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Folio - Advanced modelling and solving tasks

Advanced modelling and solving tasks for a portfolio optimization problem:
  • Automated solver tuning (foliolptune.mos)
  • Defining an integer solution callback (foliocb.mos)
  • Using the solution enumerator for multiple MIP solutions (folioenumsol.mos)
  • Handling infeasibility
    • handling infeasibility through deviation variables (folioinfeas.mos)
    • retrieving infeasible row/column from presolve (folioinfcause.mos)
    • retrieving IIS - LP or MIP infeasible (folioiis.mos, foliomiis.mos)
    • using the built-in infeasibility repair functionality (foliorep.mos)
    • same as foliorep, using an 'mpsol' object (foliorep_sol.mos)
  • Data transfer in memory
    • running foliomemio.mos with data transfer in memory (runfolio.mos)
    • same running foliomemio2.mos, grouping tables with identical index sets in "initializations" blocks (runfolio2.mos)
    • master model running several model instances in parallel (runfoliopar.mos)
  • Remote models on a distributed architecture
    • running foliomemio.mos on a remote instance of Mosel (runfoliodistr.mos)
    • master model running several model instances in parallel, each on a different (remote) instance of Mosel (runfoliopardistr.mos)
  • Remote execution via XPRD
    • See examples in the Mosel Whitepapers directory moselpar/XPRD
  • XML and JSON data formats
    • reading data from an XML file, solution output in XML format on screen and to a new file (folioxml.mos, folioxmlqp.mos)
    • generate HTML output file as an XML document (runfolioxml.mos)
    • using JSON-format data files, reading data from a JSON file, solution output in JSON format on screen and to a new file (foliojson.mos)
  • HTTP
    • starting an HTTP server managing requests from HTTP clients (foliohttpsrv.mos)
    • HTTP client exchanging XML data files with an HTTP server (foliohttpclient.mos)

Source Files

Data Files


   Mosel Example Problems

   file foliorep_sol.mos
   Modeling a MIP problem 
   to perform portfolio optimization.

   Same model as in foliomip3.mos.
   -- Infeasible model parameter values --
   -- Repairing infeasibilities --
   -- Storing solutions in an mpsol object --
  (c) 2014 Fair Isaac Corporation
      author: S.Heipcke, Sep. 2014, rev. Sep. 2018

model "Portfolio optimization with MIP"
 uses "mmxprs"

  MAXRISK = 1/3                     ! Max. investment into high-risk values
  MINREG = 0.3                      ! Min. investment per geogr. region
  MAXREG = 0.5                      ! Max. investment per geogr. region
  MAXSEC = 0.15                     ! Max. investment per ind. sector
  MAXVAL = 0.2                      ! Max. investment per share
  MINVAL = 0.1                      ! Min. investment per share
  MAXNUM = 4                        ! Max. number of different assets
  DATAFILE = "folio10.dat"          ! File with problem data

 forward procedure print_sol
 forward procedure print_violated

  SHARES: set of string              ! Set of shares
  RISK: set of string                ! Set of high-risk values among shares
  REGIONS: set of string             ! Geographical regions
  TYPES: set of string               ! Share types (ind. sectors)
  LOC: array(REGIONS) of set of string ! Sets of shares per geogr. region
  RET: array(SHARES) of real         ! Estimated return in investment
  SEC: array(TYPES) of set of string ! Sets of shares per industry sector

 initializations from DATAFILE

 public declarations
  frac: array(SHARES) of mpvar      ! Fraction of capital used per share
  buy: array(SHARES) of mpvar       ! 1 if asset is in portfolio, 0 otherwise
  Return: linctr                    ! Total return
  LimitRisk: linctr                 ! Max. percentage of high-risk values
  LimitMinReg,LimitMaxReg: array(REGIONS) of linctr  ! Min/max perc. per region
  LimitSec: array(TYPES) of linctr  ! Max. percentage per industry sector
  LimitNum: linctr                  ! Max. total number of assets

! Objective: total return
 Return:= sum(s in SHARES) RET(s)*frac(s) 

