This preview shows pages 1–17. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: BranchandCut Valid inequality: an inequality satisfied by all feasible solutions Cut: a valid inequality that is not part of the current formulation Violated cut: a cut that is not satisfied by the solution to the current LP relaxation BranchandCut Branchandcut is a generalization of branchandbound where, after solving the LP relaxation, and having not been successful in pruning the node on the basis of the LP solution, we try to find a violated cut. If one or more violated cuts are found, they are added to the formulation and the LP is solved again. If none are found, we branch. BranchandCut Given a solution to the LP relaxation of a MIP that does not satisfy all the integrality constraints, the separation problem is to find a violated cut. Cut Classification General purpose Relaxation Problem specific Cut Classification General purpose: a fractional extreme point can always be separated Gomory cuts 01 disjunctive cuts Cut Classification Relaxation cuts: 01 knapsack set Continuous 01 knapsack set Node packing Cut Classification Problem specific: generally facets, derived from problem structure blossom inequalities for matching comb inequalities for TSP LiftandProject cuts A Mixed 01 Program { } min , , , , cx Ax b x x i p i = 0 1 1 its LP Relaxation min ~ ~ ~ ~ cx Ax b Ax b where includes all bounds with optimal solution x LiftandProject cuts Generate cutting planes for any mixed 01 program: Disjunction ~ ~ ~ ~ Ax b x Ax b x x i i i = = 1 {0,1} Description of P conv Ax b x Ax b x i i i = = = ~ ~ ~ ~ 0 1 Choose a set of inequalities valid for P i that cut off x The LP relaxation The optimal fractional solution x One side of the disjunction = i x x 1 = i x The other side of the disjunction x The union of the disjunctive sets x The convexhull of the union of the disjunctive sets x One facet of the convexhull but it is also a cut!...
View
Full
Document
This note was uploaded on 03/01/2012 for the course ECON 102 taught by Professor Mehmet during the Spring '12 term at Abraham Baldwin Agricultural College.
 Spring '12
 mehmet

Click to edit the document details