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Optimization using HiGHS solverΒΆ

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

import openturns as ot
import openturns.experimental as otexp

The following example will demonstrate the use of HiGHS solver to solve the following problem:

\max x + y + 2 z

subject to:

\begin{array}{l} x + 2 y + 3 z \leq 4\\ x + y \ge 1\\ x, x, z \in \{0,1\}^3\\ \end{array}

Definition of objective function as a cost vector

cost = [1, 1, 2]

Definition of constraints in the form L<=Ax<=U

LU = ot.Interval([-1e30, 1], [4, 1e30])
A = ot.Matrix([[1, 2, 3], [1, 1, 0]])

Definition of variables types

BINARY = ot.OptimizationProblemImplementation.BINARY
variablesType = [BINARY] * 3
bounds = ot.Interval(3)

Define the linear problem

problem = otexp.LinearProblem(cost, bounds, A, LU)
problem.setVariablesType(variablesType)
problem.setMinimization(False)

Run the algorithm

algo = otexp.HiGHS(problem)
algo.setStartingPoint([0.0] * 3)

Running the solver

algo.run()

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

-- Optimal point = [1,0,1]
-- Optimal value = [3]
-- Evaluation number = 0