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INTEGER LINEAR PROGRAMMING - INTRODUCTION

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INTEGER LINEAR PROGRAMMING - INTRODUCTION INTEGER LINEAR PROGRAMMING a11x1+a12x2+ +a1nxn b1Feasible Region: Z-Polyhedron (n dimensional) maxc1x1+c2x2+ + +a12x2+ +a1nxn +am2x2+ +amnxn bmx1,...,xn2ZIntegrality 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.

• Uses branch-and-bound + Gomory cut techniques • We will examine these techniques soon. • In this lecture, • Show how to solve (mixed) integer linear programs • Continue to use AMPL format. • This is the best option for solving ILPs/MIPs

  Programming, Technique

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