GitHub

Gathering Results

After running optimize!(model), you can retrieve various information about the solutions and the solving process.

Solution Status

Termination Status

The termination status indicates how the optimization process ended:

status = termination_status(model)

Common termination statuses include:

  • OPTIMAL: The solver found an optimal solution
  • LOCALLY_SOLVED: A locally optimal solution was found
  • TIME_LIMIT: The solver stopped due to time limit
  • ITERATION_LIMIT: The solver stopped due to iteration limit

Primal Status

The primal status indicates the quality of the primal solution:

pstatus = primal_status(model)

A status of FEASIBLE_POINT indicates that a valid solution was found.

Solution Summary

For a quick overview of the optimization result:

solution_summary(model)

Retrieving Variable Values

Single Solution

Get the value of a single variable:

x_value = value(x)

Get values of an array of variables:

x_values = value.(x)

Multiple Solutions

Many QUBO solvers, especially quantum annealers and samplers, return multiple solutions. Access them using the result keyword:

# Number of solutions found
n_solutions = result_count(model)

# Access the i-th solution
for i in 1:n_solutions
    xi = value.(x, result = i)
    println("Solution $i: $xi")
end
Best Solution

By default (without specifying result), value returns the best solution found.

Objective Value

Single Solution

Get the objective value of the best solution:

obj = objective_value(model)

Multiple Solutions

Get the objective value for a specific solution:

obj_i = objective_value(model, result = i)

Compilation Information

ToQUBO.jl provides attributes to inspect the compilation process:

using MathOptInterface as MOI
using ToQUBO: Attributes

Compilation Time

Get the time spent converting your model to QUBO form:

comp_time = MOI.get(model, Attributes.CompilationTime())

Compilation Status

Check the status of the compilation:

comp_status = MOI.get(model, Attributes.CompilationStatus())

Source and Target Models

Access the intermediate models created during compilation:

# Original model (with MOI bridges applied)
source = MOI.get(model, Attributes.SourceModel())

# QUBO formulation
target = MOI.get(model, Attributes.TargetModel())

Penalty Information

Constraints are converted to penalty terms in QUBO. You can retrieve the penalty coefficients used:

Constraint Penalties

# Get the penalty used for a specific constraint
rho = MOI.get(model, Attributes.ConstraintEncodingPenalty(), constraint_ref)

Variable Encoding Penalties

For encoded variables:

# Get the penalty used for variable encoding
theta = MOI.get(model, Attributes.VariableEncodingPenalty(), variable_ref)

Example: Complete Results Retrieval

using JuMP
using ToQUBO
using QUBODrivers  # Provides ExactSampler and other solvers

# Create and solve a model
model = Model(() -> ToQUBO.Optimizer(ExactSampler.Optimizer))

@variable(model, x[1:3], Bin)
@constraint(model, c1, x[1] + x[2] <= 1)
@objective(model, Max, x[1] + 2*x[2] + 3*x[3])

optimize!(model)

# Check status
println("Termination: ", termination_status(model))
println("Primal: ", primal_status(model))

# Get best solution
if primal_status(model) == FEASIBLE_POINT
    println("Best solution: ", value.(x))
    println("Best objective: ", objective_value(model))
end

# Iterate over all solutions
println("\nAll solutions:")
for i in 1:result_count(model)
    println("  Solution $i: x = $(value.(x, result = i)), obj = $(objective_value(model, result = i))")
end
Termination: LOCALLY_SOLVED
Primal: FEASIBLE_POINT
Best solution: [0.0, 1.0, 1.0]
Best objective: 5.0

All solutions:
  Solution 1: x = [0.0, 1.0, 1.0], obj = 5.0
  Solution 2: x = [1.0, 0.0, 1.0], obj = 4.0
  Solution 3: x = [0.0, 0.0, 1.0], obj = 3.0
  Solution 4: x = [0.0, 1.0, 0.0], obj = 2.0
  Solution 5: x = [1.0, 0.0, 0.0], obj = 1.0
  Solution 6: x = [0.0, 0.0, 0.0], obj = -0.0
  Solution 7: x = [1.0, 1.0, 1.0], obj = -1.0
  Solution 8: x = [0.0, 1.0, 1.0], obj = -2.0
  Solution 9: x = [1.0, 0.0, 1.0], obj = -3.0
  Solution 10: x = [1.0, 1.0, 0.0], obj = -4.0
  Solution 11: x = [0.0, 0.0, 1.0], obj = -4.0
  Solution 12: x = [0.0, 1.0, 0.0], obj = -5.0
  Solution 13: x = [1.0, 0.0, 0.0], obj = -6.0
  Solution 14: x = [0.0, 0.0, 0.0], obj = -7.0
  Solution 15: x = [1.0, 1.0, 1.0], obj = -22.0
  Solution 16: x = [1.0, 1.0, 0.0], obj = -25.0

Working with QUBOTools

ToQUBO.jl integrates with QUBOTools.jl for advanced QUBO manipulation. You can extract the underlying QUBO model:

using ToQUBO: QUBOTools

# Get the QUBO backend from the attached MOI optimizer
qubo_model = QUBOTools.backend(unsafe_backend(model))

This allows you to:

  • Export the QUBO to various file formats
  • Analyze the QUBO structure
  • Use additional QUBOTools functionality

Next Steps