CPLEX.jl: Julia interface for The CPLEX Optimization Software

CPLEX.jl underwent a major rewrite between versions 0.6.6 and 0.7.0. Users of JuMP should see no breaking changes, but if you used the lower-level C API (e.g., for callbacks), you will need to update your code accordingly. For a full description of the changes, read this discourse post.

To revert to the old API, use:

import Pkg
Pkg.add(Pkg.PackageSpec(name = "CPLEX", version = v"0.6"))

Then restart Julia for the change to take effect.

CPLEX.jl

CPLEX.jl is a wrapper for the IBM® ILOG® CPLEX® Optimization Studio

You cannot use CPLEX.jl without having purchased and installed a copy of CPLEX Optimization Studio from IBM. However, CPLEX is available for free to academics and students.

CPLEX.jl has two components:

• a thin wrapper around the complete C API
• an interface to MathOptInterface

The C API can be accessed via CPLEX.CPXxx functions, where the names and arguments are identical to the C API. See the CPLEX documentation for details.

Note: This wrapper is maintained by the JuMP community and is not officially supported by IBM. However, we thank IBM for providing us with a CPLEX license to test CPLEX.jl on GitHub. If you are a commercial customer interested in official support for CPLEX in Julia, let them know!.

Installation

Minimum version requirement: CPLEX.jl requires CPLEX version 12.10 or 20.1.

First, obtain a license of CPLEX and install CPLEX solver, following the instructions on IBM's website. Then, set the CPLEX_STUDIO_BINARIES environment variable as appropriate and run Pkg.add("CPLEX"), then Pkg.build("CPLEX"). For example:

# On Windows, this might be
ENV["CPLEX_STUDIO_BINARIES"] = "C:\\Program Files\\CPLEX_Studio1210\\cplex\\bin\\x86-64_win\\"
import Pkg
Pkg.add("CPLEX")
Pkg.build("CPLEX")

# On OSX, this might be
ENV["CPLEX_STUDIO_BINARIES"] = "/Applications/CPLEX_Studio1210/cplex/bin/x86-64_osx/"
import Pkg
Pkg.add("CPLEX")
Pkg.build("CPLEX")

# On Unix, this might be
ENV["CPLEX_STUDIO_BINARIES"] = "/opt/CPLEX_Studio1210/cplex/bin/x86-64_linux/"
import Pkg
Pkg.add("CPLEX")
Pkg.build("CPLEX")

Note: your path may differ. Check which folder you installed CPLEX in, and update the path accordingly.

Use with JuMP

We highly recommend that you use the CPLEX.jl package with higher level packages such as JuMP.jl.

This can be done using the CPLEX.Optimizer object. Here is how to create a JuMP model that uses CPLEX as the solver.

using JuMP, CPLEX

model = Model(CPLEX.Optimizer)
set_optimizer_attribute(model, "CPX_PARAM_EPINT", 1e-8)

Parameters match those of the C API in the CPLEX documentation.

Callbacks

Here is an example using CPLEX's solver-specific callbacks.

using JuMP, CPLEX, Test

model = direct_model(CPLEX.Optimizer())
set_silent(model)

