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The characterization of strong valid inequalities for integer andmixed-integer programs is more of an artistic task than a systematicmethodology, requiring inspiration that can sometimes be elusive. Frequently,this task is facilitated by somehow exploiting the structure of problems fordevising strong valid inequalities. Subsequently, various mathematicaltechniques are utilized for proving that those inequalities, which are ofteneasily shown to be valid, are indeed strong in the sense that they representfacets or other high dimensional faces. This paper develops a method to assistmodelers in the challenge to devise strong valid inequalities. In eachiteration, the proposed algorithm generates a valid inequality by solving asuitably constructed linear mixed integer program and applies some qualitycriteria in order to determine if it is a new strong valid inequality. Toillustrate the proposed algorithm, a new Traveling Salesman Problem (TSP)formulation is developed based on a set of constraints already constructed inthe context of the Hamiltonian Cycle Problem (HCP), and then the proposedalgorithm is employed to derive a set of strong inequalities to tighten thisTSP formulation. Finally, a comparison study between the relaxation of the newTSP formulation and that of a state-of-the-art TSP formulation is conducted.The computational study confirms the effectiveness of the devised inequalitiesdue to the better quality of the relaxation provided by the new formulation.

Strong Valid Inequalities Identification for Mixed Integer Programming Problems