# Models

## Create a model

Create a model by passing an optimizer to Model:

julia> model = Model(GLPK.Optimizer)
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: EMPTY_OPTIMIZER
Solver name: GLPK

or by calling set_optimizer on an empty Model:

julia> model = Model()
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: NO_OPTIMIZER
Solver name: No optimizer attached.

julia> set_optimizer(model, GLPK.Optimizer)
Info

JuMP uses "optimizer" as a synonym for "solver." Our convention is to use "solver" to refer to the underlying software, and use "optimizer" to refer to the Julia object that wraps the solver. For example, GLPK is a solver, and GLPK.Optimizer is an optimizer.

Tip

Don't know what the fields Model mode, CachingOptimizer state mean? Read the Backends section.

Use optimizer_with_attributes to create an optimizer with some attributes initialized:

julia> model = Model(optimizer_with_attributes(GLPK.Optimizer, "msg_lev" => 0))
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: EMPTY_OPTIMIZER
Solver name: GLPK

Alternatively, you can create a function which takes no arguments and returns an initialized Optimizer object:

julia> function my_optimizer()
model = GLPK.Optimizer()
MOI.set(model, MOI.RawParameter("msg_lev"), 0)
return model
end
my_optimizer (generic function with 1 method)

julia> model = Model(my_optimizer)
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: EMPTY_OPTIMIZER
Solver name: GLPK

By default, show(model) will print a summary of the problem.

julia> model = Model(); @variable(model, x >= 0); @objective(model, Max, x);

julia> model
A JuMP Model
Maximization problem with:
Variable: 1
Objective function type: VariableRef
VariableRef-in-MathOptInterface.GreaterThan{Float64}: 1 constraint
Model mode: AUTOMATIC
CachingOptimizer state: NO_OPTIMIZER
Solver name: No optimizer attached.
Names registered in the model: x

Use print to print the formulation of the model (in IJulia, this will render as LaTeX.

julia> print(model)
Max x
Subject to
x ≥ 0.0
Warning

This format is specific to JuMP. To write the model to a file, use write_to_file instead.

Use latex_formulation to display the model in LaTeX form.

julia> latex_formulation(model)
\begin{aligned} \max\quad & x\\ \text{Subject to} \quad & x \geq 0.0\\ \end{aligned}

In IJulia (and Documenter), ending a cell in with latex_formulation will render the model in LaTeX!

latex_formulation(model)
\begin{aligned} \max\quad & x\\ \text{Subject to} \quad & x \geq 0.0\\ \end{aligned}

## Turn off output

Use set_silent and unset_silent to disable or enable printing output from the solver.

julia> model = Model(GLPK.Optimizer);

julia> set_silent(model)
true

julia> unset_silent(model)
false

## Set a time limit

Use set_time_limit_sec, unset_time_limit_sec, and time_limit_sec to manage time limits.

julia> model = Model(GLPK.Optimizer);

julia> set_time_limit_sec(model, 60.0)
60.0

julia> time_limit_sec(model)
60.0

julia> unset_time_limit_sec(model)

julia> time_limit_sec(model)
2.147483647e6

## Write a model to file

JuMP can write models to a variety of file-formats using write_to_file and Base.write.

julia> write_to_file(model, "model.mps")

julia> write(io, model; format = MOI.FileFormats.FORMAT_MPS)
Info

The supported file formats are defined by the MOI.FileFormats.FileFormat enum.

julia> MOI.FileFormats.FileFormat
Enum MathOptInterface.FileFormats.FileFormat:
FORMAT_AUTOMATIC = 0
FORMAT_CBF = 1
FORMAT_LP = 2
FORMAT_MOF = 3
FORMAT_MPS = 4
FORMAT_SDPA = 5

## Read a model from file

JuMP models can be created from file formats using read_from_file and Base.read.

julia> model = read_from_file("model.mps")
A JuMP Model
Minimization problem with:
Variables: 0
Objective function type: GenericAffExpr{Float64,VariableRef}
Model mode: AUTOMATIC
CachingOptimizer state: NO_OPTIMIZER
Solver name: No optimizer attached.

julia> seekstart(io);

julia> model2 = read(io, Model; format = MOI.FileFormats.FORMAT_MPS)
A JuMP Model
Minimization problem with:
Variables: 0
Objective function type: GenericAffExpr{Float64,VariableRef}
Model mode: AUTOMATIC
CachingOptimizer state: NO_OPTIMIZER
Solver name: No optimizer attached.

## Backends

A JuMP Model is a thin layer around a backend of type MOI.ModelLike that stores the optimization problem and acts as the optimization solver.

