(!********************************************************************* Mosel NL examples ================= file polygon6.mos ````````````````` Maximize the area of polygon of N vertices and diameter of 1. The position of vertices is indicated as (rho,theta) coordinates where rho denotes the distance to the base point (vertex with number N) and theta the angle from the x-axis. -- Formulation using a multi-valued function of type Excel Macro (XLF) -- (c) 2008 Fair Issac Corporation Creation: 2002, rev. Feb. 2013 *********************************************************************!) model "Polygon 6" uses "mmxnlp" parameters N=5 ! Number of vertices SOLVER=0 ! 0: SLP, 1: Knitro end-parameters declarations RN = 1..N Area: nlctr rho : array(RN) of mpvar ! Distance of vertex from the base point theta : array(RN) of mpvar ! Angle from x-axis D: array(RN,RN) of nlctr ! Limit on side length FunctionArg: list of nlctr ! User function arguments AreaFunction: userfunc ! User function definition k: integer end-declarations ! Objective: sum of areas. Definition of a user function AreaFunction := userfuncExcelMacro("polygonmacro.xls", "Sheet1", "ArrayArea") ! Create function arguments ! Excel functions use their first columns as input: use a list to ensure correct order forall (i in 1..N) do FunctionArg += [nlctr(rho(i))] FunctionArg += [nlctr(theta(i))] end-do ! Use the Excel user function in a formula for the objective Area := F(AreaFunction, FunctionArg, 1) ! Bounds and start values for decision variables forall (i in 1..N-1) do rho(i) >= 0,1 rho(i) <= 1 setinitval(rho(i),4*i*(N + 1 - i)/((N+1)^2)) setinitval(theta(i),M_PI*i/N) end-do ! Third side of all triangles <= 1 k := 2 forall (i in 1..N-2, j in i+1..N-1, k as counter) D(i,j) := F(AreaFunction, FunctionArg, k) <= 1 ! Vertices in increasing order forall (i in 2..N-1) theta(i) >= theta(i-1) +.01 ! Boundary conditions (last vertex above x-axis) theta(N-1) <= M_PI ! Uncomment to display user function info ! userfuncinfo(AreaFunction) ! Optional parameter settings ! setparam("xnlp_verbose", true) ! Enable XNLP output log setparam("xnlp_solver", SOLVER) ! Select the solver ! Solve the problem maximise(Area) ! Solution output writeln("Area = ", getobjval) forall (i in 1..N-1) writeln("V",i,": r=",getsol(rho(i))," theta=",getsol(theta(i))) end-model