(!********************************************************************* Mosel NL examples ================= file emfl.mos ````````````` Euclidean facility location problem Convex NLP problem Based on AMPL model emfl_eps.mod Source: http://www.orfe.princeton.edu/~rvdb/ampl/nlmodels/facloc/ *** This model cannot be run with a Community Licence for the provided data instance *** (c) 2008 Fair Issac Corporation author: S. Heipcke, Sep. 2008, rev. Jun. 2023 *********************************************************************!) model "emfl" uses "mmxnlp" parameters EPS = 0 M = 200 ! Number of existing facilities N1 = 5 N2 = 5 end-parameters declarations N = N1*N2 ! Number of new facilities RM = 1..M ! Set of existing facilities R2 = 1..2 RN = 1..N ! Set of new facilities POS: array(RM,R2) of real ! Coordinates of existing facility WEIGHTON: array(RM,RN) of real ! Weights associated with old-new connections WEIGHTNN: array(RN,RN) of real ! Weights associated with new-new connections IVAL: array(RN,R2) of real ! Start values for x x: array(RN,R2) of mpvar ! Coordinates of new facilities end-declarations forall(i in RN,j in R2) x(i,j) is_free setrandseed(3) forall(i in RM, k in 1..2) POS(i,k):= random forall(j in RN, jj in RN | j < jj) WEIGHTNN(j,jj):= 0,2 forall(j1 in 1..N1, j2 in 1..N2) do IVAL(j1+N1*(j2-1),1):= (j1-0,5)/N1 IVAL(j1+N1*(j2-1),2):= (j2-0,5)/N2 setinitval(x(j1+N1*(j2-1),1), IVAL(j1+N1*(j2-1),1)) setinitval(x(j1+N1*(j2-1),2), IVAL(j1+N1*(j2-1),2)) end-do forall(i in RM, j in RN) WEIGHTON(i,j):= if(abs(POS(i,1)-IVAL(j,1)) <= 1/(2*N1) and abs(POS(i,2)-IVAL(j,2)) <= 1/(2*N2), 0.95, if(abs(POS(i,1)-IVAL(j,1)) <= 2/(2*N1) and abs(POS(i,2)-IVAL(j,2)) <= 2/(2*N2), 0.05, 0) ) ! Objective function: distances ! A small positive constant 'EPS' is added to make sure 'sqrt' is differentiable SumEucl:= sum(i in RM,j in RN) WEIGHTON(i,j)*sqrt(EPS + sum(k in R2) (x(j,k)-POS(i,k))^2) + sum(j,jj in RN | j<jj) WEIGHTNN(j,jj)*sqrt(EPS + sum(k in R2) (x(j,k)-x(jj,k))^2) setparam("XNLP_verbose", true) ! Since this is a convex problem, it is sufficient to call a local solver setparam("xprs_nlpsolver", 1) setparam("XNLP_solver", 0) ! Solver choice: Xpress NonLinear (SLP) minimise(SumEucl) writeln("Solution: ", SumEucl.sol, " (eps), ", getsol(sum(i in RM,j in RN) WEIGHTON(i,j)*sqrt(sum(k in R2) (x(j,k)-POS(i,k))^2) + sum(j,jj in RN | j<jj) WEIGHTNN(j,jj)*sqrt(sum(k in R2) (x(j,k)-x(jj,k))^2)) ) forall(i in RN) do write(i, ": ") forall(j in R2) write(x(i,j).sol, ", ") writeln end-do end-model