Applications of Integer Programming Methods to Cages

Applications of Integer Programming Methods to Cages

The aim of this paper is to construct new small regular graphs with girth 7 using integer programming techniques. Over the last two decades solvers for integer programs have become more and more powerful and have proven to be a useful aid for many hard combinatorial problems. Despite successes in many related fields, these optimisation tools have so far been absent in the quest for small regula...

Mixed Integer Nonlinear Programming Applications

In this contribution we apply different approaches to solve four rather different MINLP problems: special extensions to time-indexed formulations of production planning problems, a production planning problem in BASF’s petrochemical division, a site analysis of one of BASF’s bigger sites, and a process design problem. The first problem is related to a useful nonlinear extension of production pl...

Methods and Applications in Integer Programming: All-Integer Column Generation and Nurse Scheduling

Integer programming can be used to provide solutions to complex decision and planning problems occurring in a wide variety of situations. Applying integer programming to a real life problem basically involves a first phase where a mathematical model is constructed, and a second phase where the problem described by the model is solved. While the nature of the challenges involved in the respectiv...

Complexity of Primal Methods in Integer Programming

One common approach to solve optimization problems is the primal method. One starts with a feasible point and then successively produces new feasible solutions with better objective function values until an optimal solution is reached. From an abstract point of view, an augmentation problem is solved in each iteration, i.e., given a feasible point find an augmenting vector, if one exists. The d...

Topics in group methods for integer programming