Given $P\subset\R^n$, a mixed-integer set $P^I=P\cap (\Z^{t}\times\R^{n-t}$), and a $k$-tuple of $n$-dimensional integral vectors $(\pi_1, \ldots, \pi_k)$ where the last $n-t$ entries of each vector is zero, we consider the relaxation of $P^I$ obtained by taking the convex hull of points $x$ in $P$ for which $ \pi_1^Tx,\ldots,\pi^T_kx$ are integral. We then define the $k$-dimensional … Read more
In this paper we analyze general Stackelberg games (SGs) and Stackelberg security games (SSGs). SGs are hierarchical adversarial games where players select actions or strategies to optimize their payoffs in a sequential manner. SSGs are a type of SGs that arise in security applications, where the strategies of the player that acts first consist in … Read more
Modularity density maximization is a clustering method that improves some issues of the commonly-used modularity maximization approach. Recently, some Mixed-Integer Linear Programming (MILP) reformulations have been proposed in the literature for the modularity density maximization problem, but they require as input the solution of a set of auxiliary binary Non-Linear Programs (NLPs). These can become … Read more
We present a generic branch-and-bound algorithm for finding all the Pareto solutions of a biobjective mixed-integer linear program. The main contributions are new algorithms for obtaining dual bounds at a node, checking node fathoming, presolve, and duality gap measurement. Our branch-and-bound is predominantly a decision space search method because the branching is performed on the … Read more
A mathematical programming approach to deal with the global configuration of resource constraints is presented. A specialized parametric programming algorithm to obtain the pareto set for the biobjective problem that appears to deal with the global configuration for 0-1-Integer Linear Programing problems is presented and implemented. Computational results for Multiconstrained Knapsack problems and Bounded Knapsack … Read more
We consider the Multilinear polytope defined as the convex hull of the set of binary points satisfying a collection of multilinear equations. Such sets are of fundamental importance in many types of mixed-integer nonlinear optimization problems, such as binary polynomial optimization. Utilizing an equivalent hypergraph representation, we study the facial structure of the Multilinear polytope … Read more
In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to … Read more
In this paper we study integer linear programming models and develop branch-and-cut algorithms to solve the Black-and-White Traveling Salesman Problem (BWTSP) (Bourgeois et al., 2003) which is a variant of the well known Traveling Salesman Problem (TSP). Two strategies to model the BWTSP have been used in the literature. The problem is either modeled on … Read more
For a fixed integer $t > 0$, we say that a $t$-branch split set (the union of $t$ split sets) is dominated by another one on a polyhedron $P$ if all cuts for $P$ obtained from the first $t$-branch split set are implied by cuts obtained from the second one. We prove that given a … Read more
The multiple traveling salesmen problem with moving targets (MT-SPMT) is a generalization of the classical traveling salesmen problem (TSP), where the targets (cities or objects) are moving over time. Additionally, for each target a visibility time window is given. The task is to find routes for several salesmen so that each target is reached exactly … Read more