The purpose of this paper is to present an overview of families of cutting planes for mixed integer programming problems. We examine the families of disjunctive inequalities, split cuts, mixed integer rounding inequalities, mixed integer Gomory cuts, intersection cuts, lift-and-project cuts, and reduceand-split cuts. In practice, mixed integer Gomory cuts are very useful in obtaining solutions ...

Mixed-integer quadratic programming (MIQP) is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of mixed-integer quadratic programming is in NP, thereby showing that it is NP-complete. This is established by showing that if the decision version of mixed-inte...

Answer set programming is a programming paradigm where a given problem is formalized as a logic program whose answer sets correspond to the solutions to the problem. In this paper, we link answer set programming with another widely applied paradigm, viz. mixed integer programming. As a theoretical result, we establish translations from non-disjunctive logic programs to linear constraints used i...

We present the application of Genetic Programming (GP) in Branch and Bound (B&B) based Mixed Integer Linear Programming (MIP). The hybrid architecture introduced employs GP as a node selection expression generator: a GP run, embedded into the B&B process, exploits the characteristics of the particular MIP problem being solved, evolving a problem-specific node selection method. The evolved metho...

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...

Robust supplier selection problem, in a scenario-based approach has been proposed, when the demand and exchange rates are subject to uncertainties. First, a deterministic multi-objective mixed integer linear programming is developed; then, the robust counterpart of the proposed mixed integer linear programming is presented using the recent extension in robust optimization theory. We discuss dec...