Mosel Language overview

Topics covered in this chapter:

Structure of a Mosel model

A Mosel model (text file with extension .mos) has the form

model model_name

  Compiler directives

  Parameters

  Body

end-model

Compiler directives

• Options are specified as a compiler directive, at the beginning of the model
• Options include explterm, which means that each statement must end with a semi-colon, and noimplicit, which forces all objects to be declared

  options explterm
  options noimplicit

• uses statements are also compiler directives

  uses "mmxprs", "mmodbc"

• Can define a version number for your model

  version 1.0.0

• Another set of compiler directives serves for the definition and configuration of namespaces

  namespace mynsp
  nssearch myns2

Run-time parameters

• Scalars (of type integer, real, boolean, or string) with a specified default value
• Their value may be reset when executing the model
• Use initializations from for inputting structured data (arrays, sets,...)
• At most one parameters block per model

Model body

• Model statements other than compiler directives and parameters, including any number of
  • declarations
  • initializations from / initializations to
  • functions and procedures

Implicit declaration

• Mosel does not require all objects to be declared
• Simple objects can be used without declaring them, if their type is obvious
• Use the noimplicit option to force all objects to be declared before using them (see item Compiler directives above)

Mosel statements

• Can extend over several lines and use spaces
• However, a line break acts as an expression terminator
• To continue an expression, it must be cut after a symbol that implies continuation (e.g. + - , * )

Data structures

array, set, list, record and any combinations thereof, e.g.,

S: set of list of integer
A: array(range) of set of real

Arrays

Array: collection of labeled objects of a given type where the label of an array entry is defined by its index tuple

declarations
  A: array(1..5) of real
  B: array(range, set of string) of integer
  x: array(1..10) of mpvar
end-declarations

A:: [4.5, 2.3, 7, 1.5, 10]
A(2):= 1.2
B:: (2..4,["ABC", "DE", "KLM"])[15,100,90,60,40,15,10,1,30]

Sets

Set: collection of objects of the same type without establishing an order among them (as opposed to arrays and lists)
Set elements are unique: if the same element is added twice the set still only contains it once.

declarations
  S: set of string
  R: range
end-declarations

S:= "A", "B", "C", "D"
R:= 1..10

Lists

List: collection of objects of the same type
A list may contain the same element several times. The order of the list elements is specified by construction.

declarations
  L: list of integer
  M: array(range) of list of string
end-declarations

L:= [1,2,3,4,5]
M:: (2..4)[['A','B','C'], ['D','E'], ['F','G','H','I']]

Records

Record: finite collection of objects of any type
Each component of a record is called a field and is characterized by its name and its type.

declarations
  ARC: array(ARCSET:range) of record
    Source,Sink: string      ! Source and sink of arc
    Cost: real               ! Cost coefficient
  end-record
end-declarations

ARC(1).Source:= "B"
ARC(3).Cost:= 1.5

User types

User types are treated in the same way as the predefined types of the Mosel language. New types are defined in declarations blocks by specifying a type name, followed by =, and the definition of the type.

declarations
  myreal = real
  myarray = array(1..10) of myreal
  COST: myarray
end-declarations

Union types

Union: container capable of holding an object of one of a predefined set of types.
Defined by specifying the set of compatible types or the predefined union type any.

declarations
  u: string or real              ! Scalar accepting 'string' or 'real'
  a: any                         ! Scalar accepting any type
 ! Defining a type name for the union of the 4 basic Mosel types:
  basictype = string or integer or real or boolean
  U: array(range) of basictype   ! Array of union type 'basictype'
end-declarations

Selection statements

if ... end-if

if c=1 then
  writeln('c equals 1')
end-if

if ... else ... end-if

if c=1 then
  writeln('c equals 1')
else
  writeln('c does not equal 1')
end-if

if ... elif ... else ... end-if

if c=1 then
  writeln('c equals 1')
elif c1 then
  writeln('c is bigger than 1')
else
  writeln('c is smaller than 1')
end-if

case ... end-case

case c of
  1,2 : writeln('c equals 1 or 2')
  3   : writeln('c equals 3')
  4..6: do
         writeln('c is in 4..6')
         writeln('c is not 1, 2 or 3')
        end-do
else
  writeln('c is not in 1..6')
end-case