From JuMP, the MOI backend can be accessed using the backend function. Let's see what the backend of a JuMP Model is:

julia> model = Model(GLPK.Optimizer)
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: EMPTY_OPTIMIZER
Solver name: GLPK

julia> b = backend(model)
MOIU.CachingOptimizer{MOI.AbstractOptimizer,MOIU.UniversalFallback{MOIU.GenericModel{Float64,MOIU.ModelFunctionConstraints{Float64}}}}
in state EMPTY_OPTIMIZER
in mode AUTOMATIC
with model cache MOIU.UniversalFallback{MOIU.GenericModel{Float64,MOIU.ModelFunctionConstraints{Float64}}}
fallback for MOIU.GenericModel{Float64,MOIU.ModelFunctionConstraints{Float64}}
with optimizer MOIB.LazyBridgeOptimizer{GLPK.Optimizer}
with 0 variable bridges
with 0 constraint bridges
with 0 objective bridges
with inner model A GLPK model

The backend is a MOIU.CachingOptimizer in the state EMPTY_OPTIMIZER and mode AUTOMATIC.

### CachingOptimizer

A MOIU.CachingOptimizer is an MOI layer that abstracts the difference between solvers that support incremental modification (e.g., they support adding variables one-by-one), and solvers that require the entire problem in a single API call (e.g., they only accept the A, b and c matrices of a linear program).

It has two parts:

1. A cache, where the model can be built and modified incrementally
julia> b.model_cache
MOIU.UniversalFallback{MOIU.GenericModel{Float64,MOIU.ModelFunctionConstraints{Float64}}}
fallback for MOIU.GenericModel{Float64,MOIU.ModelFunctionConstraints{Float64}}
2. An optimizer, which is used to solve the problem
julia> b.optimizer
MOIB.LazyBridgeOptimizer{GLPK.Optimizer}
with 0 variable bridges
with 0 constraint bridges
with 0 objective bridges
with inner model A GLPK model
Info

The LazyBridgeOptimizer section explains what a LazyBridgeOptimizer is.

The CachingOptimizer has logic to decide when to copy the problem from the cache to the optimizer, and when it can efficiently update the optimizer in-place.

A CachingOptimizer may be in one of three possible states:

• NO_OPTIMIZER: The CachingOptimizer does not have any optimizer.
• EMPTY_OPTIMIZER: The CachingOptimizer has an empty optimizer, and it is not synchronized with the cached model.
• ATTACHED_OPTIMIZER: The CachingOptimizer has an optimizer, and it is synchronized with the cached model.

A CachingOptimizer has two modes of operation:

By default Model will create a CachingOptimizer in AUTOMATIC mode. Use the caching_mode keyword to create a model in MANUAL mode:

julia> Model(GLPK.Optimizer; caching_mode = MOI.Utilities.MANUAL)
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: MANUAL
CachingOptimizer state: EMPTY_OPTIMIZER
Solver name: GLPK
Tip

Only use MANUAL mode if you have a very good reason. If you want to reduce the overhead between JuMP and the underlying solver, consider Direct mode instead.

### LazyBridgeOptimizer

The second layer that JuMP applies automatically is a LazyBridgeOptimizer. A LazyBridgeOptimizer is an MOI layer that attempts to transform constraints added by the user into constraints supported by the solver. This may involve adding new variables and constraints to the optimizer. The transformations are selected from a set of known recipes called bridges.

A common example of a bridge is one that splits an interval constrait like @constraint(model, 1 <= x + y <= 2) into two constraints, @constraint(model, x + y >= 1) and @constraint(model, x + y <= 2).

Use the bridge_constraints=false keyword to remove the bridging layer:

julia> model = Model(GLPK.Optimizer; bridge_constraints = false)
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: EMPTY_OPTIMIZER
Solver name: GLPK

julia> backend(model)
MOIU.CachingOptimizer{MOI.AbstractOptimizer,MOIU.UniversalFallback{MOIU.GenericModel{Float64,MOIU.ModelFunctionConstraints{Float64}}}}
in state EMPTY_OPTIMIZER
in mode AUTOMATIC
with model cache MOIU.UniversalFallback{MOIU.GenericModel{Float64,MOIU.ModelFunctionConstraints{Float64}}}
fallback for MOIU.GenericModel{Float64,MOIU.ModelFunctionConstraints{Float64}}
with optimizer A GLPK model
Tip

Only disable bridges if you have a very good reason. If you want to reduce the overhead between JuMP and the underlying solver, consider Direct mode instead.

## Direct mode

Using a CachingOptimizer results in an additional copy of the model being stored by JuMP in the .model_cache field. To avoid this overhead, create a JuMP model using direct_model:

julia> model = direct_model(GLPK.Optimizer())
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: DIRECT
Solver name: GLPK
Warning

Solvers that do not support incremental modification do not support direct_model. An error will be thrown, telling you to use a CachingOptimizer instead.

The benefit of using direct_model is that there are no extra layers (e.g., Cachingoptimizer or LazyBridgeOptimizer) between model and the provided optimizer:

julia> typeof(backend(model))
GLPK.Optimizer

A downside of direct mode is that there is no bridging layer. Therefore, only constraints which are natively supported by the solver are supported. For example, GLPK.jl does not implement constraints of the form l <= a' x <= u.

julia> @variable(model, x[1:2]);

julia> @constraint(model, 1 <= x[1] + x[2] <= 2)
ERROR: Constraints of type MathOptInterface.ScalarAffineFunction{Float64}-in-MathOptInterface.Interval{Float64} are not supported by the solver.
[...]