In this paper we study the bilevel linear programming problem with multiple objective functions at the upper level, with particular focus on the bi-objective case. We examine some properties of this problem and propose a methodological approach based on the reformulation of the problem as a multiobjective mixed 0-1 linear programming problem. The basic idea consists in applying a reference poin...

In this paper we present a rather new approach to apply mixed-integer optimization to the cryptanalysis of cryptographic primitives. We focus on the stream cipher Trivium, that has been recommended by the eSTREAM stream cipher project, and the lightweight block cipher Ktantan. Using these examples we explain how the problem of solving a non-linear multivariate Boolean equation system can be for...

we study the problem of reconstructing binary images from four projections data in a fuzzy environment. given the uncertainly projections,w e want to find a binary image that respects as best as possible these projections. we provide an iterative algorithm based on fuzzy integer programming and linear membership functions.

Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the nondominated points‎. ‎Whereas determining the ‎ideal point is an easy work‎, ‎because it is equivalent to optimize a ‎convex function (linear function) over a con...

For many years the mathematical programming community has realized the practical importance of developing algorithmic tools for tackling mixed integer optimization problems. Given our ability to solve linear optimization problems efficiently, one is inclined to think that a mixed integer program with both continuous and discrete variables is easier than a pure integer programming problem since ...

This paper considers the solution of Mixed Integer Nonlinear Programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer part. This approach is largely due to the existence of packaged software for solving Nonlinear Programming (NLP) and Mixed Integer Linear Programming problems. In contrast, an integ...

We present new exact and heuristic algorithms for the prizecollecting Steiner tree problem. The exact algorithm rst reduces the size of the input graph while preserving equivalence of the optimal solutions and then uses mixed integer linear programming to solve the resulting instance. For our heuristic, we reduce the size of the instance graph further, but without guaranteeing the equivalence o...