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piecewise_vb.vb
' Copyright 2022, Gurobi Optimization, LLC ' This example considers the following separable, convex problem: ' ' minimize f(x) - y + g(z) ' subject to x + 2 y + 3 z <= 4 ' x + y >= 1 ' x, y, z <= 1 ' ' where f(u) = exp(-u) and g(u) = 2 u^2 - 4 u, for all real u. It ' formulates and solves a simpler LP model by approximating f and ' g with piecewise-linear functions. Then it transforms the model ' into a MIP by negating the approximation for f, which corresponds ' to a non-convex piecewise-linear function, and solves it again. Imports System Imports Gurobi Class piecewise_vb Shared Function f(u As Double) As Double Return Math.Exp(-u) End Function Shared Function g(u As Double) As Double Return 2 * u * u - 4 * u End Function Shared Sub Main() Try ' Create environment Dim env As New GRBEnv() ' Create a new model Dim model As New GRBModel(env) ' Create variables Dim lb As Double = 0.0, ub As Double = 1.0 Dim x As GRBVar = model.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "x") Dim y As GRBVar = model.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "y") Dim z As GRBVar = model.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "z") ' Set objective for y model.SetObjective(-y) ' Add piecewise-linear objective functions for x and z Dim npts As Integer = 101 Dim ptu As Double() = New Double(npts - 1) {} Dim ptf As Double() = New Double(npts - 1) {} Dim ptg As Double() = New Double(npts - 1) {} For i As Integer = 0 To npts - 1 ptu(i) = lb + (ub - lb) * i / (npts - 1) ptf(i) = f(ptu(i)) ptg(i) = g(ptu(i)) Next model.SetPWLObj(x, ptu, ptf) model.SetPWLObj(z, ptu, ptg) ' Add constraint: x + 2 y + 3 z <= 4 model.AddConstr(x + 2 * y + 3 * z <= 4.0, "c0") ' Add constraint: x + y >= 1 model.AddConstr(x + y >= 1.0, "c1") ' Optimize model as an LP model.Optimize() Console.WriteLine("IsMIP: " & model.IsMIP) Console.WriteLine(x.VarName & " " & x.X) Console.WriteLine(y.VarName & " " & y.X) Console.WriteLine(z.VarName & " " & z.X) Console.WriteLine("Obj: " & model.ObjVal) Console.WriteLine() ' Negate piecewise-linear objective function for x For i As Integer = 0 To npts - 1 ptf(i) = -ptf(i) Next model.SetPWLObj(x, ptu, ptf) ' Optimize model as a MIP model.Optimize() Console.WriteLine("IsMIP: " & model.IsMIP) Console.WriteLine(x.VarName & " " & x.X) Console.WriteLine(y.VarName & " " & y.X) Console.WriteLine(z.VarName & " " & z.X) Console.WriteLine("Obj: " & model.ObjVal) ' Dispose of model and environment model.Dispose() env.Dispose() Catch e As GRBException Console.WriteLine("Error code: " + e.ErrorCode & ". " + e.Message) End Try End Sub End Class