In the classic Integer Programming Feasibility (IPF) problem, objective is to decide whether, for a given $$m \times n$$ matrix A and an m-vector $$b=(b_1,\dots , b_m)$$ there non-negative integer n-vector x such that $$Ax=b$$ . Solving important step in numerous algorithms it obtain understanding of precise complexity this problem as function natural parameters input. The pseudo-polynomial tim...

A conic integer program is an integer programming problem with conic constraints. Many problems in finance, engineering, statistical learning, and probabilistic optimization are modeled using conic constraints. Here we study mixed-integer sets defined by second-order conic constraints. We introduce general-purpose cuts for conic mixed-integer programming based on polyhedral conic substructures ...

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 ...

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...