Parametric tabu-search for mixed integer programs

A parametric form of tabu-search is proposed for solving mixed integer programming (MIP) problems that creates and solves a series of linear programming (LP) problems embodying branching inequalities as weighted terms in the objective function. The approach extends and modifies a parametric branch and bound procedure of Glover, replacing its tree search memory by the adaptive memory framework of tabu-search and introducing new associated strategies that are more flexible than the mechanisms of branch and bound. We also introduce new types of intensification and diversification procedures based on scatter search and frequency analysis, and also based on a variant of adaptive memory called model embedded memory. In one form this approach incorporates recency and frequency memory within the objective function structure of the parameterized LP formulations. In another form it generates valid inequalities from the optimized objective of the parameterized LP problem, and uses these as a supplement to traditional types of tabu memory. The integrated parametric approach affords a spectrum of variations that include useful simplifications for pure 0–1 MIP problems and problems with special structures, such as GUB constraints. The approach exploits both spatial and logical relationships, and is appropriate for discovering feasible solutions, as in the case of satisfiability problems. It is particularly designed to provide adaptive strategies for problems that are difficult for branch and bound and for branch and cut procedures, as opposed to problems these latter methods can handle effectively, and hence can be used to complement or supplement these more traditional types of methods.