# This is very, very important!!! Only use callbacks in single-threaded mode.
MOI.set(model, MOI.NumberOfThreads(), 1)

@variable(model, 0 <= x <= 2.5, Int)
@variable(model, 0 <= y <= 2.5, Int)
@objective(model, Max, y)
cb_calls = Clong[]
function my_callback_function(cb_data::CPLEX.CallbackContext, context_id::Clong)
    # You can reference variables outside the function as normal
    push!(cb_calls, context_id)
    # You can select where the callback is run
    if context_id != CPX_CALLBACKCONTEXT_CANDIDATE
        return
    end
    ispoint_p = Ref{Cint}()
    ret = CPXcallbackcandidateispoint(cb_data, ispoint_p)
    if ret != 0 || ispoint_p[] == 0
        return  # No candidate point available or error
    end
    # You can query CALLBACKINFO items
    valueP = Ref{Cdouble}()
    ret = CPXcallbackgetinfodbl(cb_data, CPXCALLBACKINFO_BEST_BND, valueP)
    @info "Best bound is currently: $(valueP[])"
    # As well as any other C API
    x_p = Vector{Cdouble}(undef, 2)
    obj_p = Ref{Cdouble}()
    ret = CPXcallbackgetincumbent(cb_data, x_p, 0, 1, obj_p)
    if ret == 0
        @info "Objective incumbent is: $(obj_p[])"
        @info "Incumbent solution is: $(x_p)"
        # Use CPLEX.column to map between variable references and the 1-based
        # column.
        x_col = CPLEX.column(cb_data, index(x))
        @info "x = $(x_p[x_col])"
    else
        # Unable to query incumbent.
    end

    # Before querying `callback_value`, you must call:
    CPLEX.load_callback_variable_primal(cb_data, context_id)
    x_val = callback_value(cb_data, x)
    y_val = callback_value(cb_data, y)
    # You can submit solver-independent MathOptInterface attributes such as
    # lazy constraints, user-cuts, and heuristic solutions.
    if y_val - x_val > 1 + 1e-6
        con = @build_constraint(y - x <= 1)
        MOI.submit(model, MOI.LazyConstraint(cb_data), con)
    elseif y_val + x_val > 3 + 1e-6
        con = @build_constraint(y + x <= 3)
        MOI.submit(model, MOI.LazyConstraint(cb_data), con)
    end
end
MOI.set(model, CPLEX.CallbackFunction(), my_callback_function)
optimize!(model)
@test termination_status(model) == MOI.OPTIMAL
@test primal_status(model) == MOI.FEASIBLE_POINT
@test value(x) == 1
@test value(y) == 2

Annotations for automatic Benders' decomposition

Here is an example of using CPLEX's annotation feature for automatic Benders' decomposition:

using JuMP, CPLEX

function add_annotation(
    model::JuMP.Model,
    variable_classification::Dict;
    all_variables::Bool = true,
)
    num_variables = sum(length(it) for it in values(variable_classification))
    if all_variables
        @assert num_variables == JuMP.num_variables(model)
    end
    indices, annotations = CPXINT[], CPXLONG[]
    for (key, value) in variable_classification
        for variable_ref in value
            push!(indices, variable_ref.index.value - 1)
            push!(annotations, CPX_BENDERS_MASTERVALUE + key)
        end
    end
    cplex = backend(model)
    index_p = Ref{CPXINT}()
    CPXnewlongannotation(
        cplex.env,
        cplex.lp,
        CPX_BENDERS_ANNOTATION,
        CPX_BENDERS_MASTERVALUE,
    )
    CPXgetlongannotationindex(
        cplex.env,
        cplex.lp,
        CPX_BENDERS_ANNOTATION,
        index_p,
    )
    CPXsetlongannotations(
        cplex.env,
        cplex.lp,
        index_p[],
        CPX_ANNOTATIONOBJ_COL,
        length(indices),
        indices,
        annotations,
    )
    return
end

# Problem

function illustrate_full_annotation()
    c_1, c_2 = [1, 4], [2, 3]
    dim_x, dim_y = length(c_1), length(c_2)
    b = [-2; -3]
    A_1, A_2 = [1 -3; -1 -3], [1 -2; -1 -1]
    model = JuMP.direct_model(CPLEX.Optimizer())
    set_optimizer_attribute(model, "CPXPARAM_Benders_Strategy", 1)
    @variable(model, x[1:dim_x] >= 0, Bin)
    @variable(model, y[1:dim_y] >= 0)
    variable_classification = Dict(0 => [x[1], x[2]], 1 => [y[1], y[2]])
    @constraint(model, A_2 * y + A_1 * x .<= b)
    @objective(model, Min, c_1' * x + c_2' * y)
    add_annotation(model, variable_classification)
    optimize!(model)
    x_optimal = value.(x)
    y_optimal = value.(y)
    println("x: $(x_optimal), y: $(y_optimal)")
end

