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
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
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
We present a parallel large neighborhood search framework for finding high quality primal solutions for generic Mixed Integer Programs (MIPs). The approach simultaneously solves a large number of sub-MIPs with the dual objective of reducing infeasibility and optimizing with respect to the original objective. Both goals are achieved by solving restricted versions of two auxiliary … Read more
We introduce a new technique to generate good feasible points of mixed-integer nonlinear optimization problems. It makes use of the so-called inner parallel set of the relaxed feasible set, which was employed in O. Stein, Error bounds for mixed integer linear optimization problems, Mathematical Programming, Vol. 156 (2016), 101-123, as well as O. Stein, Error … Read more