- Generated by
1.13.2
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CONOPT
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QPBandB: Multi Threaded implementation of QP4 MINLP model The implementation shows how to implement a parallel Branch & Bound procedure that still is deterministic independent of the order in which the sub-models are solved (within the framework defined here with Work-pools).
When testing that the sequential and parallel algorithms uses the same number of nodes we have a test that the solves are identical even when run with different threads. This is some kind of test that CONOPT Solves are reproducable and that there are no un-initialized values used in the algorithm.
For more information about the individual callbacks, please have a look at the source code.
Definition in file mp_qpbandb.f90.
Data Types | |
| type | bb_data::bbnode |
| type | bb_data::bbnodeptr |
| type | bb_data::controlv |
Functions/Subroutines | |
| subroutine | bb_data::remove_activenode (node) |
| subroutine | bb_data::return_freenode (node) |
| subroutine | bb_data::get_freenode (node) |
| subroutine | bb_data::deallocate_nodes |
| subroutine | bb_data::add_activenode (node) |
| subroutine | bb_data::add2workpool (node) |
| subroutine | bb_data::list_node (node) |
| subroutine | bb_data::list_nodes |
| subroutine | bb_data::select_var (node, ib) |
| subroutine | bb_data::create_workpool |
| subroutine | bb_data::solve_workpool |
| real function | rndx () |
| subroutine | defdata |
| program | qp_threads |
| Main program. A simple setup and call of CONOPT. | |
| integer function | bb_option (ncall, rval, ival, lval, usrmem, name) |
| Sets runtime options. | |
| subroutine | bandb_solve |
| integer function | qp_readmatrix (lower, curr, upper, vsta, type, rhs, esta, colsta, rowno, value, nlflag, n, m, nz, usrmem) |
| Define information about the model. | |
| integer function | qp_fdeval (x, g, jac, rowno, jcnm, mode, ignerr, errcnt, n, nz, thread, usrmem) |
| Compute nonlinear terms and non-constant Jacobian elements. | |
| integer function | qp_2ddir (x, dx, d2g, rowno, jcnm, nodrv, n, nj, thread, usrmem) |
| Computes the second derivative of a constraint in a direction. | |
| integer function | qp_2dlagrstr (rowno, colno, nodrv, n, m, nhess, usrmem) |
| Specify the structure of the Lagrangian of the Hessian. | |
| integer function | qp_2dlagrval (x, u, rowno, colno, value, nodrv, n, m, nhess, usrmem) |
| Compute the Lagrangian of the Hessian. | |
| integer function | bb_status (modsta, solsta, iter, objval, usrmem) |
| integer function | bb_solution (xval, xmar, xbas, xsta, yval, ymar, ybas, ysta, n, m, usrmem) |
| integer function | bb_message (smsg, dmsg, nmsg, llen, usrmem, msgv) |
| integer function | bb_errmsg (rowno, colno, posno, msglen, usrmem, msg) |
| real function rndx |
Definition at line 537 of file mp_qpbandb.f90.
| subroutine defdata |
Definition at line 550 of file mp_qpbandb.f90.
| program qp_threads |
Main program. A simple setup and call of CONOPT.
Definition at line 609 of file mp_qpbandb.f90.
| integer function bb_option | ( | integer | ncall, |
| real*8 | rval, | ||
| integer | ival, | ||
| integer | lval, | ||
| real*8, dimension(*) | usrmem, | ||
| character(len=*) | name ) |
Sets runtime options.
where:
NCALL: The sequence number of the call. NCALL is defined by CONOPT and starts with Base (0 for C and 1 for Fortran) first time Option is called. If Option is called from within MemEst and later from CONOPT itself then NCALL starts from Base in each sequence of calls.NAME: The name of a CONOPT CR-cell defined by the modeler. See Options for a list of user definable CR-cells and their interpretation. Note that the name has 8 characters and all 8 characters must be defined, if necessary with trailing blanks. When the modeler returns a name with 8 blanks, it indicates that there are no more definitions for CR-cells.RVAL: The value to be assigned to 'NAME' if the cell contains a real value.IVAL: The value to be assigned to 'NAME' if the cell contains an integer value.LVAL: The value to be assigned to 'NAME' if the cell contains a logical value. A zero represents .false. and a nonzero value represents .true.USRMEM: User memory as defined in coidef_usrmem() (Only for Fortran and C API). Definition at line 884 of file mp_qpbandb.f90.