! Limit the percentage of high-risk values
 LimitRisk:= sum(s in RISK) frac(s) <= MAXRISK

! Limits on geographical distribution
 forall(r in REGIONS) do
  LimitMinReg(r):= sum(s in LOC(r)) frac(s) >= MINREG
  LimitMaxReg(r):= sum(s in LOC(r)) frac(s) <= MAXREG

! Diversification across industry sectors
 forall(t in TYPES) LimitSec(t):= sum(s in SEC(t)) frac(s) <= MAXSEC

! Spend all the capital
 sum(s in SHARES) frac(s) = 1
! Upper bounds on the investment per share
 forall(s in SHARES) frac(s) <= MAXVAL

! Limit the total number of assets
 LimitNum:= sum(s in SHARES) buy(s) <= MAXNUM

 forall(s in SHARES) do
  buy(s) is_binary                  ! Turn variables into binaries
  frac(s) <= MAXVAL*buy(s)                 ! Linking the variables
  frac(s) >= MINVAL*buy(s)                 ! Linking the variables

! Display Optimizer log
! setparam("XPRS_verbose", true)

! Solve the problem
! maximize(XPRS_LIN,Return)
!**** Infeasibility repair + reporting ****

  Alrp,Agrp: array(linctr) of real  ! Selectors for LEG / GEQ constraints
  Albp,Aubp: array(mpvar) of real   ! Selector for lower / upper bounds on vars
  rstat: array(range) of string     ! Status message text

 probstat:= getprobstat
 case probstat of
  XPRS_OPT: writeln("Problem solved")
  XPRS_INF: do 
             ! Must use the detailed infeasibility repair method since
	     ! only some constraints of each type may be relaxed
              forall(r in REGIONS) Alrp(LimitMaxReg(r)):=1
	      forall(t in TYPES) Alrp(LimitSec(t)):=1
              forall(r in REGIONS) Agrp(LimitMinReg(r)):=1

	      rstat::(0..5)["relaxed optimum found", 
	        "relaxed problem infeasible", "relaxed problem unbounded", 
                "solution nonoptimal for original objective",
                "error", "numerical instability"]

	      while (delta<10) do
	       setparam("XPRS_MAXTIME", -10)
!	       setparam("XPRS_VERBOSE", false)

               ! Option 'r': repairinfeas reports the relaxed constraints/bounds
                repairinfeas(Alrp, Agrp, Albp, Aubp, 'r', delta, "")
		repstatus:= getprobstat
                write("delta = ", delta, ": ")
                case probstat of
                  XPRS_OPT: writeln("Relaxed problem solved")
                  XPRS_INF: writeln("Relaxed problem infeasible")
                  XPRS_OTH: writeln("Relaxed problem unbounded") 
                  XPRS_UNF: writeln("Repairinfeas has been terminated")
                  else writeln("Unknown problem status")

               ! Display the relaxed solution
               ! Programmatic checking of constraint violations
                delta:= delta*10
  XPRS_OTH: writeln("Problem unbounded") 
  XPRS_UNF: writeln("Optimization unfinished")
  else writeln("Unknown problem status")

!**** Solution printing ****
 procedure print_sol
  writeln("  Total return: ", getsol(Return))
  forall(s in SHARES | getsol(frac(s))>0)
   writeln("  ", s, ": ", getsol(frac(s))*100, "% (", getsol(buy(s)), ")")

!**** Display violated  constraints ****
 procedure print_violated
   Solution: mpsol
   AllCtr: set of linctr
  writeln(" Violated (relaxed) constraints:")
  forall(c in AllCtr) 
   case gettype(c) of
    CT_EQ:  if abs(getsol(Solution,c))>EPS then
             writeln("   = constraint ", getname(c), " by ", getsol(Solution,c))
    CT_GEQ: if getsol(Solution,c)<-EPS then
             writeln("  >= constraint ", getname(c), " by ", getsol(Solution,c))
    CT_LEQ: if getsol(Solution,c)>EPS then
             writeln("  <= constraint ", getname(c), " by ", getsol(Solution,c))


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