  Two essential ingredients of modern mixed-integer programming (MIP) solvers
are diving heuristics that simulate a partial depth-first search in a
branch-and-bound search tree and conflict analysis of infeasible subproblems to
learn valid constraints. So far, these techniques have mostly been studied
independently: primal heuristics under the aspect of finding high-quality
feasible solutions early during the solving process and conflict analysis for
fathoming nodes of the search tree and improving the dual bound. Here, we
combine both concepts in two different ways. First, we develop a diving
heuristic that targets the generation of valid conflict constraints from the
Farkas dual. We show that in the primal this is equivalent to the optimistic
strategy of diving towards the best bound with respect to the objective
function. Secondly, we use information derived from conflict analysis to
enhance the search of a diving heuristic akin to classical coefficient diving.
The computational performance of both methods is evaluated using an
implementation in the source-open MIP solver SCIP. Experiments are carried out
on publicly available test sets including Miplib 2010 and Cor@l.
