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For many mixed-integer programming (MIP) problems, high-quality dual boundscan be obtained either through advanced formulation techniques coupled with astate-of-the-art MIP solver, or through semidefinite programming (SDP)relaxation hierarchies. In this paper, we introduce an alternative boundingapproach that exploits the "combinatorial implosion" effect by solving portionsof the original problem and aggregating this information to obtain a globaldual bound. We apply this technique to the one-dimensional and two-dimensionalfloor layout problems and compare it with the bounds generated by bothstate-of-the-art MIP solvers and by SDP relaxations. Specifically, we provethat the bounds obtained through the proposed technique are at least as good asthose obtained through SDP relaxations, and present computational results thatthese bounds can be significantly stronger and easier to compute than thesealternative strategies, particularly for very difficult problem instances.

Beating the SDP bound for the floor layout problem: A simple combinatorial idea