(!****************************************************** Mosel Example Problems ====================== file foliocbio.mos `````````````````` Modeling a MIP problem to perform portfolio optimization. Same model as in foliomip3.mos. -- Defining an integer solution callback to write out solution information to external program -- *** This model cannot be run with a Community Licence for the provided data instance *** (c) 2011 Fair Isaac Corporation author: S.Heipcke, July 2011, rev. Mar. 2022 *******************************************************!) model "Portfolio optimization with MIP" uses "mmxprs" uses "mmjobs" parameters MAXRISK = 1/3 ! Max. investment into high-risk values MINREG = 0.2 ! Min. investment per geogr. region MAXREG = 0.5 ! Max. investment per geogr. region MAXSEC = 0.25 ! Max. investment per ind. sector MAXVAL = 0.2 ! Max. investment per share MINVAL = 0.1 ! Min. investment per share MAXNUM = 15 ! Max. number of different assets DATAFILE = "folio250.dat" ! File with problem data OUTPUTFILE = "sol10out.dat" ! File for solution output FRACSOL = "FRAC" ! Locations for solution output BUYSOL = "BUY" NUMSHARES = "NUMSHARES" RETSOL = "RETSOL" SOLCOUNT = "SOLCOUNT" end-parameters forward procedure printsol declarations SHARES,S: 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 end-declarations initializations from DATAFILE RISK RET LOC SEC end-initializations 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 end-declarations ! Objective: total return Return:= sum(s in SHARES) RET(s)*frac(s) ! Limit the percentage of high-risk values sum(s in RISK) frac(s) <= MAXRISK ! Limits on geographical distribution forall(r in REGIONS) do sum(s in LOC(r)) frac(s) >= MINREG sum(s in LOC(r)) frac(s) <= MAXREG end-do ! Diversification across industry sectors forall(t in TYPES) 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 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 end-do ! Display Optimizer log setparam("XPRS_verbose", true) ! Adapt Mosel comparison tolerance to Optimizer feasibility tolerance setparam("zerotol", getparam("XPRS_feastol")/10) ! Set a MIP solution callback setcallback(XPRS_CB_INTSOL, ->printsol) ! Solve the problem maximize(Return) if getprobstat <> XPRS_OPT then exit(1); end-if !******** Solution output******** !**** Auxiliary function creating an array of solution values **** function getvalues(v: array(SHARES) of mpvar): dynamic array(S) of real forall(s in SHARES | v(s).sol<>0) returned(s):= v(s).sol end-function !**** Definition of the MIP solution callback function **** procedure printsol initializations to OUTPUTFILE evaluation of getparam("XPRS_MIPSOLS") as SOLCOUNT evaluation of sum(s in SHARES | buy(s).sol<>0) 1 as NUMSHARES evaluation of getsol(Return) as RETSOL evaluation of getvalues(frac) as FRACSOL evaluation of getvalues(buy) as BUYSOL end-initializations end-procedure end-model