Try our new documentation site (beta).


multiobj_vb.vb


' Copyright 2019, Gurobi Optimization, LLC

' Want to cover three different sets but subject to a common budget of
' elements allowed to be used. However, the sets have different priorities to
' be covered; and we tackle this by using multi-objective optimization.

Imports Gurobi

Class multiobj_vb

    Shared Sub Main()

        Try
            ' Sample data
            Dim groundSetSize As Integer = 20
            Dim nSubsets As Integer = 4
            Dim Budget As Integer = 12

            Dim [Set] As Double(,) = New Double(,) { _
                {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, _
                {0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1}, _
                {0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0}, _
                {0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0}}

            Dim SetObjPriority As Integer() = New Integer() {3, 2, 2, 1}
            Dim SetObjWeight As Double() = New Double() {1.0, 0.25, 1.25, 1.0}
            Dim e As Integer, i As Integer, status As Integer, nSolutions As Integer

            ' Create environment
            Dim env As New GRBEnv("multiobj_vb.log")

            ' Create initial model
            Dim model As New GRBModel(env)
            model.ModelName = "multiobj_vb"

            ' Initialize decision variables for ground set:
            ' x[e] == 1 if element e is chosen for the covering.
            Dim Elem As GRBVar() = model.AddVars(groundSetSize, GRB.BINARY)
            For e = 0 To groundSetSize - 1
                Dim vname As String = "El" & e.ToString()
                Elem(e).VarName = vname
            Next

            ' Constraint: limit total number of elements to be picked to be at most
            ' Budget
            Dim lhs As New GRBLinExpr()
            For e = 0 To groundSetSize - 1
                lhs.AddTerm(1.0, Elem(e))
            Next
            model.AddConstr(lhs, GRB.LESS_EQUAL, Budget, "Budget")

            ' Set global sense for ALL objectives
            model.ModelSense = GRB.MAXIMIZE

            ' Limit how many solutions to collect
            model.Parameters.PoolSolutions = 100

            ' Set and configure i-th objective
            For i = 0 To nSubsets - 1
                Dim vname As String = String.Format("Set{0}", i)
                Dim objn As New GRBLinExpr()
                For e = 0 To groundSetSize - 1
                    objn.AddTerm([Set](i, e), Elem(e))
                Next

                model.SetObjectiveN(objn, i, SetObjPriority(i), SetObjWeight(i), _
                                    1.0 + i, 0.01, vname)
            Next

            ' Save problem
            model.Write("multiobj_vb.lp")

            ' Optimize
            model.Optimize()

            ' Status checking
            status = model.Status

            If status = GRB.Status.INF_OR_UNBD OrElse _
               status = GRB.Status.INFEASIBLE OrElse _
               status = GRB.Status.UNBOUNDED Then
                Console.WriteLine("The model cannot be solved " & _
                         "because it is infeasible or unbounded")
                Return
            End If
            If status <> GRB.Status.OPTIMAL Then
                Console.WriteLine("Optimization was stopped with status {0}", status)
                Return
            End If

            ' Print best selected set
            Console.WriteLine("Selected elements in best solution:")
            Console.Write(vbTab)
            For e = 0 To groundSetSize - 1
                If Elem(e).X < 0.9 Then
                    Continue For
                End If
                Console.Write("El{0} ", e)
            Next
            Console.WriteLine()

            ' Print number of solutions stored
            nSolutions = model.SolCount
            Console.WriteLine("Number of solutions found: {0}", nSolutions)

            ' Print objective values of solutions
            If nSolutions > 10 Then
                nSolutions = 10
            End If
            Console.WriteLine("Objective values for first {0} solutions:", nSolutions)
            For i = 0 To nSubsets - 1
                model.Parameters.ObjNumber = i

                Console.Write(vbTab & "Set" & i)
                For e = 0 To nSolutions - 1
                    model.Parameters.SolutionNumber = e
                    Console.Write("{0,8}", model.ObjNVal)
                Next
                Console.WriteLine()
            Next

            model.Dispose()
            env.Dispose()

        Catch e As GRBException
            Console.WriteLine("Error code = {0}", e)
            Console.WriteLine(e.Message)

        End Try
    End Sub
End Class

Try Gurobi for Free

Choose the evaluation license that fits you best, and start working with our Expert Team for technical guidance and support.

Evaluation License
Get a free, full-featured license of the Gurobi Optimizer to experience the performance, support, benchmarking and tuning services we provide as part of our product offering.
Academic License
Gurobi supports the teaching and use of optimization within academic institutions. We offer free, full-featured copies of Gurobi for use in class, and for research.
Cloud Trial

Request free trial hours, so you can see how quickly and easily a model can be solved on the cloud.

Search

Gurobi Optimization