optgra_module Module

Near-linear optimization tool tailored for s/c trajectory design.

This is a modernization of the original Fortran 77 code from: pyoptgra. It has been extensively refactored. The old common blocks were removed, and all data is now encapsulated in a single optgra class.

History

  • Original code by J. Schoenmaekers et al. (ESA) from pyoptgra.
  • Jacob Williams, Feb 2025 : created new version.

Uses

  • module~~optgra_module~~UsesGraph module~optgra_module optgra_module iso_fortran_env iso_fortran_env module~optgra_module->iso_fortran_env

Variables

Type Visibility Attributes Name Initial
integer, private, parameter :: wp = real64

Real working precision if not specified [8 bytes]
integer, public, parameter :: optgra_wp = wp

Working real precision
integer(kind=ip), private, parameter :: name_len = 80

max string length for var names
integer(kind=ip), private, parameter :: str_len = 256

max string length for str prints

Abstract Interfaces

abstract interface

  • private subroutine calval_f(me, varvec, Valcon, i)

    FUNCTION FOR VALUES INPUT AND OUTPUT NOT SCALED

    Arguments

    Type IntentOptional Attributes Name
    class(optgra), intent(inout) :: me
    real(kind=wp), intent(in), dimension(:) :: varvec

    size is Numvar
    real(kind=wp), intent(out), dimension(:) :: Valcon

    size is Numcon+1
    integer, intent(in) :: i

    JW: THIS IS NOT DOCUMENTED ? IFLAG?

abstract interface

  • private subroutine calder_f(me, varvec, convec, Dercon)

    FUNCTION FOR VALUES AND DERIVATIVES INPUT AND OUTPUT NOT SCALED

    Arguments

    Type IntentOptional Attributes Name
    class(optgra), intent(inout) :: me
    real(kind=wp), intent(in), dimension(:) :: varvec

    size is Numvar
    real(kind=wp), intent(out), dimension(:) :: convec

    size is Numcon+1
    real(kind=wp), intent(out), dimension(:,:) :: Dercon

    size is Numcon+1,Numvar

Derived Types

type, public ::  optgra

Main class for OPTGRA algorithm.

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Components

Type Visibility Attributes Name Initial
integer(kind=ip), private :: numvar = 0

number of variables
real(kind=wp), private, dimension(: ), allocatable :: varval
integer(kind=ip), private, dimension(: ), allocatable :: vartyp
real(kind=wp), private, dimension(: ), allocatable :: varsca
character(len=name_len), private, dimension(: ), allocatable :: varstr
integer(kind=ip), private, dimension(: ), allocatable :: varlen
real(kind=wp), private, dimension(: ), allocatable :: varref
real(kind=wp), private, dimension(: ), allocatable :: vardes
real(kind=wp), private, dimension(: ), allocatable :: vargrd
real(kind=wp), private, dimension(: ), allocatable :: vardir
real(kind=wp), private, dimension(: ), allocatable :: funvar
real(kind=wp), private, dimension(: ), allocatable :: senvar
integer(kind=ip), private :: numcon = 0

number of constraints
real(kind=wp), private, dimension(: ), allocatable :: conval
integer(kind=ip), private, dimension(: ), allocatable :: contyp
integer(kind=ip), private, dimension(: ), allocatable :: conpri
real(kind=wp), private, dimension(: ), allocatable :: consca
character(len=name_len), private, dimension(: ), allocatable :: constr
integer(kind=ip), private, dimension(: ), allocatable :: conlen
real(kind=wp), private, dimension(: ), allocatable :: conref
real(kind=wp), private, dimension(: ), allocatable :: senqua
real(kind=wp), private, dimension(: ), allocatable :: sencon
real(kind=wp), private, dimension(: ), allocatable :: sendel
integer(kind=ip), private, dimension(: ), allocatable :: senact
integer(kind=ip), private :: optmet = 2

optimization method
integer(kind=ip), private :: maxite = 10

maximum number of iterations
integer(kind=ip), private :: corite = 10
integer(kind=ip), private :: optite = 10
integer(kind=ip), private :: divite = 10
integer(kind=ip), private :: cnvite = 10
real(kind=wp), private :: Varmax = 10.0_wp

