! XNLP example demonstrating the role of setting the value of penalty multipliers
! and demonstrating the effect of the penalty terms in the solution process
! and also the role of nonlinear infeasiblity
!
! This is an SLP specific example.
! In this example a hihgly combinatorial and hihgly nonlienar problem is solved.
! The high constraint nonlinear gives rise to very large violations that needs
! attention otherwise SLP overcompensates.
! The example also demonstrates how feasibility and integrality might interact in
! an MINLP search.
!
! This example demonstrates a particular non-linear optimization concept as related
! to Xpress NonLinear.
! The version of the example is for Xpress 7.5.
!
! (c) 2013 Fair Isaac Corporation
! author: Zsolt Csizmadia
!
! Based on AMPL model seven11.mod by M.J.Chlond
! Source: alt.math.recreational
! Mosel version by S.Heipcke
model "seven11"
uses "mmxnlp", "mmsystem"
! A function to translate the status of the solver ot text
public function nlpstatustext(val: integer): text
case val of
XNLP_STATUS_UNSTARTED: returned:= "NLP solving not started."
XNLP_STATUS_LOCALLY_OPTIMAL: returned:= "Local optimum found."
XNLP_STATUS_OPTIMAL: returned:= "Optimal solution found."
XNLP_STATUS_LOCALLY_INFEASIBLE: returned:= "NLP locally infeasible."
XNLP_STATUS_INFEASIBLE: returned:= "Problem is infeasible."
XNLP_STATUS_UNBOUNDED: returned:= "Problem is unbounded."
XNLP_STATUS_UNFINISHED: returned:= "NLP solving unfinished."
end-case
end-function
declarations
m = 4 ! Number of variables
M = 1..m
x: array(M) of mpvar
start : real;
end-declarations
!setparam("xnlp_verbose",true)
forall(i in M) x(i) is_integer
forall(i in M) x(i) >= 1
forall(i in M) x(i) <= 708
711 = sum(i in M) x(i)
711000000 = x(1)*x(2)*x(3)*x(4)
! Solve the problem using SLP
writeln("Solving seven11 using defaults:")
setparam("xnlp_solver",XNLP_SOLVER_XSLP)
start := gettime
minimize(0)
writeln(" solver returned status = ",nlpstatustext(getparam("XNLP_STATUS")),
" in ", gettime-start,"s")
writeln
writeln
! The solution out of the box with SLP will fail due to unresonable error costs
! and automatic row enforcement
! This is due to the very large deviation from the nonlienar surface, and the
! consequent very large error cost
setcallback(XSLP_CB_INTSOL, "IntegerSolutionCallback")
! Set the initial errorcost small. This can be done freely, as there is no
! net objective in the model to consider
! Observe the unexpected objetcive values in the MIP search
! As the very last iteration shows, those are in fact the errorcosts!
setparam("xslp_errormaxcost",1)
writeln("Solving seven11 using reduced errormaxcost:")
start := gettime
minimize(0)
writeln(" solver returned status = ",nlpstatustext(getparam("XNLP_STATUS")),
" in ", gettime-start,"s")
writeln
writeln
! The solution is to address the accuracy in terms of the feasibility of the
! nonlienar constraints
setparam("xslp_ecftol_a",1e-6)
setparam("xslp_ecftol_r",1e-6)
writeln("Solving seven11 using reduced errormaxcost and stricter feasibility ",
"requirements:")
start := gettime
minimize(0)
writeln(" solver returned status = ",nlpstatustext(getparam("XNLP_STATUS")),
" in ", gettime-start,"s")
writeln
writeln
! final solution printing
forall(i in M) writeln(i, ": ", getsol(x(i)))
! Printing a solution while performing the MIP search
function IntegerSolutionCallback:integer
writeln("+Integer solution:")
write(" ")
forall(i in M) write("x(",i,")=", getsol(x(i))," ")
writeln
writeln(" Sum = ", sum(i in M) getsol(x(i)))
writeln(" Prod = ", floor(x(1).sol*x(2).sol*x(3).sol*x(4).sol))
end-function
end-model
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