gc_pwl_func_vb.vb.
'版权所有2019，Gurobi O狗万app足彩ptimization，LLC''这个例子考虑以下非核解非线性问题''最大化2 x + y'对exp（x）+ 4 sqrt（y）<= 9'x，Y> = 0''我们向您展示两种解决方法：'1）使用分段 - 线性方法来处理一般函数'约束（如exp和sqrt）。' a) Add two variables ' u = exp(x) ' v = sqrt(y) ' b) Compute points (x, u) of u = exp(x) for some step length (e.g., x ' = 0, 1e-3, 2e-3, ..., xmax) and points (y, v) of v = sqrt(y) for ' some step length (e.g., y = 0, 1e-3, 2e-3, ..., ymax). We need to ' compute xmax and ymax (which is easy for this example, but this ' does not hold in general). ' c) Use the points to add two general constraints of type ' piecewise-linear. ' ' 2) Use the Gurobis built-in general function constraints directly (EXP ' and POW). Here, we do not need to compute the points and the maximal ' possible values, which will be done internally by Gurobi. In this ' approach, we show how to "zoom in" on the optimal solution and ' tighten tolerances to improve the solution quality. Imports System Imports Gurobi Class gc_pwl_func_vb Shared Function f(u As Double) As Double Return Math.Exp(u) End Function Shared Function g(u As Double) As Double Return Math.Sqrt(u) End Function Shared Sub printsol(m As GRBModel, x As GRBVar, _ y As GRBVar, u As GRBVar, v As GRBVar) Console.WriteLine("x = " & x.X & ", u = " & u.X) Console.WriteLine("y = " & y.X & ", v = " & v.X) Console.WriteLine("Obj = " & m.ObjVal) ' Calculate violation of exp(x) + 4 sqrt(y) <= 9 Dim vio As Double = f(x.X) + 4 * g(y.X) - 9 If vio < 0.0 Then vio = 0.0 End If Console.WriteLine("Vio = " & vio) End Sub Shared Sub Main() Try ' Create environment Dim env As New GRBEnv() ' Create a new m Dim m As New GRBModel(env) Dim lb As Double = 0.0 Dim ub As Double = GRB.INFINITY Dim x As GRBVar = m.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "x") Dim y As GRBVar = m.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "y") Dim u As GRBVar = m.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "u") Dim v As GRBVar = m.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "v") ' Set objective m.SetObjective(2*x + y, GRB.MAXIMIZE) ' Add linear constraint m.AddConstr(u + 4*v <= 9, "l1") ' PWL constraint approach Dim intv As Double = 1e-3 Dim xmax As Double = Math.Log(9.0) Dim npts As Integer = Math.Ceiling(xmax/intv) + 1 Dim xpts As Double() = new Double(npts -1) {} Dim upts As Double() = new Double(npts -1) {} For i As Integer = 0 To npts - 1 xpts(i) = i*intv upts(i) = f(i*intv) Next Dim gc1 As GRBGenConstr = m.AddGenConstrPWL(x, u, xpts, upts, "gc1") Dim ymax As Double = (9.0/4.0)*(9.0/4.0) npts = Math.Ceiling(ymax/intv) + 1 Dim ypts As Double() = new Double(npts -1) {} Dim vpts As Double() = new Double(npts -1) {} For i As Integer = 0 To npts - 1 ypts(i) = i*intv vpts(i) = g(i*intv) Next Dim gc2 As GRBGenConstr = m.AddGenConstrPWL(y, v, ypts, vpts, "gc2") ' Optimize the model and print solution m.Optimize() printsol(m, x, y, u, v) ' General function approach with auto PWL translation by Gurobi m.Reset() m.Remove(gc1) m.Remove(gc2) m.Update() Dim gcf1 As GRBGenConstr = m.AddGenConstrExp(x, u, "gcf1", "") Dim gcf2 As GRBGenConstr = m.AddGenConstrPow(y, v, 0.5, "gcf2", "") m.Parameters.FuncPieceLength = 1e-3 ' Optimize the model and print solution m.Optimize() printsol(m, x, y, u, v) ' Use optimal solution to reduce the ranges and use smaller pclen to solve x.LB = Math.Max(x.LB, x.X-0.01) x.UB = Math.Min(x.UB, x.X+0.01) y.LB = Math.Max(y.LB, y.X-0.01) y.UB = Math.Min(y.UB, y.X+0.01) m.Update() m.Reset() m.Parameters.FuncPieceLength = 1e-5 ' Optimize the model and print solution m.Optimize() printsol(m, x, y, u, v) ' Dispose of model and environment m.Dispose() env.Dispose() Catch e As GRBException Console.WriteLine("Error code: " + e.ErrorCode + ". " + e.Message) End Try End Sub End Class
