Many important practical computations, such as scheduling, combinatorial, and optimization problems, use techniques known as integer programming to find the best combination of many variables. In ...

Formulations of mathematical programs often require that some of the decision variables take only integer values. Consider the formulation You can follow the same steps to identify binary variables.

Write down the Linear Program (LP) relaxation of an IP Plot the graphical representation of an IP and find the optimal solution Understand the relationship between optimal solution of an IP and the ...

This paper gives integer linear programming (ILP) models for scheduling the League Phase of one of the most popular professional club competitions in the world, UEFA Champion’s League. There are 36 ...

Learning directed acyclic graphs (DAGs) from data is a challenging task both in theory and in practice, because the number of possible DAGs scales superexponentially with the number of nodes. In this ...

This book presents the state-of-the-art methods in Linear Integer Programming, including some new algorithms and heuristic methods developed by the authors in recent years. Topics as Characteristic ...

The resources available for conserving biodiversity are limited, and so protected areas need to be established in places that will achieve objectives for minimal cost. Two of the main algorithms for ...