# Optimization using bonmin¶

In this example we are going to explore mixed-integer non linear problems optimization using the bonmin interface. %%

import openturns as ot

ot.Log.Show(ot.Log.NONE)


List available algorithms

for algo in ot.Bonmin.GetAlgorithmNames():
print(algo)

B-BB
B-OA
B-QG
B-Hyb
B-Ecp
B-iFP


Details and references on bonmin algorithms are available here .

## Setting up and solving a simple problem¶

The following example will demonstrate the use of bonmin “BB” algorithm to solve the following problem:

such that:

The theoretical minimum is reached for . At this point, the objective function value is

N.B.: OpenTURNS requires equality and inequality constraints to be stated as and , respectively. Thus the inequalities above will have to be restated to match this requirement:

Definition of objective function

objectiveFunction = ot.SymbolicFunction(["x0", "x1", "x2", "x3"], ["-x0 -x1 -x2"])

# Definition of variables bounds
bounds = ot.Interval(
[0, 0, 0, 0],
[1, 1e99, 1e99, 5],
[True, True, True, True],
[True, False, False, True],
)

# Definition of constraints
# Constraints in OpenTURNS are defined as g(x) = 0 and h(x) >= 0
#    No equality constraint -> nothing to do
#    Inequality constraints:
h = ot.SymbolicFunction(
["x0", "x1", "x2", "x3"],
["-(x1-0.5)^2 - (x2-0.5)^2 + 0.25", "x1 - x0", "-x0 - x2 - x3 + 2"],
)

# Definition of variables types
CONTINUOUS = ot.OptimizationProblemImplementation.CONTINUOUS
BINARY = ot.OptimizationProblemImplementation.BINARY
INTEGER = ot.OptimizationProblemImplementation.INTEGER
variablesType = [BINARY, CONTINUOUS, CONTINUOUS, INTEGER]

# Setting up Bonmin problem
problem = ot.OptimizationProblem(objectiveFunction)
problem.setBounds(bounds)
problem.setVariablesType(variablesType)
problem.setInequalityConstraint(h)

bonminAlgorithm = ot.Bonmin(problem, "B-BB")
bonminAlgorithm.setMaximumEvaluationNumber(10000)
bonminAlgorithm.setMaximumIterationNumber(1000)
bonminAlgorithm.setStartingPoint([0, 0, 0, 0])



Running the solver

bonminAlgorithm.run()

# Retrieving the results
result = bonminAlgorithm.getResult()
print(" -- Optimal point = " + str(result.getOptimalPoint()))
print(" -- Optimal value = " + str(result.getOptimalValue()))
print(" -- Evaluation number = " + str(result.getInputSample().getSize()))

-- Optimal point = [1,1,0.502856,0]
-- Optimal value = [-2.50286]
-- Evaluation number = 147