Branch—and—Price Algorithm

Abstract

In this chapter we aim at handling problems observed in chapters 2 and 3. When we tackle RRT problems with standard B&B methods we suffer from four main obstacles so far:

• The problem size is determined by more than n(n − 1)² variables and more than 3n(n−1)/2 constraints and allows exact solution only for rather small instances

• Solutions to LP relaxations in general are highly fractional and provide poor lower bounds

• When setting variables to integer values in a B&B framework we often experience fractional values coming up for other variables due to model inherent symmetry

• Cost oriented node order strategies are difficult to implement since fixing variables has intractable consequences for other variables due to the compact structure of time constrained SLS problems