Loops

forall

forall(f in FAC, t in TIME)
  make(f,t) = MAXCAP(f,t)

forall(t in TIME) do
  use(t) = MAXUSE(t)
  buy(t) = MAXBUY(t)
end-do

with

equivalent to a forall loop stopped after the first iteration

with f='F1', t=1 do
  make(f,t) = MAXCAP(f,t)
end-do

while

i := 1
while (i = 10) do
  write(' ', i)
  i += 1
end-do

repeat ... until

i := 1
repeat
  write(' ', i)
  i += 1
until (i  10)

break, next

• break jumps out of the current loop
• break n jumps out of n nested loops (where n is a positive integer)
• next jumps to the beginning of the next iteration of the current loop

counter

• Use the construct as counter to specify a counter variable in a bounded loop (i.e., forall or aggregate operators such as sum). At each iteration, the counter is incremented

cnt:=0.0
writeln("Average of odd numbers in 1..10: ",
        (sum(cnt as counter, i in 1..10 | isodd(i)) i) / cnt)

Operators

Assignment operators

i := 10
i += 20        ! Same as i := i + 20
i -=  5        ! Same as i := i - 5

Assignment operators with linear constraints

 

C := 5*x + 2*y = 20
D := C + 7*y

then D is

D := 5*x + 9*y - 20

The constraint type is dropped with :=

C := 5*x + 2*y = 20
C += 7*y

then C is

C := 5*x + 9*y = 20

The constraint type is retained with +=, -=

Arithmetic operators

 

standard:	+ - * /
power:	^
int. division/remainder:	mod div
sum:	sum(i in 1..10) ...
product:	prod(i in 1..10) ...
minimum/maximum:	min(i in 1..10) ...
count:	count(i in 1..10 | isodd(i))

Linear and non-linear expressions

 
Decision variables can be combined into linear or non-linear expressions using the arithmetic operators

• module mmxprs only works with linear constraints, so no prod, min, max, ...
• other solver modules, e.g., mmnl, mmxnlp, also accept (certain) non-linear expressions

Logical operators

 

constants:	true, false
standard:	and, or, not
AND:	and(i in 1..10) ...
OR:	or(i in 1..10) ...
comparison:	<, >, =, <>, <=, >=

Set operators

 

constants:	{'A', 'B'}
union:	+
union:	union(i in 1..10) ...
intersection:	*
intersection:	inter(i in 1..10) ...
difference:	-

Set comparison operators

 

subset:	Set1 <= Set2
superset:	Set1 >= Set2
equals:	Set1 = Set2
not equals:	Set1 <> Set2
element of:	"Oil5" in Set1
not element of:	"Oil5" not in Set1

List operators

 

constants:	[1, 2, 3]
concatenation:	+, sum
truncation:	-
equals:	L1 = L2
not equals:	L1 <> L2
enumeration:	i in L (within forall, sum etc.)

Union and reference operators

 
testing properties of unions:

! u declared as a union type, such as 'any'
writeln(u is array of integer)
writeln(u is not procedure)

'reference to' operator:

L:= [-cos,-sin,-arctan,-exp]
forall(f in L) writeln(f(0.5))

Built in functions and procedures

The following is a list of built in functions and procedures of the Mosel language (excluding modules). Functions return a value; procedures do not.