function illustrate_partial_annotation()
    c_1, c_2 = [1, 4], [2, 3]
    dim_x, dim_y = length(c_1), length(c_2)
    b = [-2; -3]
    A_1, A_2 = [1 -3; -1 -3], [1 -2; -1 -1]
    model = JuMP.direct_model(CPLEX.Optimizer())
    # Note that the "CPXPARAM_Benders_Strategy" has to be set to 2 if partial
    # annotation is provided. If "CPXPARAM_Benders_Strategy" is set to 1, then
    # the following error will be thrown:
    # `CPLEX Error  2002: Invalid Benders decomposition.`
    set_optimizer_attribute(model, "CPXPARAM_Benders_Strategy", 2)
    @variable(model, x[1:dim_x] >= 0, Bin)
    @variable(model, y[1:dim_y] >= 0)
    variable_classification = Dict(0 => [x[1]], 1 => [y[1], y[2]])
    @constraint(model, A_2 * y + A_1 * x .<= b)
    @objective(model, Min, c_1' * x + c_2' * y)
    add_annotation(model, variable_classification; all_variables = false)
    optimize!(model)
    x_optimal = value.(x)
    y_optimal = value.(y)
    println("x: $(x_optimal), y: $(y_optimal)")
end

Download Details:

Author: jump-dev
Source Code: https://github.com/jump-dev/CPLEX.jl 
License: MIT license

#julia #interface #optimization 

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Buddha Community

CPLEX.jl: Julia interface for The CPLEX Optimization Software

CPLEX.jl underwent a major rewrite between versions 0.6.6 and 0.7.0. Users of JuMP should see no breaking changes, but if you used the lower-level C API (e.g., for callbacks), you will need to update your code accordingly. For a full description of the changes, read this discourse post.

To revert to the old API, use:

import Pkg
Pkg.add(Pkg.PackageSpec(name = "CPLEX", version = v"0.6"))

Then restart Julia for the change to take effect.

CPLEX.jl

CPLEX.jl is a wrapper for the IBM® ILOG® CPLEX® Optimization Studio

You cannot use CPLEX.jl without having purchased and installed a copy of CPLEX Optimization Studio from IBM. However, CPLEX is available for free to academics and students.

CPLEX.jl has two components:

• a thin wrapper around the complete C API
• an interface to MathOptInterface

The C API can be accessed via CPLEX.CPXxx functions, where the names and arguments are identical to the C API. See the CPLEX documentation for details.

Note: This wrapper is maintained by the JuMP community and is not officially supported by IBM. However, we thank IBM for providing us with a CPLEX license to test CPLEX.jl on GitHub. If you are a commercial customer interested in official support for CPLEX in Julia, let them know!.

Installation

Minimum version requirement: CPLEX.jl requires CPLEX version 12.10 or 20.1.

First, obtain a license of CPLEX and install CPLEX solver, following the instructions on IBM's website. Then, set the CPLEX_STUDIO_BINARIES environment variable as appropriate and run Pkg.add("CPLEX"), then Pkg.build("CPLEX"). For example:

# On Windows, this might be
ENV["CPLEX_STUDIO_BINARIES"] = "C:\\Program Files\\CPLEX_Studio1210\\cplex\\bin\\x86-64_win\\"
import Pkg
Pkg.add("CPLEX")
Pkg.build("CPLEX")

# On OSX, this might be
ENV["CPLEX_STUDIO_BINARIES"] = "/Applications/CPLEX_Studio1210/cplex/bin/x86-64_osx/"
import Pkg
Pkg.add("CPLEX")
Pkg.build("CPLEX")

# On Unix, this might be
ENV["CPLEX_STUDIO_BINARIES"] = "/opt/CPLEX_Studio1210/cplex/bin/x86-64_linux/"
import Pkg
Pkg.add("CPLEX")
Pkg.build("CPLEX")

Note: your path may differ. Check which folder you installed CPLEX in, and update the path accordingly.

