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D The Matlab Interface Routines  Callback Routines
D.1 xpcb_bl
Purpose
Xpress
^{MP} Barrier Log Callback routine
Calling Syntax
[quit,xpcontrol] = xpcb_bl(x, slack, pi, rc, Prob)
Description of Input
x 
Solution vector x with decision variable values (n × 1 vector) 
slack 
Vector of slack variables. 
pi 
Lagrange multipliers for the linear constraints, i.e.
the dual variables. 
rc 
Lagrange multipliers for the inequality variable
constraints, i.e. the reduced costs. 
Prob 
A structure. If TOMLAB calls xpress, then Prob is the standard
TOMLAB problem structure, otherwise the user optionally can set:
Prob.P = ProblemNumber;, where ProblemNumber is some integer.
When the callback routine is called then the
arrays that define the current problem are added
as fields in Prob.
The additional fields are Prob.QP.c,
Prob.QP.F,
Prob.x_L, Prob.x_U,
Prob.A, Prob.b_L, Prob.b_U.
Also Prob.MIP.KNAPSACK is set
and variables defining the set of integer variables. 
Description of Output
quit 
Return flag. If nonzero, Xpress^{MP} will exit. 
xpcontrol 
Structure with the control fields that the user wishes to be set in Xpress^{MP} 
Global Parameters Used


xpControlVariables 
Structure with all Xpress^{MP} ontrol variables.
Set before the callback. 
xpProblemAttrib 
Structure with all Xpress^{MP} roblem attributes.
Set before the callback. 

Description
At each iteration
running the barrier algorithm,
this routine is called.
Examples
Default some printing is done, and the user should instead write
the Matlab statements wanted.
The definition of a few control variables are shown as comments.
See Also
See the documentation for the Xpress
^{MP} routine
XPRSsetcbbarlog.
D.2 xpcb_gl
Purpose
Xpress
^{MP} Global Log Callback routine
Calling Syntax
[quit,xpcontrol] = xpcb_gl(x, xBIS, Prob)
Description of Input
x 
Latest solution vector x with decision variable values (n × 1
vector).
If control variable MIPINFEAS = 0, then x is a new integer solution.
If MIPINFEAS > 0, then x is the latest simplex solution. 
xBIS 
Solution vector xBIS with best integer solution found (n × 1 vector),
otherwise empty.
If control variable MIPINFEAS = 0, then xBIS
is the best integer solution found before this step.
The new integer solution might or might not be an improvement.
If MIPINFEAS > 0, then xBIS
is either empty, or the best integer solution found so far. 
Description of Input
Prob 
A structure. If TOMLAB calls xpress, then Prob is the standard
TOMLAB problem structure, otherwise the user optionally can set:
Prob.P = ProblemNumber;, where ProblemNumber is some integer.
When the callback routine is called then the
arrays that define the current problem are added
as fields in Prob.
The additional fields are Prob.QP.c,
Prob.QP.F,
Prob.x_L, Prob.x_U,
Prob.A, Prob.b_L, Prob.b_U. 
Description of Output
quit 
Return flag. If nonzero, Xpress^{MP} will exit. 
xpcontrol 
Structure with the control fields that the user wishes to be set in Xpress^{MP} 
Global Parameters Used


xpControlVariables 
Structure with all Xpress^{MP} control variables.
Set before the callback. 
xpProblemAttrib 
Structure with all Xpress^{MP} problem attributes.
Set before the callback. 
Description
This is the global log callback routine.
How often it is called is dependent on the control variable
MIPLOG:

