In this paper we present algorithms to approximate the solution for the multiparametric 0-1-mixed integer linear programming problem relative to the objective function. We consider the uncertainty for the parameters that de fine the cost vector corresponding to a subset of 0-1-variables by assuming that each parameter belongs to a known interval. We suppose that we … Read more
A wide range of problems can be modeled as Mixed Integer Linear Programming (MIP) problems using standard formulation techniques. However, in some cases the resulting MIP can be either too weak or too large to be effectively solved by state of the art solvers. In this survey we review advanced MIP formulation techniques that result … Read more
We give an algorithm for testing the extremality of minimal valid functions for Gomory and Johnson’s infinite group problem, that are piecewise linear (possibly discontinuous) with rational breakpoints. This is the first set of necessary and sufficient conditions that can be tested algorithmically, for deciding extremality in this important class of minimal valid functions. ArticleDownload … Read more
We consider a class of linear programs involving a set of covering constraints of which at most k are allowed to be violated. We show that this covering linear program with violation is strongly NP-hard. In order to improve the performance of mixed-integer programming (MIP) based schemes for these problems, we introduce and analyze a … Read more
We consider semi-continuous network flow problems, that is, a class of network flow problems where some of the variables are restricted to be semi-continuous. We introduce the semi-continuous inflow set with variable upper bounds as a relaxation of general semi-continuous network flow problems. Two particular cases of this set are considered, for which we present … Read more
We present a new method for solving bin packing problems, including two-constraint variants, based on an arc flow formulation with side constraints. Conventional formulations for bin packing problems are usually highly symmetric and provide very weak lower bounds. The arc flow formulation proposed provides a very strong lower bound, and is able to break symmetry … Read more
Many combinatorial optimization problems have natural formulations as submodular minimization problems over well-studied combinatorial structures. A standard approach to these problems is to linearize the objective function by introducing new variables and constraints, yielding an extended formulation. We propose two new approaches for constrained submodular minimization problems. The first is a linearization approach that requires … Read more
In this paper, a mathematical formulation for the islanding of power networks is presented. Given an area of uncertainty in the network, the proposed approach uses mixed integer linear programming to isolate uncertain components and create islands, by intentionally (i) cutting lines, (ii) shedding loads and (iii) switching generators, while maximizing load supply. A key … Read more
Implementations of the Simplex method differ only in very specific aspects such as the pivot rule. Similarly, most relaxation methods for mixed-integer programming differ only in the type of cuts and the exploration of the search tree. Implementing instances of those frameworks would therefore be more efficient if linear and mixed-integer programming solvers let users … Read more
A wide range of problems arising in practical applications can be formulated as Mixed-Integer Nonlinear Programs (MINLPs). For the case in which the objective and constraint functions are convex, some quite effective exact and heuristic algorithms are available. When non-convexities are present, however, things become much more difficult, since then even the continuous relaxation is … Read more