maximum distance per iteration
real(kind=wp), private :: varsnd = 1.0_wp

perturbation for 2nd order derivatives
real(kind=wp), private :: varstp = 1.0_wp
integer(kind=ip), private :: varder = 1

derivatives computation mode
real(kind=wp), private, dimension(: ), allocatable :: varper
integer(kind=ip), private :: loglun = output_unit

log file unit
integer(kind=ip), private :: loglev = 1

log level
integer(kind=ip), private :: loglup = output_unit

pygmo log file unit
integer(kind=ip), private :: verbos = 0

pygmo verbosity
integer(kind=ip), private :: fevals = 0

pygmo: number of const fun evals
integer(kind=ip), private :: pygfla = 0

pygmo: flag indicating status of optimization
integer(kind=ip), private :: numite = 0

number of iterations
integer(kind=ip), private :: matlev = 0
integer(kind=ip), private :: tablun = output_unit

logical unit for writing table
integer(kind=ip), private :: tablev = 0

level of tab
integer(kind=ip), private :: senopt = 0

sensitivity optimization mode
integer(kind=ip), private :: numact = 0
integer(kind=ip), private, dimension(: ), allocatable :: actcon
integer(kind=ip), private, dimension(: ), allocatable :: confix
integer(kind=ip), private, dimension(: ), allocatable :: conact
real(kind=wp), private, dimension(:,:), allocatable :: conder
real(kind=wp), private, dimension(:,:), allocatable :: conred
real(kind=wp), private, dimension(:,:), allocatable :: sender
procedure(calval_f), private, pointer :: calval => null()

function for values
procedure(calder_f), private, pointer :: calder => null()

function for derivatives

Type-Bound Procedures

procedure, public :: initialize

set up the problem
procedure, public :: solve => ogexec

solve the problem
procedure, public :: destroy => ogclos

free memory when finished
procedure, public :: ogsens
procedure, public :: ogssst
procedure, public :: oggsst
procedure, private :: ogrigt
procedure, private :: ogincl
procedure, private :: ogexcl
procedure, private :: ogeval
procedure, private :: ogcorr
procedure, private :: ogopti
procedure, private :: ogleft
procedure, private :: ogpwri
procedure, private :: ogwrit
procedure, private :: ogpwri_start
procedure, private :: ogpwri_end

Functions

private function ogleft(me, Actinp) result(Actout)

LEFT-MULTIPLIES VECTOR LOWER TRIANGULAR MATRIX OBTAINED BY REDUCTION AND SUBSEQUENT INVERSION OF DERIVATIVES OF ACTIVE CONSTRAINTS

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Arguments

Type IntentOptional Attributes Name
class(optgra), intent(inout) :: me
real(kind=wp), intent(in) :: Actinp(me%Numcon)

VECTOR INITAL

Return Value real(kind=wp), (me%Numcon)

VECTOR FINAL

private function ogrigt(me, Actinp) result(Actout)

RIGHT-MULTIPLIES VECTOR LOWER TRIANGULAR MATRIX OBTAINED BY REDUCTION AND SUBSEQUENT INVERSION OF DERIVATIVES OF ACTIVE CONSTRAINTS

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Arguments

Type IntentOptional Attributes Name
class(optgra), intent(inout) :: me
real(kind=wp), intent(in) :: Actinp(me%Numcon)

VECTOR INITAL

Return Value real(kind=wp), (me%Numcon)

VECTOR FINAL


Subroutines

private subroutine initialize(me, Numvar, Numcon, Calval, Calder, Delcon, Conpri, Consca, Constr, Conlen, Contyp, Varder, Varper, Varmax, Varsnd, Maxite, Itecor, Iteopt, Itediv, Itecnv, Loglup, Verbos, Senopt, Varsca, Varstr, Varlen, Vartyp, Loglun, Loglev, Matlev, Tablun, Tablev, Optmet)

Initialize the class. This should be the first routine called.

