\& & \min \quad \displaystyle \left(\left(x - 0.5\right)^{2}\right) & \\\text{{where}} & & & \\& x & 0\text{-dim integer variable}\\ & & \text{lower bound: }(-2) & \\ & & \text{upper bound: }2 & \\\end{array}$

If you solve this problem as is, the solution you get is x=0 or x=1. This is because x can only be an integer.

solver = jz.JijMINLPSolver(config="config.toml")

# if `relaxed_variables` is not specified
response = solver.sample_model(problem, {})
sampleset = response.get_sampleset()
sampleset[0].var_values

{'x': SparseVarValues(name="x", values={(): 1}, shape=()}

On the other hand, If you specify x to relaxed_variables, the solution you get is x=0.5. This is because x is treated as a continuous variable.

solver = jz.JijMINLPSolver(config="config.toml")

# if `relaxed_variables` is specified
response = solver.sample_model(problem, {}, relaxed_variables=["x"])
sampleset = response.get_sampleset()
sampleset[0].var_values

{'x': SparseVarValues(name="x", values={(): 0.49972729891145246}, shape=(), var_type=VarType.CONTINUOUS)}

JijMINLPParameters

name	type	default	description
gap_limit	Optional[float]	None	If the relative gap is less than the specified value, the solver stops.
time_limit	Optional[float]	None	The maximum time in seconds to run the solver.
solutions_limit	Optional[int]	None	When the given number of solutions has been found, the solver stops.

JijMINLPSolver.sample_model

name	type	default	description
fixed_variables	Optional[FixedVariables]	None	The dictionary of variables to be fixed.
relaxed_variables	Optional[list[str]]	None	The labels of the variables to be relaxed to continuous.
ignored_constraints	Optional[list[str]	None	The list of constraint names to be ignored.
parameters	Optional[JijSAParameters]	None	Parameters for JijMINLPSolver.
max_wait_time	Optional[Union[int, float]]	None	The number of timeout [sec] for post request. If None, 600 (one minute) will be set. Please note that this argument is for the jijzept timeout and not for configuring solver settings, such as solving time.
sync	bool	True	If True, synchronous mode is enabled.
queue_name	Optional[str]	None	Queue name.