| subroutine bandb_solve |
Definition at line 907 of file mp_qpbandb.f90.
| integer function qp_readmatrix | ( | real*8, dimension(n), intent(inout) | lower, |
| real*8, dimension(n), intent(inout) | curr, | ||
| real*8, dimension(n), intent(inout) | upper, | ||
| integer, dimension(n), intent(inout) | vsta, | ||
| integer, dimension(m), intent(out) | type, | ||
| real*8, dimension(m), intent(inout) | rhs, | ||
| integer, dimension(m), intent(inout) | esta, | ||
| integer, dimension(n+1), intent(inout) | colsta, | ||
| integer, dimension(nz), intent(out) | rowno, | ||
| real*8, dimension(nz), intent(inout) | value, | ||
| integer, dimension(nz), intent(inout) | nlflag, | ||
| integer, intent(in) | n, | ||
| integer, intent(in) | m, | ||
| integer, intent(in) | nz, | ||
| type (bbnode) | usrmem ) |
Define information about the model.
where:
LOWER: Vector of lower bounds on the variables. CONOPT will fill the vector with a special internal value that represent minus infinity or no lower bound before issuing the callback.CURR: Vector of initial values of the variables. CONOPT will fill the vector with the default initial value of zero before issuing the callback.UPPER: Vector of upper bounds on the variables. CONOPT will fill the vector with a special internal value that represent plus infinity or no upper bound before issuing the callback.VSTA: Vector of initial status values for the variable. VSTA is only used if coidef_inistat() was called with IniStat = 1 or 2.
If IniStat = 1 the value of VSTA must be defined as:
CURR = LOWER or CURR = UPPER) or super-basic, andand if IniStat = 2 the value of VSTA must be defined as:
IniStat = 1 is simple to implement by hand, while IniStat = 2 is consistent with the output status defined in the Solution callback method. Note that if the numerical value in CURR are inconsistent with the status value, the numerical values will be used.
If IniStat = 0 (the default value) CONOPT will not use VSTA and you do not have to define it.
TYPE: Vector of equation types. The values of TYPE have the following meaning:
There is no default value for TYPE so it must be defined for all constraints. Note that CONOPT does not accept ranges.
RHS: Vector of right hand sides values. The default value is zero.ESTA: Vector of initial status values for the slacks in the constraints. ESTA is only used if coidef_inistat() was called with IniStat = 1 or 2.
If IniStat = 1 the value of ESTA must be defined as:
and if IniStat = 2 the value of ESTA must be defined as:
Again, IniStat = 1 is simple to implement by hand, while IniStat = 2 is consistent with the output status defined in Solution callback method.
If IniStat = 0 (the default value) then CONOPT will not use ESTA.
COLSTA: Vector of start of column pointers. All non-zero Jacobian elements must be sorted by column, i.e. all elements in column i comes before all elements in column i+1. COLSTA points to the first element in each column. If you have selected Base = 1 (Fortran conventions) then COLSTA must therefore satisfy: COLSTA(1) = 1 and COLSTA(N+1) = NZ+1. If you have selected Base = 0 (C conventions) then COLSTA must therefore satisfy: COLSTA[0] = 0 and COLSTA[N] = NZ. COLSTA must in both cases be increasing.ROWNO: Vector of row or equation numbers of the non-zeros. The numbers must be in the range 1 through M inclusive if you have defined Base = 1 (Fortran conventions) and in the range 0 to M-1 inclusive if you have defined Base = 0 (C conventions). Although the columns are sorted, the rows do not have to be sorted within each column.VALUE: Vector of values of the Jacobian elements. VALUE must be defined for all constant Jacobian elements, i.e. elements for which the following NLFLAG = 0. VALUE does not have to be defined for varying Jacobian elements.NLFLAG: Vector of nonlinearity flags:
NLFLAG is not read if the model is linear, i.e. if NLNZ = 0, otherwise it must be defined. Note that if you have an LP model, you should probably select a specialized LP algorithm instead of CONOPT.