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Arguments

Type IntentOptional Attributes Name
class(optgra), intent(out) :: me
integer(kind=ip), intent(in) :: Numvar

NUMBER OF VARIABLES
integer(kind=ip), intent(in) :: Numcon

NUMBER OF CONSTRAINTS
procedure(calval_f) :: Calval

FUNCTION FOR VALUES -> INPUT AND OUTPUT NOT SCALED
procedure(calder_f) :: Calder

FUNCTION FOR VALUES AND DERIVATIVES -> INPUT AND OUTPUT NOT SCALED
real(kind=wp), intent(in) :: Delcon(Numcon+1)

CONSTRAINTS DELTAS (CONSTRAINT + MERIT CONVERGENCE THRESHOLDS)
integer(kind=ip), intent(in) :: Conpri(Numcon+1)

CONSTRAINTS PRIORITY (1:NUMCON) -> 1-N

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real(kind=wp), intent(in) :: Consca(Numcon+1) Read more…
character(len=name_len), intent(in) :: Constr(Numcon+1)

CONIABLES NAME STRING
integer(kind=ip), intent(in) :: Conlen(Numcon+1)

CONIABLES NAME LENGTH
integer(kind=ip), intent(in) :: Contyp(Numcon+1)

CONSTRAINTS TYPE (1:NUMCON)

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integer(kind=ip), intent(in) :: Varder

DERIVATIVES COMPUTATION MODE

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real(kind=wp), intent(in) :: Varper(Numvar)

VARIABLES PERTURBATION FOR DERIVATIVES -> NOT SCALED
real(kind=wp), intent(in) :: Varmax

MAXIMUM DISTANCE PER ITERATION -> SCALED
real(kind=wp), intent(in) :: Varsnd

PERTURBATION FOR 2ND ORDER DERIVATIVES -> SCALED
integer(kind=ip), intent(in) :: Maxite

maximum number of iterations
integer(kind=ip), intent(in) :: Itecor

number of constraint correction iterations in the beginning. If no feasible solution is found within that many iterations, Optgra aborts
integer(kind=ip), intent(in) :: Iteopt

some other iter input ?
integer(kind=ip), intent(in) :: Itediv

some other iter input ?
integer(kind=ip), intent(in) :: Itecnv

some other iter input ?
integer(kind=ip), intent(in) :: Loglup

LOGICAL UNIT FOR WRITING PYGMO LOG
integer(kind=ip), intent(in) :: Verbos

VERBOSITY LEVEL:

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integer(kind=ip), intent(in) :: Senopt

sensitivity optimization mode

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real(kind=wp), intent(in) :: Varsca(Numvar)

VARIABLES SCALE FACTOR
character(len=name_len), intent(in) :: Varstr(Numvar)

VARIABLES NAME STRING
integer(kind=ip), intent(in) :: Varlen(Numvar)

VARIABLES NAME LENGTH
integer(kind=ip), intent(in) :: Vartyp(Numvar)

VARIABLES TYPE

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integer(kind=ip), intent(in) :: Loglun

LOGICAL UNIT FOR WRITING LOG
integer(kind=ip), intent(in) :: Loglev

LEVEL OF LOG:

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integer(kind=ip), intent(in) :: Matlev

LEVEL OF LOG:

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integer(kind=ip), intent(in) :: Tablun

logical unit for writing table
integer(kind=ip), intent(in) :: Tablev

LEVEL OF TAB

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integer(kind=ip), intent(in) :: Optmet

OPTIMIZATION METHOD:

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private subroutine ogclos(me)

DEALLOCATION OF ARRAYS

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Arguments

Type IntentOptional Attributes Name
class(optgra), intent(inout) :: me

private subroutine ogcorr(me, Varacc, Finish, Toterr, Norerr, error)

CORRECTION PART

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Arguments

Type IntentOptional Attributes Name
class(optgra), intent(inout) :: me
real(kind=wp), intent(inout) :: Varacc
integer(kind=ip), intent(out) :: Finish
real(kind=wp) :: Toterr
real(kind=wp) :: Norerr
logical, intent(out) :: error

if there was a fatal error

private subroutine ogeval(me, Valvar, Valcon, Varder, Dercon)

COMPUTES SCALED CONTRAINTS+MERIT AND DERIVATIVES FROM SCALED VARIABLES

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Arguments

Type IntentOptional Attributes Name
class(optgra), intent(inout) :: me
real(kind=wp), intent(in) :: Valvar(me%Numvar)

