@misc{BertholdGleixner, author = {Berthold, Timo and Gleixner, Ambros}, title = {Undercover: a primal MINLP heuristic exploring a largest sub-MIP}, issn = {1438-0064}, doi = {10.1007/s10107-013-0635-2}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14631}, number = {12-07}, abstract = {We present Undercover, a primal heuristic for nonconvex mixed-integer nonlinear programming (MINLP) that explores a mixed-integer linear subproblem (sub-MIP) of a given MINLP. We solve a vertex covering problem to identify a minimal set of variables that need to be fixed in order to linearize each constraint, a so-called cover. Subsequently, these variables are fixed to values obtained from a reference point, e.g., an optimal solution of a linear relaxation. We apply domain propagation and conflict analysis to try to avoid infeasibilities and learn from them, respectively. Each feasible solution of the sub-MIP corresponds to a feasible solution of the original problem. We present computational results on a test set of mixed-integer quadratically constrained programs (MIQCPs) and general MINLPs from MINLPLib. It turns out that the majority of these instances allow for small covers. Although general in nature, the heuristic appears most promising for MIQCPs, and complements nicely with existing root node heuristics in different state-of-the-art solvers.}, language = {en} } @misc{Berthold, author = {Berthold, Timo}, title = {Primal MINLP Heuristics in a nutshell}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42170}, abstract = {Primal heuristics are an important component of state-of-the-art codes for mixed integer nonlinear programming (MINLP). In this article we give a compact overview of primal heuristics for MINLP that have been suggested in the literature of recent years. We sketch the fundamental concepts of different classes of heuristics and discuss specific implementations. A brief computational experiment shows that primal heuristics play a key role in achieving feasibility and finding good primal bounds within a global MINLP solver.}, language = {en} }