XSLP_MIPALGORITHM determines the strategy of
XSLPglobal for solving MINLP problems. The recommended approach is to
solve the problem first without reference to the global variables. This can be handled
automatically by setting bit 0 of
XSLP_MIPALGORITHM; if done manually, then
optimize using the "l" option to prevent the Optimizer presolve from changing the problem.
Some versions of the optimizer re-run the initial node as part of the global search; it is
possible to initiate a new SLP optimization at this point by relaxing or fixing step bounds
(use bits 2 and 3). If step bounds are fixed for a class of variable, then the variables
in that class will not change their value in any child node.
At each node, it is possible to relax or fix step bounds. It is recommended that step bounds
are relaxed, so that the new problem can be solved starting from its parent, but without
undue restrictions cased by step bounding (use bit 4). Exceptionally, it may be
preferable to restrict the freedom of child nodes by relaxing fewer types of step
bound or fixing the values of some classes of variable (use bit 5).
When the optimal node has been found, it is possible to fix the global variables and then
re-optimize with SLP. Step bounds can be relaxed or fixed for this optimization as well
(use bits 7 and 8).
Although it is ultimately necessary to solve the optimal node to convergence, individual
nodes can be truncated after
XSLP_MIPITERLIMIT SLP iterations. Set
bit 6 to activate this feature.
The normal MISLP algorithm uses SLP at each node. One alternative strategy is to use
the MIP optimizer for solving each SLP iteration. Set bit 9 to implement this strategy
("MIP within SLP").
Another strategy is to solve the problem to convergence ignoring the nature of the global
variables. Then, fixing the linearization, use MIP to find the optimal setting of the
global variables. Then, fixing the global variables, but varying the linearization, solve
to convergence. Set bit 10 to implement this strategy ("SLP then MIP").
For mode details about MISLP algorithms and strategies, see the separate section.