N: Number of variables as defined in coidef_numvar().M: Number of constraints as defined in coidef_numcon().NZ: Number of Jacobian elements as defined in coidef_numnz().USRMEM: User memory as defined in coidef_usrmem() (Only for Fortran and C API).The lower bounds in LOWER must be less than or equal to the upper bounds in UPPER. Some of the bounds may be -INF or +INF, which are the bounds CONOPT assigns by default. If a bound is infinite, the user should normally not change the corresponding entry in LOWER or UPPER. If it is more convenient for the modeler to assign a value representing infinity it should be done using the values that are present in LOWER and UPPER when ReadMatrix is called, for example taken from the first element before any assignments are done. As an alternative, you may define the numerical value of Infinity to be used by the solution algorithm in option RTMAXV and store the same value in UPPER and -RTMAXV in LOWER.
The values in CURR, both those defined by the modeler and those defined by default, are without warning moved to the nearest bound if they are outside the bounds.
LOWER and UPPER. Definition at line 972 of file mp_qpbandb.f90.
| integer function qp_fdeval | ( | real*8, dimension(n), intent(in) | x, |
| real*8, intent(inout) | g, | ||
| real*8, dimension(n), intent(inout) | jac, | ||
| integer, intent(in) | rowno, | ||
| integer, dimension(nz), intent(in) | jcnm, | ||
| integer, intent(in) | mode, | ||
| integer, intent(in) | ignerr, | ||
| integer, intent(inout) | errcnt, | ||
| integer, intent(in) | n, | ||
| integer, intent(in) | nz, | ||
| integer, intent(in) | thread, | ||
| type (bbnode) | usrmem ) |
Compute nonlinear terms and non-constant Jacobian elements.
where:
X: Vector with the point of evaluation. The point is provided by CONOPT.G: Scalar function value: The value of G must be returned by the modeler if MODE = 1 or 3, otherwise it will be ignored. If FVincLin defined in coidef_fvinclin() is 0, the default value, then G should return the sum of the nonlinear terms in row number ROWNO, and if FVincLin is 1 then G should return the sum of both linear and nonlinear terms. The nonlinear terms are defined as all terms that correspond to Jacobian elements with NLFLAG = 1 when loading the model. Constant terms in nonlinear constraints may be included in G provided RHS in ReadMatrix is adjusted correspondingly. Constant terms in linear constraints may also be defined here provided FVforAll is given the non default value 1 in coidef_fvforall(). In summary, G should include the following, depending on FVincLin and FVforAll:| FVforAll \ FVincLin | 0 | 1 |
|---|---|---|
| 0 | G includes nonlinear terms only. FDEval is only called for nonlinear rows. | G includes linear and nonlinear terms. FDEval is only called for nonlinear rows. |
| 1 | G includes nonlinear and constant terms. FDEval is called for all rows. | G includes linear, nonlinear, and constant terms. FDEval is called for all rows. |
JAC: Vector of Jacobian values. All the nonlinear Jacobian values in row number ROWNO (and only these) should be evaluated. The indices in JAC are the indices of the variables, i.e. the derivative with respect to X(I) should be returned in JAC(I). JAC must be returned by the modeler if MODE = 2 or 3; otherwise it must be ignored.ROWNO: Scalar with the number of the row for which nonlinearities are to be evaluated. Is provided by CONOPT. Note that if FVforAll = 0, the default value, then FDEval will only be called for nonlinear rows, and constant terms in linear rows must therefore be included in RHS in ReadMatrix. If FVforAll = 1 then FDEval will be called for all rows, and the linear constraints must return any constant term that is not included in the right hand side. CONOPT will initialize G to zero so FDEval can just return for linear rows without constant terms. In summary, FDEval will be called for the following values of ROWNO, depending on FVforAll:
The row numbers are consistent with the Base selected by the modeler.
