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)

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

Print the model

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

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)

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

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:

• AUTOMATIC: The CachingOptimizer changes its state when necessary. For example, optimize! will automatically call attach_optimizer (an optimizer must have been previously set). Attempting to add a constraint or perform a modification not supported by the optimizer results in a drop to EMPTY_OPTIMIZER mode.
• MANUAL: The user must change the state of the CachingOptimizer using MOIU.reset_optimizer(::JuMP.Model), MOIU.drop_optimizer(::JuMP.Model), and MOIU.attach_optimizer(::JuMP.Model). Attempting to perform an operation in the incorrect state results in an error.

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

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

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

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.
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