(!********************************************************************* Mosel NL examples ================= file sphere.mos ``````````````` Find the eqilibrium state distribution of electrons positioned on a conducting sphere. Nonconvex NLP problem. - Alternative objective functions selected via parameter ALG - Based on AMPL model fekete.mod Source: http://www.orfe.princeton.edu/~rvdb/ampl/nlmodels/fekete/ *** This model cannot be run with a Community Licence for the provided data instance *** (c) 2013 Fair Issac Corporation author: S. Heipcke, Mar. 2013, rev. Jun. 2023 *********************************************************************!) model "Points on sphere" uses "mmxnlp" parameters NP = 50 MDIM = 3 ALG = 2 ! 0: minimize z, 1: maximize Separation, 2: minimize Potential end-parameters declarations POINTS = 1..NP ! Set of points to place DIMS = 1..MDIM ! Dimensions x: array(POINTS, DIMS) of mpvar ! Coordinate tuples z: mpvar ! Objective variable end-declarations ! Set initial values (= randomly distributed points on the sphere) setrandseed(3) if MDIM=2 then forall(i in POINTS) do theta(i):= 2*M_PI*random setinitval(x(i,1), cos(theta(i)) ) setinitval(x(i,2), sin(theta(i)) ) end-do elif MDIM=3 then forall(i in POINTS) do theta(i):= 2*M_PI*random phi(i):= M_PI*random setinitval(x(i,1), cos(theta(i))*sin(phi(i)) ) setinitval(x(i,2), sin(theta(i))*sin(phi(i)) ) setinitval(x(i,3), cos(phi(i)) ) end-do end-if forall (i in 1..NP, j in DIMS) x(i,j) is_free ! Alternative objective function definitions forall (i,j in POINTS | i<j) in <=z Separation:=sum(i,j POINTS Potential:=sum(i,j All points lie on the sphere x(i,k)^2=1.0 Setting up and solving problem In this example we will use a local since it can be time consuming to solve global optimality case ALG of Maximize separation between Minimize potential energy else optimization goal end-case Test whether solution is available nlstat:=getparam("XNLP_STATUS") if>XNLP_STATUS_LOCALLY_OPTIMAL and nlstat<>XNLP_STATUS_OPTIMAL then writeln("No solution found.") exit(0) end-if ! Display the results writeln("Value of z = ", z.sol) writeln("Potential = ", Potential.sol) writeln("Separation = ", Separation.sol) forall(i in POINTS) do write(" x(", i, ") = [") forall(k in DIMS) write(x(i,k).sol, if(k