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INTEGER LINEAR PROGRAMMING - INTRODUCTION

INTEGER LINEAR PROGRAMMING - INTRODUCTION INTEGER LINEAR PROGRAMMING a11x1+a12x2+ +a1nxn b1 Feasible Region: Z-Polyhedron (n dimensional) maxc1x1+c2x2+ + +a12x2+ +a1nxn +am2x2+ +amnxn bmx1,..,xn2 ZIntegrality Constraint INTEGER LINEAR PROGRAMMING Relaxation to a (real-valued) LINEAR Program How does the LP relaxation answer relate to the ILP answer? Integrality Gap Complexity of INTEGER LINEAR Programs NP-Completeness Some special cases of ILPs. Algorithms: Branch-And-Bound Gomory-Chvatal Cuts INTEGER LINEAR PROGRAMMING : LP RELAXATION 1.

Integer Linear Programming • Relaxation to a (real-valued) Linear Program • How does the LP relaxation answer relate to the ILP answer? • Integrality Gap • Complexity of Integer Linear Programs • NP-Completeness • Some special cases of ILPs. • Algorithms: • Branch-And-Bound • Gomory-Chvatal Cuts

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