A new reduction method in integer programming

Global optimization of mixed-integer polynomial programming problems: A new method based on Grobner Bases theory

Mixed-integer polynomial programming (MIPP) problems are one class of mixed-integer nonlinear programming (MINLP) problems where objective function and constraints are restricted to the polynomial functions. Although the MINLP problem is NP-hard, in special cases such as MIPP problems, an efficient algorithm can be extended to solve it. In this research, we propose an algorit...

A new approach for solving neutrosophic integer programming problems

Linear programming is one of the most important usages of operation research methods in real life, that includes of one objective function and one or several constraints which can be in the form of equality and inequality. Most of the problems in the real world are include of inconsistent and astute uncertainty, because of this reason we can’t obtain the optimal solution easily. In this paper, ...

Lattice Reduction, Integer Programming, and Knapsacks

We will discuss knapsack problems that arise in certain computa− tional number theory settings. A common theme is that the search space for the standard real relaxation is large; in a sense this trans− lates to a poor choice of variables. Lattice reduction methods have been developed in the past few years to improve handling of such problems. We show explicitly how they may be applied to comput...

New Approaches to Integer Programming

The IntSat Method for Integer Linear Programming

Conflict-Driven Clause-Learning (CDCL) SAT solvers can automatically solve very large real-world problems. To go beyond, and in particular in order to solve and optimize problems involving linear arithmetic constraints, here we introduce IntSat, a generalization of CDCL to Integer Linear Programming (ILP). Our simple 1400-line C++ prototype IntSat implementation already shows some competitivene...