Sandpile group or Abelian sandpile model was the first example of a self-organized critical system studied by Bak, Tang and Wiesenfeld. It is well known that these recurrent configurations can be characterized as optimal solution certain non-linear optimization problems. We show graph correspond to solutions some integer linear programs. More precisely, we present two new programming models, on...

We define difficult optimization problems as problems which cannot be solved to optimality or to any guaranteed bound by any standard solver within a reasonable time limit. The problem class we have in mind are mixed integer programming (MIP) problems. Optimization and especially mixed integer optimization is often appropriate and frequently used to model real world optimization problems. While...

This paper extends the proposed method by Jahanshahloo et al. (2004) (a method for generating all the efficient solutions of a 0–1 multi-objective linear programming problem, Asia-Pacific Journal of Operational Research). This paper considers the recession direction for a multi-objective integer linear programming (MOILP) problem and presents necessary and sufficient conditions to have unbounde...

1 To appear as a chapter of the Handbook of Algorithms edited by M. Abstract Integer programming is an expressive framework for modeling and solving discrete optimization problems that arise in a variety of contexts in the engineering sciences. Integer programming representations work with implicit algebraic constraints (linear equations and inequalities on integer valued variables) to capture ...