Use with JuMP

We highly recommend that you use the CPLEX.jl package with higher level packages such as JuMP.jl.

This can be done using the CPLEX.Optimizer object. Here is how to create a JuMP model that uses CPLEX as the solver.

using JuMP, CPLEX

model = Model(CPLEX.Optimizer)
set_optimizer_attribute(model, "CPX_PARAM_EPINT", 1e-8)

Parameters match those of the C API in the CPLEX documentation.

Callbacks

Here is an example using CPLEX's solver-specific callbacks.

using JuMP, CPLEX, Test

model = direct_model(CPLEX.Optimizer())
set_silent(model)

# This is very, very important!!! Only use callbacks in single-threaded mode.
MOI.set(model, MOI.NumberOfThreads(), 1)

@variable(model, 0 <= x <= 2.5, Int)
@variable(model, 0 <= y <= 2.5, Int)
@objective(model, Max, y)
cb_calls = Clong[]
function my_callback_function(cb_data::CPLEX.CallbackContext, context_id::Clong)
    # You can reference variables outside the function as normal
    push!(cb_calls, context_id)
    # You can select where the callback is run
    if context_id != CPX_CALLBACKCONTEXT_CANDIDATE
        return
    end
    ispoint_p = Ref{Cint}()
    ret = CPXcallbackcandidateispoint(cb_data, ispoint_p)
    if ret != 0 || ispoint_p[] == 0
        return  # No candidate point available or error
    end
    # You can query CALLBACKINFO items
    valueP = Ref{Cdouble}()
    ret = CPXcallbackgetinfodbl(cb_data, CPXCALLBACKINFO_BEST_BND, valueP)
    @info "Best bound is currently: $(valueP[])"
    # As well as any other C API
    x_p = Vector{Cdouble}(undef, 2)
    obj_p = Ref{Cdouble}()
    ret = CPXcallbackgetincumbent(cb_data, x_p, 0, 1, obj_p)
    if ret == 0
        @info "Objective incumbent is: $(obj_p[])"
        @info "Incumbent solution is: $(x_p)"
        # Use CPLEX.column to map between variable references and the 1-based
        # column.
        x_col = CPLEX.column(cb_data, index(x))
        @info "x = $(x_p[x_col])"
    else
        # Unable to query incumbent.
    end

    # Before querying `callback_value`, you must call:
    CPLEX.load_callback_variable_primal(cb_data, context_id)
    x_val = callback_value(cb_data, x)
    y_val = callback_value(cb_data, y)
    # You can submit solver-independent MathOptInterface attributes such as
    # lazy constraints, user-cuts, and heuristic solutions.
    if y_val - x_val > 1 + 1e-6
        con = @build_constraint(y - x <= 1)
        MOI.submit(model, MOI.LazyConstraint(cb_data), con)
    elseif y_val + x_val > 3 + 1e-6
        con = @build_constraint(y + x <= 3)
        MOI.submit(model, MOI.LazyConstraint(cb_data), con)
    end
end
MOI.set(model, CPLEX.CallbackFunction(), my_callback_function)
optimize!(model)
@test termination_status(model) == MOI.OPTIMAL
@test primal_status(model) == MOI.FEASIBLE_POINT
@test value(x) == 1
@test value(y) == 2

Annotations for automatic Benders' decomposition

Here is an example of using CPLEX's annotation feature for automatic Benders' decomposition:

