Integer Linear Programming in Computational Biology: Overview of ILP, and New Results for Traveling Salesman Problems in Biology

Abstract

Integer linear programming (ILP) is a powerful and versatile technique for framing and solving hard optimization problems of many types. In the last several years, ILP has become widely used in computational biology, although predominantly by computationally and mathematically trained researchers, such as Bernard Moret. In an effort to reach a broader set of researchers, this chapter begins with an introduction to ILP, illustrated by the phenomena of cliques and independent sets in biological graphs. Then, the focus shifts to new research results on the use of ILP to solve traveling salesman problems, using compact ILP formulations. Such formulations have been largely declared useless in the optimization literature. However, in this chapter, I argue that the correct compact formulation can be very effective for problems of the size and structure that arise in computational biology. These empirical results, and some additional arguments, then bring into question the relevance of the concept of strength of an ILP formulation as a predictor of the speed that it will be solved.