RLT Hierarchy for General Discrete Mixed-Integer Problems
Thus far, we have been focusing on 0–1 mixed-integer programming problems and have developed a general theory for generating a hierarchy of tight relaxations leading to the convex hull representation. However, in many applications, we encounter problems in which the decision variables are required to take on more general discrete or integer values as opposed to simply zero or one values. Of particular interest in this context are classes of problems involving variables that are restricted to taken on only a few discrete values, that are possibly not even consecutive integers, for which one might expect to have weak ordinary linear programming relaxations. In this chapter, we demonstrate how one can generate a hierarchy of relaxations leading to the convex hull representation for such general bounded variable discrete optimization problems.
KeywordsValid Inequality Redundant Constraint Distinct Index Original Constraint Tight Relaxation
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