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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