SCALED VARIABLES: valvar(var) = x_var / varsca(var)
real(kind=wp), intent(out) :: Valcon(me%Numcon+1)

SCALED CONTRAINTS+MERIT AND DERIVATIVES:

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integer(kind=ip), intent(in) :: Varder

DERIVATIVES COMPUTATION MODE

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real(kind=wp), intent(out) :: Dercon(me%Numcon+1,me%Numvar)

derivatives of scaled valcon w.r.t. scaled valvar: dercon(con,var) = d(valcon(con))/d(valvar(var))

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private subroutine ogexcl(me, Exc, error)

REMOVE CONSTRAINT TO ACTIVE SET AND REDUCES DERIVATIVES

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Arguments

Type IntentOptional Attributes Name
class(optgra), intent(inout) :: me
integer(kind=ip), intent(in) :: Exc

CONSTRAINT TO BE REMOVED SEQUENCE NUMBER IN ACTIVE LIST
logical, intent(out) :: error

if there was a fatal error (constraints singular)

private subroutine ogexec(me, Valvar, Valcon, Finopt, Finite)

Main routine.

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Arguments

Type IntentOptional Attributes Name
class(optgra), intent(inout) :: me
real(kind=wp), intent(inout) :: Valvar(me%Numvar)

VARIABLES VALUE -> NOT SCALED
real(kind=wp), intent(out) :: Valcon(me%Numcon+1)

CONSTRAINTS VALUE (1:NUMCON) MERIT VALUE (1+NUMCON) -> NOT SCALED
integer(kind=ip), intent(out) :: Finopt

TERMINATION STATUS

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integer(kind=ip), intent(out) :: Finite

?

private subroutine oggsst(me, Varsen, Quasen, Consen, Actsen, Dersen, Actsav, Consav, Redsav, Dersav, Actnum)

NEAR-LINEAR OPTIMIZATION TOOL SENSITIVITY ANALYSIS

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Arguments

Type IntentOptional Attributes Name
class(optgra), intent(inout) :: me
real(kind=wp), intent(out) :: Varsen(me%Numvar)

STORED VARIABLES VALUE
real(kind=wp), intent(out) :: Quasen(me%Numcon+1)

STORED CONSTRAINTS CORRECTION VECTOR
real(kind=wp), intent(out) :: Consen(me%Numcon+1)

STORED CONSTRAINTS VALUE
integer(kind=ip), intent(out) :: Actsen(me%Numcon+1)

STORED CONSTRAINTS ACTIVE
real(kind=wp), intent(out) :: Dersen(me%Numcon+1,me%Numvar)

STORED DERIVATIVE
integer(kind=ip), intent(out) :: Actsav(me%Numcon+1)

STORED ACTIVE CONSTRAINTS
integer(kind=ip), intent(out) :: Consav(me%Numcon+4)

STORED ACTIVE CONSTRAINTS
real(kind=wp), intent(out) :: Redsav(me%Numcon+3,me%Numvar)

STORED DERIVATIVE
real(kind=wp), intent(out) :: Dersav(me%Numcon+3,me%Numvar)

STORED DERIVATIVE
integer(kind=ip), intent(out) :: Actnum

NUMBER OF ACTIVE CONSTRAINTS

private subroutine ogincl(me, Inc)

ADDS CONSTRAINT TO ACTIVE SET AND REDUCES DERIVATIVES

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Arguments

Type IntentOptional Attributes Name
class(optgra), intent(inout) :: me
integer(kind=ip), intent(in) :: Inc

CONSTRAINT TO BE INCLUDED

private subroutine ogopti(me, Varacc, Finish, Desnor, error)

OPTIMIZATION PART

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Arguments

Type IntentOptional Attributes Name
class(optgra), intent(inout) :: me
real(kind=wp), intent(inout) :: Varacc

ITERATION SCALED DISTANCE ACCUMULATED
integer(kind=ip), intent(out) :: Finish

0=LIMIT 1=OPTIM
real(kind=wp) :: Desnor
logical, intent(out) :: error

if there was a fatal error

private subroutine ogpwri(me, Objval, Numvio, Convio)

