Toshiba

SQBM+ is an optimization solution derived from the Simulated Bifurcation Machine, a combinatorial optimization solver built on the Simulated Bifurcation Algorithm developed by Toshiba Corporation.

Solvers

Model	Solvers
Quadratic Unconstrained Binary Optimization (QUBO)	toshiba.qubo
Polynomial Unconstrained Binary Optimization (PUBO)	toshiba.pubo
Quadratic Programming Problems	toshiba.qplib
Matrix Market	toshiba.qplib
QPLIB	toshiba.qplib

Quadratic Unconstrained Binary Optimization (QUBO)

import strangeworks as sw
from strangeworks_optimization import StrangeworksOptimizer
from strangeworks_optimization_models.parameter_models import ToshibaParameterModel
from dimod import BinaryQuadraticModel

sw.authenticate(api_key)

linear = {1: -2, 2: -2, 3: -3, 4: -3, 5: -2}
quadratic = {(1, 2): 2, (1, 3): 2, (2, 4): 2, (3, 4): 2, (3, 5): 2, (4, 5): 2}
model = BinaryQuadraticModel(linear, quadratic, "BINARY")

options = ToshibaParameterModel(algo=0, maxout=100, loops=10)

solver = "toshiba.qubo"

so = StrangeworksOptimizer(
    model=model, 
    solver=solver, 
    options=options)
sw_job = so.run()

print(f"Job slug: {sw_job.slug}")
print(f"Job status: {so.status(sw_job.slug)}")

results = so.results(sw_job.slug)

Polynomial Unconstrained Binary Optimization (PUBO)

QPLIB files can also be used to encode PUBO problems. PUBO stands for Polynomial Unconstrained Binary Optimization.

import strangeworks as sw
from strangeworks_optimization import StrangeworksOptimizer
from strangeworks_optimization_models.parameter_models import ToshibaParameterModel
from strangeworks_optimization_models.problem_models import QplibFile

sw.authenticate(api_key)

options = ToshibaParameterModel(algo=0, maxout=100, loops=10)

solver = "toshiba.pubo"

model = QplibFile.read_file("path/to/qplib/file.qplib")

so = StrangeworksOptimizer(
    model=model, 
    solver=solver, 
    options=options)

sw_job = so.run()

print(f"Job slug: {sw_job.slug}")
print(f"Job status: {so.status(sw_job.slug)}")

results = so.results(sw_job.slug)

Matrix Market

Matrix Market is a NIST-sponsored repository of test matrices for use in numerical algorithms.

You can download Matrix Market files from the Matrix Market website.

import strangeworks as sw
from strangeworks_optimization import StrangeworksOptimizer
from strangeworks_optimization_models.parameter_models import ToshibaParameterModel
from strangeworks_optimization_models.problem_models import MatrixMarket

sw.authenticate(api_key)

options = ToshibaParameterModel(algo=0, maxout=100, loops=10)

solver = "toshiba.qubo"

model = MatrixMarket.read_file("path/to/matrixmarket/file.txt")

so = StrangeworksOptimizer(
    model=model, 
    solver=solver, 
    options=options)

sw_job = so.run()

print(f"Job slug: {sw_job.slug}")
print(f"Job status: {so.status(sw_job.slug)}")

results = so.results(sw_job.slug)

Parameters

from strangeworks_optimization_models.parameter_models import ToshibaParameterModel

options = ToshibaParameterModel(.....)

The ToshibaParameterModel is designed to configure the parameters for the SQBM+. For detailed information on each parameter and how to set them up for your specific optimization problems, please refer to the official User Manual for SQBM+ AWS AMI v2.0.1.

Parameter	Type	Description
steps	int	Specifies the number of steps in a computation request.
loops	int	Specifies the number of loops in SQBM+ computation.
timeout	int	Specifies the maximum computation time (timeout) in seconds.
target	float	Specifies the end condition of a computation request.
maxout	int	Specifies the upper limit of the number of solutions to be outputted.
maxwait	int	Specifies the upper limit of the number of solutions to be outputted.
algo	int	Specifies the algorithm to be used.
dt	float	Specifies the time per step.
C	float	Corresponds to the constant ξ0, appearing in the paper by Goto, Tatsumura, & Dixon (2019, p. 2), which is the theoretical basis of SQBM+.
blocks	int	Specify the number of blocks of GPUs used to find a solution. If 0 (zero) is specified, the value of 'blocks' will be auto-adjusted. Specify an integer between 0 and 40.
multishot	int	When you specify multishot, SQBM+ will get multiple solutions, which start from different initial decision variable values but other parameters are the same. The number of solution is multishot number. Default value is 0, which automatically decide multishot from problem size. If multishot > 1, SQBM+ will have less overhead. Specify an integer between 0 and 10.

QPLIB

QPLIB is a collection of test problems for quadratic programming (QP) and quadratic unconstrained binary optimization (QUBO).

QPLIB 🔗.

import strangeworks as sw
from strangeworks_optimization import StrangeworksOptimizer
from strangeworks_optimization_models.parameter_models import ToshibaParameterModel
from strangeworks_optimization_models.problem_models import QplibFile

sw.authenticate(api_key)

options = ToshibaParameterModel(algo=0, maxout=100, loops=10)

solver = "toshiba.qplib"

model = QplibFile.read_file("path/to/qplib/file.qplib")

so = StrangeworksOptimizer(
    model=model, 
    solver=solver, 
    options=options)

sw_job = so.run()

print(f"Job slug: {sw_job.slug}")
print(f"Job status: {so.status(sw_job.slug)}")

results = so.results(sw_job.slug)

Parameters

from strangeworks_optimization_models.parameter_models import ToshibaParameterModel

options = ToshibaParameterModel(.....)

Parameter	Type	Description
PD3Orate	int	Parameter that determines the number of PD3O algorithm execution steps. SQBM+ searches for solutions using the SB algorithm, but if PD3Orate is set to anything other than 0, it also searches for solutions using another algorithm (called the PD3O algorithm). For the steps of the SB algorithm, the PD3O algorithm performs PD3Orate*steps times to update decision variables.
phi	float	Parameters that determine the behavior of the PD3O algorithm. Specify a real number between 0 and 1. If it is close to 0, it behaves like the SB algorithm. If it is close to 1, it narrows the search range of solutions, but it may find a better solution than the SB algorithm.