Disjunctive cuts in branch-and-but-and-price algorithms ... - gerad

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How about generic cuts on the variables of the compact formulation • We have a pretty good idea about such cuts should be handeled in a BAP algorithm (well studied in the literature). • Wouldn’t it be nice if we could ”flip a switch” and our integrality gap is decreased by 30 or 40% • ... at the cost of more rows in the master problem and increased separation time
Our candidate: Disjunctive cuts in the variables of the compact formulation • Dates back to a technical report by E. Balas from 1974. • Was shown to be useful in practice by Balas, Ceria, Cornuéjols (1993). • Includes or is equivalent to a number of other generic cutting planes: Lift-andproject cuts, split cuts, intersection cuts, gomory mixed integer cuts • Is included in some form in both CPLEX and Xpress-MP.
Page 1 and 2: Disjunctive cuts in branch-and-but-
Page 3 and 4: Motivation • Our goal: Solve diff
Page 5: Motivation: Branch-cut-and-price
Page 9 and 10: Our IP problem (compact formulation
Page 11 and 12: Our IP problem (compact formulation
Page 15 and 16: Objective x 2 x 1 1 2 3 4 5 6 7
Page 17: Objective x 2 x 1 1 2 3 4 5 6 7
Page 24: Separation algorithm
Page 29 and 30: Compact formulation
Page 31 and 32: Disjunctive cuts for the CVRP • S
Page 33 and 34: Solving the CVRP - Pricing • Shor
Page 35 and 36: Results - SPPCC-2CE Gap (%) Gap clo
Page 37 and 38: Results - SPPCC-2CE Gap (%) Gap clo
Page 39 and 40: Results - ESPPCC Gap (%) Cap cuts 0
Page 41 and 42: Effects of parameters Gap (%) Gap c
Page 43 and 44: Best methods for the CVRP • FLLPR
Page 45 and 46: Used in a framework that does autom

Disjunctive cuts in branch-and-but-and-price algorithms ... - gerad

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