using JuMP, CPLEX

function add_annotation(
    model::JuMP.Model,
    variable_classification::Dict;
    all_variables::Bool = true,
)
    num_variables = sum(length(it) for it in values(variable_classification))
    if all_variables
        @assert num_variables == JuMP.num_variables(model)
    end
    indices, annotations = CPXINT[], CPXLONG[]
    for (key, value) in variable_classification
        for variable_ref in value
            push!(indices, variable_ref.index.value - 1)
            push!(annotations, CPX_BENDERS_MASTERVALUE + key)
        end
    end
    cplex = backend(model)
    index_p = Ref{CPXINT}()
    CPXnewlongannotation(
        cplex.env,
        cplex.lp,
        CPX_BENDERS_ANNOTATION,
        CPX_BENDERS_MASTERVALUE,
    )
    CPXgetlongannotationindex(
        cplex.env,
        cplex.lp,
        CPX_BENDERS_ANNOTATION,
        index_p,
    )
    CPXsetlongannotations(
        cplex.env,
        cplex.lp,
        index_p[],
        CPX_ANNOTATIONOBJ_COL,
        length(indices),
        indices,
        annotations,
    )
    return
end

# Problem

function illustrate_full_annotation()
    c_1, c_2 = [1, 4], [2, 3]
    dim_x, dim_y = length(c_1), length(c_2)
    b = [-2; -3]
    A_1, A_2 = [1 -3; -1 -3], [1 -2; -1 -1]
    model = JuMP.direct_model(CPLEX.Optimizer())
    set_optimizer_attribute(model, "CPXPARAM_Benders_Strategy", 1)
    @variable(model, x[1:dim_x] >= 0, Bin)
    @variable(model, y[1:dim_y] >= 0)
    variable_classification = Dict(0 => [x[1], x[2]], 1 => [y[1], y[2]])
    @constraint(model, A_2 * y + A_1 * x .<= b)
    @objective(model, Min, c_1' * x + c_2' * y)
    add_annotation(model, variable_classification)
    optimize!(model)
    x_optimal = value.(x)
    y_optimal = value.(y)
    println("x: $(x_optimal), y: $(y_optimal)")
end

function illustrate_partial_annotation()
    c_1, c_2 = [1, 4], [2, 3]
    dim_x, dim_y = length(c_1), length(c_2)
    b = [-2; -3]
    A_1, A_2 = [1 -3; -1 -3], [1 -2; -1 -1]
    model = JuMP.direct_model(CPLEX.Optimizer())
    # Note that the "CPXPARAM_Benders_Strategy" has to be set to 2 if partial
    # annotation is provided. If "CPXPARAM_Benders_Strategy" is set to 1, then
    # the following error will be thrown:
    # `CPLEX Error  2002: Invalid Benders decomposition.`
    set_optimizer_attribute(model, "CPXPARAM_Benders_Strategy", 2)
    @variable(model, x[1:dim_x] >= 0, Bin)
    @variable(model, y[1:dim_y] >= 0)
    variable_classification = Dict(0 => [x[1]], 1 => [y[1], y[2]])
    @constraint(model, A_2 * y + A_1 * x .<= b)
    @objective(model, Min, c_1' * x + c_2' * y)
    add_annotation(model, variable_classification; all_variables = false)
    optimize!(model)
    x_optimal = value.(x)
    y_optimal = value.(y)
    println("x: $(x_optimal), y: $(y_optimal)")
end

Download Details:

Author: jump-dev
Source Code: https://github.com/jump-dev/CPLEX.jl 
License: MIT license

#julia #interface #optimization 

ML Optimization pt.1 - Gradient Descent with Python

So far in our journey through the Machine Learning universe, we covered several big topics. We investigated some regression algorithms, classification algorithms and algorithms that can be used for both types of problems (SVM**, **Decision Trees and Random Forest). Apart from that, we dipped our toes in unsupervised learning, saw how we can use this type of learning for clustering and learned about several clustering techniques.

We also talked about how to quantify machine learning model performance and how to improve it with regularization. In all these articles, we used Python for “from the scratch” implementations and libraries like TensorFlow, Pytorch and SciKit Learn. The word optimization popped out more than once in these articles, so in this and next article, we focus on optimization techniques which are an important part of the machine learning process.

In general, every machine learning algorithm is composed of three integral parts:

1. A loss function.
2. Optimization criteria based on the loss function, like a cost function.
3. Optimization technique – this process leverages training data to find a solution for optimization criteria (cost function).