JCNM: Vector with a list of column numbers for the nonlinear nonzero Jacobian elements in the current row. It is only defined when MODE = 2 or 3. JCNM and NJ are provided for modelers that may find this information useful; it can be ignored by others. The numbers are consistent with the Base (Fortran or C conventions) selected by the modeler.MODE: Scalar indicator for mode of evaluation, provided by CONOPT:ROWNO and return the value in G.ROWNO and return them in JAC.IGNERR: Scalar that indicates whether CONOPT assumes the point to be safe (0) or potentially unsafe (1). During certain parts of the optimization CONOPT will make very long steps and it is not unlikely that one of the constraints is not defined. If an error is encountered while IGNERR is 1, this error is not included in the ErrLim limit, and the modeler may skip any error messages that otherwise should be issued from FDEval.ERRCNT: Scalar Function Evaluation Error Indicator. FDEval must set this argument to 1 each time a function value cannot be computed. The counts are accumulated by CONOPT (except when IGNERR = 1). If their sum exceeds the ErrLim value defined in coidef_errlim(), CONOPT will stop the optimization, communicate the solution to the modeler with solver status SOLSTA = 5 (Evaluation Error Limit) in callback routine Status, and return control to the modeler. If ERRCNT has been set by FDEval then G and JAC will not be used and CONOPT will in general try to backtrack to a "safe" point. Note that CONOPT assumes that all functions are defined for all values of the variables between their bounds. CONOPT will never call FDEval with X outside the bounds specified in ReadMatrix. Also see the Progress callback routine for an alternative way of stopping CONOPT.NEWPT: Scalar new point indicator, provided by CONOPT:
ROWNO has changed but the nonlinear variables in X have not changed. Some variables that are linear in all constraints may also have been changed.NEWPT is provided by CONOPT as a service to the modeler. It may be used to calculate and reuse terms that depend on X but are common among several equations, e.g. when some of the equations represent simultaneous sets of differential equations solved by an expensive integration routine.
N: Number of variables as defined in coidef_numvar().NJ: Number of nonlinear nonzero Jacobian elements in the current row and number of elements in the JCNM vector. JCNM is only defined when MODE = 2 or 3; when MODE = 1 then NJ has the value 1 and JCNM points to a random vector.THREAD: In some multi-threading environments multiple copies of FDEval can be called at the same time, (see Multi Threading). THREAD will hold the number of the thread for the current call of FDEval. THREAD is in the interval from 0 to the maximum number of threads allowed for FDEval.USRMEM: User memory as defined in coidef_usrmem() (Only for Fortran and C API).You should notice the difference between the ERRCNT and the return code of FDEval. A nonzero value returned in ERRCNT indicates that the current point defined in X is bad. The function value G or the derivatives JAC could not be computed and CONOPT should try to backtrack to a safe point. A nonzero value returned as the value of FDEval indicates that there is a serious or permanent error and there is no reason to continue the optimization. The return code on FDEval can for example be used if a data file is not found, or if FDEval is called with a value of ROWNO that was not expected.
Definition at line 1122 of file mp_qpbandb.f90.
| integer function qp_2ddir | ( | real*8, dimension(n), intent(in) | x, |
| real*8, dimension(n), intent(in) | dx, | ||
| real*8, dimension(n), intent(out) | d2g, | ||
| integer, intent(in) | rowno, | ||
| integer, dimension(nj), intent(in) | jcnm, | ||
| integer, intent(inout) | nodrv, | ||
| integer, intent(in) | n, | ||
| integer, intent(in) | nj, | ||
| integer, intent(in) | thread, | ||
| type (bbnode) | usrmem ) |
Computes the second derivative of a constraint in a direction.