MIPLOG = 0. No printout in global.
 MIPLOG = 1. Print out summary statement at the end.
 MIPLOG = 2. Print out all solutions found, i.e. all integer valued solutions.
 MIPLOG = 3. Print out each node.
 MIPLOG < 0. Print out each −MIPLOG^{th} node.
The default value is
MIPLOG = −100. If to apply the simple
KNAPSACK heuristic that is programmed as an example in this callback
routine, then
xpcontrol.
MIPLOG = 3 should be set.
The following logic describes what x and xBIS are set as,
and the relations to the problem attributes that contains function values.
if XPRS_MIPINFEAS > 0
x is LP solution, f(x) = XPRS_LPOBJVAL
xBIS is empty or the best integer solution, f(x) = XPRS_MIPOBJVAL
XPRS_MIPOBJVAL == 1E20 before the first integer solution is found
end
if XPRS_MIPINFEAS == 0
if XPRS_LPOBJVAL == XPRS_MIPOBJVAL
x is the best integer solution found, f(x) = XPRS_LPOBJVAL
xBIS is the old best integer solution found, unknown f(xBIS).
f(xBIS) could be computed as Prob.QP.c' * xBIS;
else
x is the a new integer solution, but not the best, f(x) = XPRS_LPOBJVAL
xBIS is the best integer solution found, f(xBIS) = XPRS_MIPOBJVAL
end
end
Examples
The routine writes out the node number, the node depth,
the best bound and the best integer solution so far found.
The Matlab code shows an implementation of a simple heuristic,
an Xpress
^{MP} standard example similar to the example file:
\xpressmp\examples\optimizer\knapsack\knapsack.c.
This implementation assumes that a minimum problem is solved.
The heuristic is used if
Prob.
MIP.
KNAPSACK is
true.
Also
xpcontrol.
MIPLOG = 3 must be set.
See Also
See the documentation for the Xpress
^{MP} routine
XPRSsetcbgloballog.
D.3 xpcb_il
Purpose
Xpress
^{MP} Simplex Log Callback routine
Calling Syntax
[quit,xpcontrol] = xpcb_il(x, slack, pi, rc, Prob)
Description of Input
x 
Solution vector x with decision variable values (n × 1 vector) 
slack 
Vector of slack variables. 
pi 
Lagrange multipliers for the linear constraints, i.e.
the dual variables. 
rc 
Lagrange multipliers for the inequality variable
constraints, i.e. the reduced costs. 
Prob 
A structure. If TOMLAB calls xpress, then Prob is the standard
TOMLAB problem structure, otherwise the user optionally can set:
Prob.P = ProblemNumber;, where ProblemNumber is some integer.
When the callback routine is called then the
arrays that define the current problem are added
as fields in Prob.
The additional fields are Prob.QP.c,
Prob.QP.F,
Prob.x_L, Prob.x_U,
Prob.A, Prob.b_L, Prob.b_U. 
Description of Output
quit 
Return flag. If nonzero, Xpress^{MP} will exit. 
xpcontrol 
Structure with the control fields that the user wishes to be set in Xpress^{MP} 
Global Parameters Used


xpControlVariables 
Structure with all Xpress^{MP} control variables.
Set before the callback. 
xpProblemAttrib 
Structure with all Xpress^{MP} problem attributes.
Set before the callback. 
Description
Called at the 0 and last simplex iteration,
as well as each LPLOG iteration,
where LPLOG is the XPRS_LPLOG control variable.
Examples
Default the routine prints the problem number, the
iteration number and the current
value of the objective function.
The user could instead write
the Matlab statements wanted.
The definition of a few control variables are shown as comments.
See Also
See the documentation for the Xpress
^{MP} routine
XPRSsetcblplog.
Bugs
The variables
x,
slack,
pi and
rc are just set as empty.
It is not possible to retrieve these variables during the simplex
iterations. They will probably be deleted later on.
D.4 xpcb_ucb
Purpose
Xpress
^{MP} User Choose Branching Variable Callback routine
Calling Syntax
[iPtr, iDir, estdeg, xpcontrol] = xpcb_ucb(iPtr, iDir, estdeg, Prob)
Description of Input
iPtr 
Pointer to the variable or the set to branch. 
iDir 
1 or 3 ( for sets) means upward branch. 0 or 2 ( for sets) means downward
branch. 
estdeg 
Estimated degradation using the selected variable or set. 
Prob 
A structure. If TOMLAB calls xpress, then Prob is the standard
TOMLAB problem structure, otherwise the user optionally can set:
Prob.P = ProblemNumber;, where ProblemNumber is some integer.
When the callback routine is called then the
arrays that define the current problem are added
as fields in Prob.
The additional fields are Prob.QP.c,
Prob.QP.F,
Prob.x_L, Prob.x_U,
Prob.A, Prob.b_L, Prob.b_U. 
Description of Output
iPtr 
Pointer to the variable or the set to branch. 
iDir 
1 or 3 ( for sets) means upward branch. 0 or 2 ( for sets) means downward
branch. 
estdeg 
Estimated degradation using the selected variable or set. 
xpcontrol 
Structure with the control fields that the user wishes to be set in Xpress^{MP} 
Global Parameters Used