As you were able to see in previous articles, some algorithms were created intuitively and didn’t have optimization criteria in mind. In fact, mathematical explanations of why and how these algorithms work were done later. Some of these algorithms are Decision Trees and kNN. Other algorithms, which were developed later had this thing in mind beforehand. SVMis one example.

During the training, we change the parameters of our machine learning model to try and minimize the loss function. However, the question of how do you change those parameters arises. Also, by how much should we change them during training and when. To answer all these questions we use optimizers. They put all different parts of the machine learning algorithm together. So far we mentioned Gradient Decent as an optimization technique, but we haven’t explored it in more detail. In this article, we focus on that and we cover the grandfather of all optimization techniques and its variation. Note that these techniques are not machine learning algorithms. They are solvers of minimization problems in which the function to minimize has a gradient in most points of its domain.

Dataset & Prerequisites

Data that we use in this article is the famous Boston Housing Dataset . This dataset is composed 14 features and contains information collected by the U.S Census Service concerning housing in the area of Boston Mass. It is a small dataset  with only 506 samples.

For the purpose of this article, make sure that you have installed the following _Python _libraries:

• **NumPy **– Follow this guide if you need help with installation.
• **SciKit Learn **– Follow this guide if you need help with installation.
• Pandas – Follow this guide if you need help with installation.

Once installed make sure that you have imported all the necessary modules that are used in this tutorial.

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import SGDRegressor

Apart from that, it would be good to be at least familiar with the basics of linear algebra, calculus and probability.

Why do we use Optimizers?

Note that we also use simple Linear Regression in all examples. Due to the fact that we explore optimizationtechniques, we picked the easiest machine learning algorithm. You can see more details about Linear regression here. As a quick reminder the formula for linear regression goes like this:

where w and b are parameters of the machine learning algorithm. The entire point of the training process is to set the correct values to the w and b, so we get the desired output from the machine learning model. This means that we are trying to make the value of our error vector as small as possible, i.e. to find a global minimum of the cost function.

One way of solving this problem is to use calculus. We could compute derivatives and then use them to find places where is an extrema of the cost function. However, the cost function is not a function of one or a few variables; it is a function of all parameters of a machine learning algorithm, so these calculations will quickly grow into a monster. That is why we use these optimizers.

#ai #machine learning #python #artificaial inteligance #artificial intelligence #batch gradient descent #data science #datascience #deep learning #from scratch #gradient descent #machine learning #machine learning optimizers #ml optimization #optimizers #scikit learn #software #software craft #software craftsmanship #software development #stochastic gradient descent

Understanding Gradient Descent with Python

So far in our journey through the Machine Learning universe, we covered several big topics. We investigated some regression algorithms, classification algorithms and algorithms that can be used for both types of problems (SVM, Decision Trees and Random Forest). Apart from that, we dipped our toes in unsupervised learning, saw how we can use this type of learning for clustering and learned about several clustering techniques.

We also talked about how to quantify machine learning model performance and how to improve it with regularization. In all these articles, we used Python for “from the scratch” implementations and libraries like TensorFlow, Pytorch and SciKit Learn. The word optimization popped out more than once in these articles, so in this article, we focus on optimization techniques which are an important part of the machine learning process.

#ai #machine learning #python #artificaial inteligance #artificial intelligence #batch gradient descent #data science #datascience #deep learning #from scratch #gradient descent #machine learning optimizers #ml optimization #optimizers #scikit learn #software #software craft #software craftsmanship #software development

Gurobi.jl: Julia interface for Gurobi Optimizer

Gurobi.jl

Gurobi.jl is a wrapper for the Gurobi Optimizer.

It has two components:

• a thin wrapper around the complete C API
• an interface to MathOptInterface

The C API can be accessed via Gurobi.GRBxx functions, where the names and arguments are identical to the C API. See the Gurobi documentation for details.

Note: This wrapper is maintained by the JuMP community and is not officially supported by Gurobi. However, we thank Gurobi for providing us with a license to test Gurobi.jl on GitHub. If you are a commercial customer interested in official support for Gurobi in Julia, let them know!.