where:
X: Vector with the point in which the directional second derivatives should be computed. Defined by CONOPT.DX: Vector with the direction in which the directional second derivatives should be computed. Defined by CONOPT.D2G: Vector returning the directional second derivative. The relevant positions (see JCNM below) will be zero on entry to 2DDir.ROWNO: The constraint for which the directional second derivatives should be computed. Defined by CONOPT. 2DDir will be called for one constraint at a time and only for nonlinear constraints.JCNM: List of column numbers for the variables that appear nonlinearly in the current constraint. JCNM and NJ (see below) are provided as a service to modelers that may find this information useful; it can be ignored by others.NODRV: Must be set to 1 if the directional second derivatives for some reason could not be computed, for example because some of them were not defined. CONOPT will not use any output from a point that returned a nonzero NODRV.N: The number of variables in the model as defined in coidef_numvar(). Provided by CONOPT.NJ: The number of variables appearing nonlinearly in the current constraint. Defined by CONOPT.THREAD: In some multi-threading environments multiple copies of FDEval can be called at the same time, (see Multi Threading). THREAD will hold the number of the thread for the current call of FDEval. THREAD is in the interval from 0 to the maximum number of threads allowed for FDEval.USRMEM: User memory as defined in coidef_usrmem() (Only for Fortran and C API). Definition at line 1191 of file mp_qpbandb.f90.
| integer function qp_2dlagrstr | ( | integer, dimension(nhess) | rowno, |
| integer, dimension(nhess) | colno, | ||
| integer | nodrv, | ||
| integer | n, | ||
| integer | m, | ||
| integer | nhess, | ||
| type (bbnode) | usrmem ) |
Specify the structure of the Lagrangian of the Hessian.
where:
ROWNO: Vector of row numbers of the lower triangular part of the Hessian. Must be defined by the modeler when MODE = 2 and is provided as a help to the modeler when MODE = 3.COLNO: Vector of column numbers of the lower triangular part of the Hessian. Must be defined by the modeler when MODE = 2 and is provided as a help to the modeler when MODE = 3. The elements of the Hessian must be sorted column wise, i.e. COLNO must be non-decreasing. Within each column the elements must be sorted row-wise, i.e. the elements of ROWNO must be increasing for sequences for which COLNO is constant. The row and column numbers are interpreted according to Base, i.e. they are between 1 and N when Base = 1 (Fortran conventions) and between 0 and N-1 when Base = 0 (C conventions).NODRV: Can be set to 1 if the derivatives for some reason could not be computed, for example because some of them were not defined. Is initialized to 0 by CONOPT. CONOPT will not use second order methods in the current point if NODRV is 1.N: The number of variables in the model as defined in coidef_numvar(). Provided by CONOPT.M: The number of constraints in the model as defined in coidef_numcon(). Provided by CONOPT.NHESS: The number of nonzero elements in the Hessian. When MODE = 1 CONOPT will define the maximum number of elements it will accept in NHESS, and 2DLagrVal must return the actual number of element. If the actual number is larger than the input value of NHESS then CONOPT will not use the Hessian of the Lagrangian and 2DLagrVal will not be called again. When MODE > 1 NHESS is defined by CONOPT as the value provided by the modeler in the first call.USRMEM: User memory as defined in coidef_usrmem() (Only for Fortran and C API). Definition at line 1230 of file mp_qpbandb.f90.
| integer function qp_2dlagrval | ( | real*8, dimension(n) | x, |
| real*8, dimension(m) | u, | ||
| integer, dimension(nhess) | rowno, | ||
| integer, dimension(nhess) | colno, | ||
| real*8, dimension(nhess) | value, | ||
| integer | nodrv, | ||
| integer | n, | ||
| integer | m, | ||
| integer | nhess, | ||
| type (bbnode) | usrmem ) |
Compute the Lagrangian of the Hessian.