Dynamic array handling

create    exists    delcell   isdynamic

Freeze (finalize) a dynamic set

finalize

Rounding functions

ceil      floor     round     abs

Mathematical functions

exp       log       ln        sqrt
cos       sin       arctan
isodd

Special real values

isfinite  isinf     isnan 

Random number generator

random    setrandseed

Minimum/maximum of a list of values

v := minlist(5, 7, 2, 9)
w := maxlist(CAP(1), CAP(2))

Inline ``if'' function

MAX_INVEN(t) := if(t  MAX_TIME, 1000, 0)

Inven(t) := stock(t) = buy(t) - sell(t) +
              if(t  1, stock(t-1), 0)

Matrix export to file

exportprob    ! Outputs LP/MIP portion handled by
! Mosel core; use solver-specific routines such as
! 'writeprob' of mmxprs for complete matrix output

File handling

fopen         fclose        fselect
getfid        getfname      getreadcnt
iseof         fflush        fskipline
fwrite[_] / fwriteln[_]
read / readln   write[_] / writeln[_]  

String handling

strfmt        substr        _

Access and modify model objects

getcoeff[s]   setcoeff      getvars
gettype       settype       makesos1     makesos2
sethidden     ishidden      setname      setrange
getnbdim      getsize
getelt        getfirst      getlast      findfirst
findlast      gethead       gettail      cutelt
cutfirst      cutlast       cuthead      cuttail
reverse       getreverse    splithead    splittail

Access solution values

getobjval
getsol        getrcost
getslack      getact        getdual

Exit from a model

exit

Mosel controls

getparam      setparam    localsetparam  restoreparam

Date/time

currentdate   currenttime   timestamp

Bit value handling

bitflip       bitneg        bitset
bitshift      bittest       bitval

Handling unions

geteltype     getstruct     gettypeid    isdefined

Miscellaneous

asproc        assert        compare      datablock
dumpcallstack memoryuse     newmuid
publish       unpublish     reset
setioerr      setmatherr    versionnum    versionstr

• Overloading of subroutines
  • Some functions or procedures are overloaded: a single subroutine can be called with different types and numbers of arguments
• Additional subroutines are provided by Mosel library modules, which extend the basic Mosel language, e.g.,
  • mmxprs: Xpress Optimizer
  • mmodbc: ODBC data connection
  • mmsheet: accessing spreadsheets
  • mmsystem: system calls; text handling; date and time types
  • mmjobs: handling multiple models and (remote) Mosel instances
  • mmsvg: graphics
  ⇒See the `Mosel Language Reference Manual' for full details
• User-defined functions and procedures
  • You can also write your own functions and procedures within a Mosel model
  • Structure of subroutines is similar to a model (may have declarations blocks)
  • User subroutines may define overloaded versions of built in subroutines
  ⇒See examples in Chapter Functions and procedures
• Packages
  • Additional subroutines may also be provided through packages (Mosel libraries written in the Mosel language as opposed to Mosel modules that are implemented in C)
  ⇒See the Chapter Packages for further detail

Constraint handling

Ctr1:= 2*x + y = 10        ! Named constraints
Ctr2:= x is_integer

2*x + y = 10               ! Anonymous constraints
y = 5

Named constraints can be

accessed:

val:= getact(Ctr)
getvars(Ctr, vars)

hidden:

sethidden(Ctr, true)

redefined:

Ctr:= x+y = 10
Ctr:= 2*x+5*y = 5

modified:

Ctr += 2*x
settype(Ctr, CT_UNB)

deleted (reset):

Ctr:= 0

Anonymous constraints are constraints that are specified without assigning them to a linctr variable. Bounds are (to Mosel) just simple constraints without a name. Anonymous constraints are applied in the optimization problem just like ordinary constraints. The only difference is that it is not possible to refer to them again, either to modify them, or to examine their solution value.

Problem handling

• Mosel can handle several problems in a given model file. A default problem is associated with every model.
• Built in type mpproblem to identify mathematical programming problems
  • The same decision variable (type mpvar) may be used in several problems
  • Constraints (type linctr) belong to the problem where they are defined
• The statement with allows to open a problem (= select the active problem):

 declarations
   myprob: mpproblem
 end-declarations
 ...
 with myprob do
   x+y = 0
 end-do

• Modules can define other specific problem types. New problem types can also be defined by combining existing ones, for instance:

  mypbtyp = mpproblem and somepbtype

• Problem types support assignment: P1:= P2
  and additive assignment: P1 += P2