xpControlVariables 
Structure with all Xpress^{MP} control variables.
Set before the callback. 
xpProblemAttrib 
Structure with all Xpress^{MP} problem attributes.
Set before the callback. 
Description
At each global iteration, the
User Choose Branching Variable Callback routine
is called. It gives the user the possibility to set the wanted
branching variable.
New
values for the control variables are also possible to return.
Examples
Default the node number, the branch pointer, the direction and
the estimated degradation is printed.
The user should instead write
the Matlab statements to set
the branch pointer, the direction and
the estimated degradation.
See Also
See the documentation for the Xpress
^{MP} routine
XPRSsetcbchgbranch.
It is
demonstrated how to choose branching on the most
fractional integer.
D.5 xpcb_ucn
Purpose
Xpress
^{MP} User Node CutOff Callback routine
Calling Syntax
[xpcontrol] = xpcb_ucn(node, Prob)
Description of Input
node 
Node selected by Xpress^{MP} 
Prob 
A structure. If TOMLAB calls xpress, then Prob is the standard
TOMLAB problem structure, otherwise the user optionally can set:
Prob.P = ProblemNumber;, where ProblemNumber is some integer.
When the callback routine is called then the
arrays that define the current problem are added
as fields in Prob.
The additional fields are Prob.QP.c,
Prob.QP.F,
Prob.x_L, Prob.x_U,
Prob.A, Prob.b_L, Prob.b_U. 
Description of Output
xpcontrol 
Structure with the control fields that the user wishes to be set in Xpress^{MP} 
Global Parameters Used


xpControlVariables 
Structure with all Xpress^{MP} control variables.
Set before the callback. 
xpProblemAttrib 
Structure with all Xpress^{MP} problem attributes.
Set before the callback. 
Description
Declares a user node cutoff callback function, called every time a
node is cut off as a result of an improved integer solution being found
during the Branch and Bound search.
New
values for the control variables may be returned as sub fields in
the
xpcontrol variable.
Examples
Default the node number
is printed.
See Also
See the documentation for the Xpress
^{MP} routine
XPRSsetcbnodecutoff.
D.6 xpcb_uin
Purpose
Xpress
^{MP} User Infeasible Node Callback routine
Calling Syntax
[xpcontrol] = xpcb_uin(Prob)
Description of Input
Prob 
A structure. If TOMLAB calls xpress, then Prob is the standard
TOMLAB problem structure, otherwise the user optionally can set:
Prob.P = ProblemNumber;, where ProblemNumber is some integer.
When the callback routine is called then the
arrays that define the current problem are added
as fields in Prob.
The additional fields are Prob.QP.c,
Prob.QP.F,
Prob.x_L, Prob.x_U,
Prob.A, Prob.b_L, Prob.b_U. 
Description of Output
xpcontrol 
Structure with the control fields that the user wishes to be set in Xpress^{MP} 
Global Parameters Used


xpControlVariables 
Structure with all Xpress^{MP} control variables.
Set before the callback. 
xpProblemAttrib 
Structure with all Xpress^{MP} problem attributes.
Set before the callback. 
Description
At each global iteration, when an infeasible node is found
the User Infeasible Node Callback routine
is called.
The infeasible node is picked up using the global
structure
xpProblemAttrib.
NODES.
New values for the control variables is returned as sub fields in
the
xpcontrol variable.
Examples
Default the infeasible node number
is printed.
See Also
See the documentation for the Xpress
^{MP} routine
XPRSsetcbinfnode.
D.7 xpcb_uis
Purpose
Xpress
^{MP} User Integer Solution Callback routine
Calling Syntax
[xpcontrol] = xpcb_uis(Prob)
Description of Input
Prob 
A structure. If TOMLAB calls xpress, then Prob is the standard
TOMLAB problem structure, otherwise the user optionally can set:
Prob.P = ProblemNumber;, where ProblemNumber is some integer.
When the callback routine is called then the
arrays that define the current problem are added
as fields in Prob.
The additional fields are Prob.QP.c,
Prob.QP.F,
Prob.x_L, Prob.x_U,
Prob.A, Prob.b_L, Prob.b_U. 
Description of Output
xpcontrol 
Structure with the control fields that the user wishes to be set in Xpress^{MP} 
Global Parameters Used


xpControlVariables 
Structure with all Xpress^{MP} control variables.
Set before the callback. 
xpProblemAttrib 
Structure with all Xpress^{MP} problem attributes.
Set before the callback. 
Description
At each global iteration, when an integer solution is found
the
User Integer Solution Callback routine
is called.
The integer valued node is picked up using the global
structure
xpProblemAttrib.
NODES.
New values for the control variables is returned as sub fields in
the
xpcontrol variable.
Examples
Default the node number with an integer solution is printed,
together with the objective function value.
See Also
See the documentation for the Xpress
^{MP} routine
XPRSsetcbintsol.
D.8 xpcb_uon
Purpose
Xpress
^{MP} User Optimal Node Callback routine
Calling Syntax
[Feasible] = xpcb_uon(Prob)
Description of Input
Prob 
A structure. If TOMLAB calls xpress, then Prob is the standard
TOMLAB problem structure, otherwise the user optionally can set:
Prob.P = ProblemNumber;, where ProblemNumber is some integer.
When the callback routine is called then the
arrays that define the current problem are added
as fields in Prob.
The additional fields are Prob.QP.c,
Prob.QP.F,
Prob.x_L, Prob.x_U,
Prob.A, Prob.b_L, Prob.b_U. 
Description of Output
Feasible 
If 0, the node is accepted as optimal. 
Global Parameters Used


