task_serialize

Purpose

Creates a Task Serializer branching scheme that serializes the tasks passed in argument. The branching consists in choosing one task to schedule. Then a branch is created for each possible duration for this task. Once the duration is determined a branch is created for each posssible starting values for this task. When the start and the duration are fixed, the task is scheduled and the process is repeated until all the tasks are serialized.
Scheduling/taskSerializer.png

Synopsis

function task_serialize(taskSelector:string or function, durationHeuristic:string or function, startHeuristic:string or function, tasks:set of cptask) : cpbranching

function task_serialize(taskSelector:string or function, durationHeuristic:string or function, startHeuristic:string or function, tasks:array of cptask) : cpbranching

function task_serialize(taskSelector:string or function, durationHeuristic:string or function, startHeuristic:string or function, tasks:set of cptask, limit:integer) : cpbranching

function task_serialize(taskSelector:string or function, durationHeuristic:string or function, startHeuristic:string or function, tasks:array of cptask, limit:integer) : cpbranching

function task_serialize(taskSelector:string or function, durationHeuristic:string or function, startHeuristic:string or function, tasks:set of cptask, limit:integer, varOrder:integer) : cpbranching

function task_serialize(taskSelector:string or function, durationHeuristic:string or function, startHeuristic:string or function, tasks:array of cptask, limit:integer, varOrder:integer) : cpbranching

function task_serialize(taskSelector:string or function, durationHeuristic:string or function, startHeuristic:string or function, assignSelector:string or function, assignHeuristic:string or function, tasks:array of cptask, limit:integer, varOrder:integer) : cpbranching

function task_serialize(taskSelector:string or function, durationHeuristic:string or function, startHeuristic:string or function, assignSelector:string or function, assignHeuristic:string or function, tasks:set of cptask, limit:integer, varOrder:integer) : cpbranching

Arguments

taskSelector

the task selector (pre-defined constant, name of user-defined function or reference to user-defined function)

durationHeuristic

the task duration assignment heuristic (pre-defined constant, name of user-defined function or reference to user-defined function)

startHeuristic

the task start time assignment heuristic (pre-defined constant, name of user-defined function or reference to user-defined function)

assignSelector

a variable selection heuristic to choose among assignments of resources provided, produced, required or consumed by the task (pre-defined constant, name of user-defined function or reference to user-defined function)

assignHeuristic

a value selection heuristic (pre-defined constant, name of user-defined function or reference to user-defined function)

tasks

the set of tasks to be serialized.

limit

discrepancy limit: value 0 means strictly following the branching scheme, positive values indicate the permissible number of deviations from the branching scheme. It can be set to MAX_INT for no limitations.

varOrder

the branching order of the variables resource assignment (A), start (S) and duration (D) of one task, values can be:

0	A→D→S
1	A→S→D
2	D→S→A
3	D→A→S
4	S→D→A
5	S→A→D

Return value

The resulting Task Serializer branching scheme

Example

The following example shows how to use the task_serialize branching scheme to solve a small cumulative scheduling problem:

model "Tasks serialization example"
 uses "kalis"

 declarations
  Masonry, Carpentry, Roofing, Windows, Facade, Garden, Plumbing,
    Ceiling, Painting, MovingIn : cptask    ! Declaration of tasks
  Taskset : set of cptask
  money_available : cpresource              ! Resource declaration
 end-declarations

 forward function selectNextTask(tasks: cptasklist) : integer

! 'money_available' is a cumulative resource with max. amount of 29$
 set_resource_attributes(money_available,KALIS_DISCRETE_RESOURCE,29)

! Limit resource availability to 20$ in the time interval [0,14]
 setcapacity(money_available, 0, 14, 20)

! Setting the task durations and predecessor sets
 set_task_attributes(Masonry  , 7)
 set_task_attributes(Carpentry, 3, {Masonry})
 set_task_attributes(Roofing  , 1, {Carpentry})
 set_task_attributes(Windows  , 1, {Roofing})
 set_task_attributes(Facade   , 2, {Roofing})
 set_task_attributes(Garden   , 1, {Roofing})
 set_task_attributes(Plumbing , 8, {Masonry})
 set_task_attributes(Ceiling  , 3, {Masonry})
 set_task_attributes(Painting , 2, {Ceiling})
 set_task_attributes(MovingIn , 1, {Windows,Facade,Garden,Painting})

! Setting the resource consumptions
 consumes(Masonry  , 7, money_available)
 consumes(Carpentry, 3, money_available)
 consumes(Roofing  , 1, money_available)
 consumes(Windows  , 1, money_available)
 consumes(Facade   , 2, money_available)
 consumes(Garden   , 1, money_available)
 consumes(Plumbing , 8, money_available)
 consumes(Ceiling  , 3, money_available)
 consumes(Painting , 2, money_available)
 consumes(MovingIn , 1, money_available)

! Set of tasks to schedule
 Taskset := {Masonry, Carpentry, Roofing, Windows, Facade, Garden,
             Plumbing, Ceiling, Painting, MovingIn}

! Set the custom branching strategy using task_serialize:
! - the task serialization process will use the function
!   "selectNextTask" to look for the next task to fix
! - it will use the "KALIS_MAX_TO_MIN" value selection heuristic
!   to set the tasks duration variable
! - and the "KALIS_MIN_TO_MAX" value selection heuristic to set
!   the start of the task
 cp_set_branching(task_serialize(->selectNextTask,
                  KALIS_MAX_TO_MIN, KALIS_MIN_TO_MAX, Taskset))

! Find the optimal schedule (minimizing the makespan)
 if 0 <> cp_schedule(getmakespan) then
   cp_show_sol
 else
   writeln("No solution found")
 end-if

!-------------------------------------------------------------
! **** Function to select the next task to schedule
 function selectNextTask(tasks: cptasklist) : integer
  write("selectNextTask : ")
  declarations
   Vset,Iset: set of integer
  end-declarations

 ! Get the number of elements of "tasks"
  listsize:= getsize(tasks)

 ! Set of uninstantiated variables
  forall(i in 1..listsize)
   if not is_fixed(getstart(gettask(tasks,i))) or
      not is_fixed(getduration(gettask(tasks,i))) then
     Vset+= {i};
   end-if

  if Vset={} then
    returned:= 0
  else
  ! Get the variables with max. degree
    dmax:= max(i in Vset) getsize(getduration(gettask(tasks,i)))
    forall(i in Vset)
      if getsize(getduration(gettask(tasks,i))) = dmax then
       Iset+= {i}; end-if
    dsize:= MAX_INT

  ! Choose var. with smallest domain among those indexed by 'Iset'
    forall(i in Iset)
      if getsize(getstart(gettask(tasks,i))) < dsize then
        returned:= i
        dsize:= getsize(getstart(gettask(tasks,i)))
      end-if
  end-if

  if returned <> 0 then
   writeln(gettask(tasks,returned))
  end-if
 end-function

end-model

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