Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation Pareto front challenging. The present article shows that certain algorithms were originally devised for continuous can be successfully adapted to approximate integer, and mixed-integer, multi-objective problems. Relationships amongst variou...

In this paper we present several algorithms which combine a partial enumeration with meta-heuristics for the solution of general mixed-integer programming problems. The enumeration is based on the primal values assignable to the integer variables of the problem. We develop some algorithms for this integration, and test them using a set of well-known benchmark problems. Key-words: Enumeration, L...

Lifting is a procedure for deriving strong valid inequalities for a closed set from inequalities that are valid for its lower dimensional restrictions. It is arguably one of the most effective ways of strengthening linear programming relaxations of 0–1 programming problems. Wolsey (1977) and Gu et al. (2000) show that superadditive lifting functions lead to sequence independent lifting of valid...

Inspired by Fu et al. work [12] on modeling the exclusive-or differential property of the modulo addition as an mixed-integer programming problem, we propose a method with which any finite automaton can be formulated as an mixed-integer programming model. Using this method, we show how to construct a mixed integer programming model whose feasible region is the set of all differential patterns (...

The identification problem is formally stated as follows: Given a set Lobs of observed timed sequences that belongs to the timed language L of the unknown system T ′ and a set of places P of cardinality m, the problem consists in the identification of the net structure N , the timing structure I , and the initial marking m0 such that the timed language generated by T = 〈N,m0, I〉, named L(T ), c...

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 ...

We study a special case of a structured mixed integer programming model that arises in production planning. For the most general case of the model, called PI, we have earlier identified three families of facet–defining valid inequalities: (l, S) inequalities (introduced for the uncapacitated lot–sizing problem by Barany, Van Roy, and Wolsey), cover inequalities, and reverse cover inequalities. ...

This survey presents tools from polyhedral theory that are used in integer programming. It applies them to the study of valid inequalities for mixed integer linear sets, such as Gomory’s mixed integer cuts.

We study a mixed integer linear program with m integer variables and k nonnegative continuous variables in the form of the relaxation of the corner polyhedron that was introduced by Andersen, Louveaux, Weismantel and Wolsey [Inequalities from two rows of a simplex tableau, Proc. IPCO 2007, LNCS, vol. 4513, Springer, pp. 1–15]. We describe the facets of this mixed integer linear program via the ...

In this article we study a broad class of integer programming problems in variable dimension. We show that these so-termed n-fold integer programming problems are polynomial time solvable. Our proof involves two heavy ingredients discovered recently: the equivalence of linear optimization and so-called directed augmentation, and the stabilization of certain Graver bases. We discuss several appl...