Installation

Minimum version requirement: Gurobi.jl requires Gurobi version 9.0 or 9.1 or 9.5.

First, obtain a license of Gurobi and install Gurobi solver, following the instructions on Gurobi's website. Then, set the GUROBI_HOME environment variable as appropriate and run Pkg.add("Gurobi"), the Pkg.build("Gurobi"). For example:

# On Windows, this might be
ENV["GUROBI_HOME"] = "C:\\Program Files\\gurobi950\\win64"
# ... or perhaps ...
ENV["GUROBI_HOME"] = "C:\\gurobi950\\win64"
import Pkg
Pkg.add("Gurobi")
Pkg.build("Gurobi")

# On Mac, this might be
ENV["GUROBI_HOME"] = "/Library/gurobi950/mac64"
import Pkg
Pkg.add("Gurobi")
Pkg.build("Gurobi")

Note: your path may differ. Check which folder you installed Gurobi in, and update the path accordingly.

By default, building Gurobi.jl will fail if the Gurobi library is not found. This may not be desirable in certain cases, for example when part of a package's test suite uses Gurobi as an optional test dependency, but Gurobi cannot be installed on a CI server running the test suite. To support this use case, the GUROBI_JL_SKIP_LIB_CHECK environment variable may be set (to any value) to make Gurobi.jl installable (but not usable).

Use with JuMP

We highly recommend that you use the Gurobi.jl package with higher level packages such as JuMP.jl.

This can be done using the Gurobi.Optimizer object. Here is how to create a JuMP model that uses Gurobi as the solver.

using JuMP, Gurobi

model = Model(Gurobi.Optimizer)
set_optimizer_attribute(model, "TimeLimit", 100)
set_optimizer_attribute(model, "Presolve", 0)

See the Gurobi Documentation for a list and description of allowable parameters.

Reusing the same Gurobi environment for multiple solves

When using this package via other packages such as JuMP.jl, the default behavior is to obtain a new Gurobi license token every time a model is created. If you are using Gurobi in a setting where the number of concurrent Gurobi uses is limited (e.g. "Single-Use" or "Floating-Use" licenses), you might instead prefer to obtain a single license token that is shared by all models that your program solves. You can do this by passing a Gurobi Environment object as the first parameter to Gurobi.Optimizer. For example, the follow code snippet solves multiple problems with JuMP using the same license token:

using JuMP, Gurobi

const GRB_ENV = Gurobi.Env()

model1 = Model(() -> Gurobi.Optimizer(GRB_ENV))

# The solvers can have different options too
model2 = Model(() -> Gurobi.Optimizer(GRB_ENV))
set_optimizer_attribute(model2, "OutputFlag", 0)

Accessing Gurobi-specific attributes via JuMP

You can get and set Gurobi-specific variable, constraint, and model attributes via JuMP as follows:

using JuMP, Gurobi

model = direct_model(Gurobi.Optimizer())
@variable(model, x >= 0)
@constraint(model, c, 2x >= 1)
@objective(model, Min, x)
MOI.set(model, Gurobi.ConstraintAttribute("Lazy"), c, 2)
optimize!(model)

MOI.get(model, Gurobi.VariableAttribute("LB"), x)  # Returns 0.0
MOI.get(model, Gurobi.ModelAttribute("NumConstrs")) # Returns 1

Note that we are using JuMP in direct-mode.

A complete list of supported Gurobi attributes can be found in their online documentation.

