Xpress Callbacks in Matlab

There are eleven of the Xpress MP callbacks defined in the interface. A logical vector defines the callbacks to be used in Xpress MP. This vector is named callback and is one of the input variables to the level 1 interface routine xpress. If the ith entry of the logical vector callback is set, the corresponding callback is defined. The callback calls the m-file specified in Table 2. The user can edit this m-file directly, or make a new copy. It is important that a new copy is placed in a directory that is searched before the xpress directory when Matlab goes through the Matlab path.

Index	m-file	Description
(1)	xpcb usn	User Select Node Callback
(2)	xpcb upn	User Preprocess Node Callback
(3)	xpcb uon	User Optimal Node Callback
(4)	xpcb uin	User Infeasible Node Callback
(5)	xpcb uis	User Integer Solution Callback
(6)	xpcb ucn	User Node Cut-off Callback
(7)	xpcb ucb	User Choose Branching Variable Callback
(8)	xpcb il	Simplex Log Callback
(9)	xpcb gl	Global Log
(10)	xpcb bl	Barrier Log Callback
(11)	xpcb uop	User Output Callback

Before each call to the callback routine, the interface is defining the control variables and problem attributes as global variables in Matlab. By making the following global declarations in the callback m-file, global xpControlVariables xpProblemAttrib all control variables and problem attributes are accessible as subfields to the global variables.

The Prob structure is input to all callback m-file routines as the last parameter. If TOMLAB calls xpress, then Prob is the standard TOMLAB problem structure, otherwise the user optionally can set: P rob.P = P roblemN umber;, where ProblemNumber is some integer. If any callback is defined (see description of callback) then the arrays that define the current problem are set by the interface as fields in Prob. The defined fields are Prob.c, Prob.x L, Prob.x U, Prob.A, Prob.b L, Prob.b U and. Prob.QP.F. The user then has full access to the original problem in the callback routine.

In one of the callback routines, xpcb gl, a simple knapsack heuristic is implemented. This heuristic is also part of the standard XpressM P example files. Running the knapsack test program xpknaps, with the second input argument Run = 1 runs the knapsack heuristic in the callback. xpknaps sets Prob.MIP.KNAPSACK = 1 to enable execution of the heuristic in xpcb gl.

If there are no integer variables in the problem to be solved, i.e. a pure LP or QP problem, then the first seven callbacks as well as the 9th callback (Global Log) are automatically disabled. If the problem is a mixed-integer problem, then the 8th callback (Simplex Log Callback) is disabled. This change is made on around row 254 i xpress.m and the user may comment this row (callback(8) = 0;) to avoid it.

Test Routines in Non-Tomlab Format

A set of test routines have been defined illustrating the use of the xpress main routine. The test routines and utilities are shown in Table 3.

It is easy to call the test routines, e.g.

x = xptest1; 
x = xptest2; 
x = xptest3;

will call the three routines solving GAP problems. The xpaircrew test problem has no input parameters, just call:

xpaircrew;

The knapsack test routine runs three test examples. It is possible to change the cut strategy (third input parameter) and whether to use the knapsack heuristic in the callback routine xpcb gl (second input parameter). To run the second test example, using the simple knapsack heuristic, and aggressive cuts, the call is

xpknaps(2,1,2);

The first parameter selects the test problem. Calling without any parameters

xpknaps

is the same as the call

xpknaps(1,0,0);

The test routines and utilities.

Function	Description
abc2gap	Utility to convert a Generalized Assignment Problem (GAP) to stan- dard form for XpressM P .
xpbiptest	Test of three large binary integer linear problems.
xpiptest	Test of three large integer linear problems.
xpknaps	Test of knapsack problems.
xptest1	Test of a Generalized Assignment Problem (GAP).
xptest2	Test of the same GAP problem as xptest1, but using sos1 variables.
xptest3	Test of a Generalized Assignment Problem (GAP).