WRITE OPTIMIZATION LOG IN PYGMO FORMAT

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Arguments

Type IntentOptional Attributes Name
class(optgra), intent(inout) :: me
real(kind=wp), intent(in) :: Objval

OBJECTIVE VALUE
integer(kind=ip), intent(in) :: Numvio

NUMBER OF VIOLATED CONSTRAINTS
real(kind=wp), intent(in) :: Convio

TOTAL CONSTRAINT VIOLATION

private subroutine ogpwri_end(me, Objval, Numvio, Convio)

WRITE OPTIMIZATION END RESULT IN PYGMO FORMAT

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Arguments

Type IntentOptional Attributes Name
class(optgra), intent(inout) :: me
real(kind=wp), intent(in) :: Objval

OBJECTIVE VALUE
integer(kind=ip), intent(in) :: Numvio

NUMBER OF VIOLATED CONSTRAINTS
real(kind=wp), intent(in) :: Convio

TOTAL CONSTRAINT VIOLATION

private subroutine ogpwri_start(me)

WRITE OPTIMIZATION LOG IN PYGMO FORMAT

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Arguments

Type IntentOptional Attributes Name
class(optgra), intent(inout) :: me

private subroutine ogsens(me, Consta, Concon, Convar, Varcon, Varvar)

NEAR-LINEAR OPTIMIZATION TOOL SENSITIVITY ANALYSIS

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Arguments

Type IntentOptional Attributes Name
class(optgra), intent(inout) :: me
integer(kind=ip), intent(out) :: Consta(me%Numcon)

CONSTRAINT STATUS (0=PAS 1=ACT)
real(kind=wp), intent(out) :: Concon(me%Numcon+1,me%Numcon)

SENSITIVITY OF CONTRAINTS+MERIT W.R.T. ACTIVE CONSTRAINTS
real(kind=wp), intent(out) :: Convar(me%Numcon+1,me%Numvar)

SENSITIVITY OF CONTRAINTS+MERIT W.R.T. PARAMETERS
real(kind=wp), intent(out) :: Varcon(me%Numvar,me%Numcon)

SENSITIVITY OF VARIABLES W.R.T. ACTIVE CONSTRAINTS
real(kind=wp), intent(out) :: Varvar(me%Numvar,me%Numvar)

SENSITIVITY OF VARIABLES W.R.T. PARAMETERS -> NOT SCALED

private subroutine ogssst(me, Varsen, Quasen, Consen, Actsen, Dersen, Actsav, Consav, Redsav, Dersav, Actnum)

NEAR-LINEAR OPTIMIZATION TOOL SENSITIVITY ANALYSIS

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Arguments

Type IntentOptional Attributes Name
class(optgra), intent(inout) :: me
real(kind=wp), intent(in) :: Varsen(me%Numvar)

STORED VARIABLES VALUE
real(kind=wp), intent(in) :: Quasen(me%Numcon+1)

STORED CONSTRAINTS CORRECTION VECTOR
real(kind=wp), intent(in) :: Consen(me%Numcon+1)

STORED CONSTRAINTS VALUE
integer(kind=ip), intent(in) :: Actsen(me%Numcon+1)

STORED CONSTRAINTS ACTIVE
real(kind=wp), intent(in) :: Dersen(me%Numcon+1,me%Numvar)

STORED DERIVATIVE
integer(kind=ip), intent(in) :: Actsav(me%Numcon+1)

STORED ACTIVE CONSTRAINTS
integer(kind=ip), intent(in) :: Consav(me%Numcon+4)

STORED ACTIVE CONSTRAINTS
real(kind=wp), intent(in) :: Redsav(me%Numcon+3,me%Numvar)

STORED DERIVATIVE
real(kind=wp), intent(in) :: Dersav(me%Numcon+3,me%Numvar)

STORED DERIVATIVE
integer(kind=ip), intent(in) :: Actnum

private subroutine ogwrit(me, Lev, Str)

Write a message to the log.

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Arguments

Type IntentOptional Attributes Name
class(optgra), intent(inout) :: me
integer(kind=ip), intent(in) :: Lev

only print if Loglev is >= this
character(len=*), intent(in) :: Str

string to print