Generalized Hierarchy for Exploiting Special Structures in Mixed-Integer Zero-One Problems
In the previous chapter, we discussed a technique for generating a hierarchy of relaxations that span the spectrum from the continuous LP relaxation to the convex hull of feasible solutions for linear mixed-integer 0–1 programming problems. The key construct was to compose a set of multiplication factors based on the bounding constraints 0 ≤ x ≤ e n on the binary variables x , and to use these factors to generate implied nonlinear product constraints, then tighten these constraints using the fact that x j 2 ≡ x j ∀ j = 1, …, n, and subsequently linearize the resulting polynomial problem through a variable substitution process. This process yielded tighter representations of the problem in higher dimensional spaces.
KeywordsTravel Salesman Problem Valid Inequality Linear Programming Relaxation Product Constraint Conditional Logic
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