Callbacks

Here is an example using Gurobi's solver-specific callbacks.

using JuMP, Gurobi, Test

model = direct_model(Gurobi.Optimizer())
@variable(model, 0 <= x <= 2.5, Int)
@variable(model, 0 <= y <= 2.5, Int)
@objective(model, Max, y)
cb_calls = Cint[]
function my_callback_function(cb_data, cb_where::Cint)
    # You can reference variables outside the function as normal
    push!(cb_calls, cb_where)
    # You can select where the callback is run
    if cb_where != GRB_CB_MIPSOL && cb_where != GRB_CB_MIPNODE
        return
    end
    # You can query a callback attribute using GRBcbget
    if cb_where == GRB_CB_MIPNODE
        resultP = Ref{Cint}()
        GRBcbget(cb_data, cb_where, GRB_CB_MIPNODE_STATUS, resultP)
        if resultP[] != GRB_OPTIMAL
            return  # Solution is something other than optimal.
        end
    end
    # Before querying `callback_value`, you must call:
    Gurobi.load_callback_variable_primal(cb_data, cb_where)
    x_val = callback_value(cb_data, x)
    y_val = callback_value(cb_data, y)
    # You can submit solver-independent MathOptInterface attributes such as
    # lazy constraints, user-cuts, and heuristic solutions.
    if y_val - x_val > 1 + 1e-6
        con = @build_constraint(y - x <= 1)
        MOI.submit(model, MOI.LazyConstraint(cb_data), con)
    elseif y_val + x_val > 3 + 1e-6
        con = @build_constraint(y + x <= 3)
        MOI.submit(model, MOI.LazyConstraint(cb_data), con)
    end
    if rand() < 0.1
        # You can terminate the callback as follows:
        GRBterminate(backend(model))
    end
    return
end
# You _must_ set this parameter if using lazy constraints.
MOI.set(model, MOI.RawOptimizerAttribute("LazyConstraints"), 1)
MOI.set(model, Gurobi.CallbackFunction(), my_callback_function)
optimize!(model)
@test termination_status(model) == MOI.OPTIMAL
@test primal_status(model) == MOI.FEASIBLE_POINT
@test value(x) == 1
@test value(y) == 2

See the Gurobi documentation for other information that can be queried with GRBcbget.

Common Performance Pitfall with JuMP

Gurobi's API works differently than most solvers. Any changes to the model are not applied immediately, but instead go sit in a internal buffer (making any modifications appear to be instantaneous) waiting for a call to GRBupdatemodel (where the work is done).

This leads to a common performance pitfall that has the following message as its main symptom:

Warning: excessive time spent in model updates. Consider calling update less
frequently.

This often means the JuMP program was structured in such a way that Gurobi.jl ends up calling GRBupdatemodel each iteration of a loop. Usually, it is possible (and easy) to restructure the JuMP program in a way it stays solver-agnostic and has a close-to-ideal performance with Gurobi.

To guide such restructuring it is good to keep in mind the following bits of information:

1. GRBupdatemodel is only called if changes were done since last GRBupdatemodel (i.e., the internal buffer is not empty).
2. GRBupdatemodel is called when JuMP.optimize! is called, but this often is not the source of the problem.
3. GRBupdatemodel may be called when ANY model attribute is queried even if that specific attribute was not changed, and this often the source of the problem.
4. The worst-case scenario is, therefore, a loop of modify-query-modify-query, even if what is being modified and what is being queried are two completely distinct things.

As an example, prefer:

# GOOD
model = Model(Gurobi.Optimizer)
@variable(model, x[1:100] >= 0)
# All modifications are done before any queries.
for i = 1:100
    set_upper_bound(x[i], i)
end
for i = 1:100
    # Only the first `lower_bound` query may trigger an `GRBupdatemodel`.
    println(lower_bound(x[i]))
end

to:

# BAD
model = Model(Gurobi.Optimizer)
@variable(model, x[1:100] >= 0)
for i = 1:100
    set_upper_bound(x[i], i)
    # `GRBupdatemodel` called on each iteration of this loop.
    println(lower_bound(x[i]))
end

Using Gurobi v9.0 and you got an error like Q not PSD?

You need to set the NonConvex parameter:

model = Model(Gurobi.Optimizer)
set_optimizer_attribute(model, "NonConvex", 2)

Download Details:

Author: jump-dev
Source Code: https://github.com/jump-dev/Gurobi.jl 
License: MIT license

#julia #interface #optimize 

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