xpControlAttrib 
Structure with all Xpress^{MP} control variables.
Set before the callback. 
xpProblemVariables 
Structure with all Xpress^{MP} problem attributes.
Set before the callback. 
Description
When an optimal solution for the current node is found
the User Optimal Node Callback routine
is called.
Examples
Default the node number
and the function value is printed.
See Also
See the documentation for the Xpress
^{MP} routine
XPRSsetcboptnode.
D.9 xpcb_uop
Purpose
Xpress
^{MP} User Output Callback routine
Calling Syntax
xpcb_uop(msg, msgLevel, Prob)
Description of Input
msg 
Error message string. 
msgLevel 
Error Level 

4 
= 
Error 
3 
= 
Warning 
2 
= 
Dialogue 
1 
= 
Information 
0 
= 
Flush buffers 
1 
= 
No message 

Prob 
A structure. If TOMLAB calls xpress, then Prob is the standard
TOMLAB problem structure, otherwise the user optionally can set:
Prob.P = ProblemNumber;, where ProblemNumber is some integer.
When the callback routine is called then the
arrays that define the current problem are added
as fields in Prob.
The additional fields are Prob.QP.c,
Prob.QP.F,
Prob.x_L, Prob.x_U,
Prob.A, Prob.b_L, Prob.b_U. 
Description of Output
xpcontrol 
Structure with the control fields that the user wishes to be set in Xpress^{MP} 
Global Parameters Used


xpControlVariables 
Structure with all Xpress^{MP} control variables.
Set before the callback. 
xpProblemAttrib 
Structure with all Xpress^{MP} problem attributes.
Set before the callback. 
Description
Every time the
Xpress^{MP} solver wants to output a message, this
routine is called.
An error or warning message is always printed in the
Matlab command window, if this callback is enabled.
If the control variable
OUTPUTLOG is true, then also normal messages are printed
in the Matlab command window.
See Also
See the documentation for the Xpress
^{MP} routine
XPRSsetcbmessage.
D.10 xpcb_upn
Purpose
Xpress
^{MP} User Preprocess Node Callback routine
Calling Syntax
[Feasible] = xpcb_upn(Prob)
Description of Input
Prob 
A structure. If TOMLAB calls xpress, then Prob is the standard
TOMLAB problem structure, otherwise the user optionally can set:
Prob.P = ProblemNumber;, where ProblemNumber is some integer.
When the callback routine is called then the
arrays that define the current problem are added
as fields in Prob.
The additional fields are Prob.QP.c,
Prob.QP.F,
Prob.x_L, Prob.x_U,
Prob.A, Prob.b_L, Prob.b_U. 
Description of Output
Feasible 
A 1 shows the node is LP infeasible, a 0 that it is feasible. 
Global Parameters Used


xpControlVariables 
Structure with all Xpress^{MP} control variables.
Set before the callback. 
xpProblemAttrib 
Structure with all Xpress^{MP} problem attributes.
Set before the callback. 
Description
The
User Preprocess Node Callback routine
is called before the analysis of the node.
The user might have an efficient method in determining if the node
is LP feasible or not.
If the return flag is changed to one, the node is not further considered.
Examples
Default the node number
is printed.
See Also
See the documentation for the Xpress
^{MP} routine
XPRSsetcbprenode.
D.11 xpcb_usn
Purpose
Xpress
^{MP} User Select Node Callback routine
Calling Syntax
[xpcontrol] = xpcb_usn(node, Prob)
Description of Input
node 
Node selected by Xpress^{MP} 
Prob 
A structure. If TOMLAB calls xpress, then Prob is the standard
TOMLAB problem structure, otherwise the user optionally can set:
Prob.P = ProblemNumber;, where ProblemNumber is some integer.
When the callback routine is called then the
arrays that define the current problem are added
as fields in Prob.
The additional fields are Prob.QP.c,
Prob.QP.F,
Prob.x_L, Prob.x_U,
Prob.A, Prob.b_L, Prob.b_U. 
Description of Output
Global Parameters Used


xpControlVariables 
Structure with all Xpress^{MP} control variables.
Set before the callback. 
xpProblemAttrib 
Structure with all Xpress^{MP} problem attributes.
Set before the callback. 
Description
Every time the code backtracks to select a new node during the MIP
search, the
User Select Node Callback routine
is called.
It is then possible to return another node number,
if the user has a better strategy for selecting the new node.
Examples
Default the node number
is printed.
See Also
See the documentation for the Xpress
^{MP} routine
XPRSsetcbchgnode.
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