Integer linear programming (ILP) is an optimization method that depends on the satisfaction of a set of linear equality or inequality relationships and has solutions with integer (rather than continuous) values. An important application area of ILP is computational biology, especially genomics. This book is a significant contribution to teaching ILP applications in biology. It is perhaps the first textbook in this area.

The book’s 23 chapters are divided into two parts. The first part (12 chapters) is the textbook for the course on ILP that the author designed and taught. The second part presents more advanced topics that build on the foundation laid in Part 1. The book’s intent is to provide a practical introduction. Although it employs formal definitions and terminology, the results and conclusions from theorems are only stated and used. It downplays formal proofs.

Both parts have plenty of exercises and problems to challenge students, and both parts use examples to develop topics. Part 1 emphasizes the techniques needed to properly state the problem to be solved as an ILP problem and to formulate the script the ILP engine uses to generate solutions. This approach is used consistently throughout. The book is closely tied to the ILP solution engine Gurobi (https://www.gurobi.com/). Although this is a commercial product, academic users (that is, anyone with an .edu suffix on his or her email) are eligible for a free license.

The first part begins with an ecology problem to demonstrate the usefulness of ILP. The same problem is solved using both linear programming with fractional values in the solution and ILP. Chapters 2 through 5 present graph theory and discuss software tools. The graph theory topics emphasized here are the maximum clique problem, near cliques, motifs, and maximum parsimony. The biological examples are taken from phylogenetics.

Chapters 6 through 10 focus on the details of sequences at the molecular level: prediction of secondary structure and folding in ribonucleic acid (RNA) from just the sequence structure, amino acid side chain orientation and protein folding, minimizing crossovers in comparing phylogenies in tanglegrams, using the traveling salesman problem to assemble deoxyribonucleic acid (DNA) fragments to produce a complete DNA sequence, and molecular sequence analysis in nucleic acids and proteins to relate structure and function.

Chapter 11 departs from the biological structural topics by showing how to use ILP to analyze metabolic networks. These are modeled as Boolean networks (the component is either present or absent). As Boolean constructs, all of the logical operations (for example, AND, OR, XOR) can be used in formulating a model. Boolean networks are qualitative, but quantitative extensions incorporating mass/energy balances can be built on the qualitative framework. Chapter 12 summarizes nomenclature and idioms in ILP.

The second part presumes a greater level of comfort and competency with ILP and Gurobi. The biological topics in chapters 13 through 21 include locating genes and mutations that influence traits, identifying and correcting missing and erroneous data in sequences, using tanglegrams to introduce multi-objective optimization, deducing protein pathways, protein-protein interaction networks, identifying driver genes in cancer, generating family pedigrees, haplotype assembly, and 3D protein structure comparisons. The graph theory tools include extracting subgraphs, minimum character removal, longest common subsequences, and hierarchical clustering.

The penultimate chapter exhorts the reader to look ahead to extending the scope of biological applications, learning more about ILP solvers and engines and developing programming skills. In the last chapter, the author reflects on the power and appropriateness of ILP models. He observes that ILP has semantic value: users can understand what is taking place in the calculation instead of merely trusting a black box.

The style of writing carefully treats the scientific and technical topics in a conversational tone, much like well-crafted lectures by professors who understand what their students bring to the lecture hall. The target readership includes biology students (especially graduate students) and students in computer science and scientific computing who are interested in biology. A course using this book would serve both communities well.