where:
MODE: Distinguishes between the three modes described above.X: Vector with the point in which the Hessian of the Lagrangian should be computed. Defined by CONOPT when MODE = 3.U: The vector of weights on the individual constraints. The Lagrangian is defined as L = SUM(r in rows)U(r) . function(r). U is defined by CONOPT when MODE = 3.ROWNO: Vector of row numbers of the lower triangular part of the Hessian. Must be defined by the modeler when MODE = 2 and is provided as a help to the modeler when MODE = 3.COLNO: Vector of column numbers of the lower triangular part of the Hessian. Must be defined by the modeler when MODE = 2 and is provided as a help to the modeler when MODE = 3. The elements of the Hessian must be sorted column wise, i.e. COLNO must be non-decreasing. Within each column the elements must be sorted row-wise, i.e. the elements of ROWNO must be increasing for sequences for which COLNO is constant. The row and column numbers are interpreted according to Base, i.e. they are between 1 and N when Base = 1 (Fortran conventions) and between 0 and N-1 when Base = 0 (C conventions).VALUE: Vector returning the values of the second derivatives when MODE = 3. The individual elements must be defined in the order used for ROWNO and COLNO. VALUE will be initialized to zero when 2DLagrVal is called and it must be defined by the modeler.NODRV: Can be set to 1 if the derivatives for some reason could not be computed, for example because some of them were not defined. Is initialized to 0 by CONOPT. CONOPT will not use second order methods in the current point if NODRV is 1.N: The number of variables in the model as defined in coidef_numvar(). Provided by CONOPT.M: The number of constraints in the model as defined in coidef_numcon(). Provided by CONOPT.NHESS: The number of nonzero elements in the Hessian. When MODE = 1 CONOPT will define the maximum number of elements it will accept in NHESS, and 2DLagrVal must return the actual number of element. If the actual number is larger than the input value of NHESS then CONOPT will not use the Hessian of the Lagrangian and 2DLagrVal will not be called again. When MODE > 1 NHESS is defined by CONOPT as the value provided by the modeler in the first call.USRMEM: User memory as defined in coidef_usrmem() (Only for Fortran and C API).2DLagrVal will only be called in points in which the constraint values have been computed successfully before with FDEval. Checks for function evaluation errors can therefore usually be limited. Note that 2DLagrVal in some cases can be called in a point that is different from the last point in which FDEval was called.
The maximum number of Hessian nonzero elements accepted by CONOPT is computed as the option value RVHESS multiplied by the number of nonlinear Jacobian elements. The default value of RVHESS is 10. If the Hessian has more than 10 times as many elements as the Jacobian it is expected that it is too expensive to compute and that directional 2nd derivatives in some form are more efficient to use. The modeler may allow CONOPT to use a denser Hessian by increasing RVHESS.
There is a rudimentary debugger of the values returned by 2DLagrVal. It can be turned on by setting Debug2D in coidef_debug2d() or with the option LKDEB2. Information on the debugger including messages and error return codes can be found in Error Return Codes.
Definition at line 1259 of file mp_qpbandb.f90.
| integer function bb_status | ( | integer, intent(in) | modsta, |
| integer, intent(in) | solsta, | ||
| integer, intent(in) | iter, | ||
| real*8, intent(in) | objval, | ||
| type (bbnode) | usrmem ) |
Definition at line 1289 of file mp_qpbandb.f90.
| integer function bb_solution | ( | real*8, dimension(n), intent(in) | xval, |
| real*8, dimension(n), intent(in) | xmar, | ||
| integer, dimension(n), intent(in) | xbas, | ||
| integer, dimension(n), intent(in) | xsta, | ||
| real*8, dimension(m), intent(in) | yval, | ||
| real*8, dimension(m), intent(in) | ymar, | ||
| integer, dimension(m), intent(in) | ybas, | ||
| integer, dimension(m), intent(in) | ysta, | ||
| integer, intent(in) | n, | ||
| integer, intent(in) | m, | ||
| type (bbnode) | usrmem ) |
Definition at line 1313 of file mp_qpbandb.f90.
| integer function bb_message | ( | integer, intent(in) | smsg, |
| integer, intent(in) | dmsg, | ||
| integer, intent(in) | nmsg, | ||
| integer, dimension(*), intent(in) | llen, | ||
| type (bbnode) | usrmem, | ||
| character(len=133), dimension(*), intent(in) | msgv ) |
Definition at line 1349 of file mp_qpbandb.f90.
| integer function bb_errmsg | ( | integer, intent(in) | rowno, |
| integer, intent(in) | colno, | ||
| integer, intent(in) | posno, | ||
| integer, intent(in) | msglen, | ||
| type (bbnode) | usrmem, | ||
| character(len=*), intent(in) | msg ) |
Definition at line 1383 of file mp_qpbandb.f90.
1.13.2