Split cuts in the plane
We provide a polynomial time cutting plane algorithm based on split cuts to solve integer programs in the plane. We also prove that the split closure of a polyhedron in the plane has polynomial size. ArticleDownload View PDF
Branch and Cut Algorithms
Computational study of a branching algorithm for the maximum k-cut problem
This work considers the graph partitioning problem known as maximum k-cut. It focuses on investigating features of a branch-and-bound method to efficiently obtain global solutions. An exhaustive experimental study is carried out for two main components of a branch-and-bound algorithm: computing bounds and branching strategies. In particular, we propose the use of a variable neighborhood … Read more
Compact Formulations for Split Delivery Routing Problems
Split delivery routing problems are concerned with serving the demand of a set of customers with a fleet of capacitated vehicles at minimum cost, where a customer can be served by more than one vehicle if beneficial. They generalize traditional variants of routing problems and have applications in commercial as well as humanitarian logistics. Previously, … Read more
Multi-objective Optimization Based Algorithms for Solving Mixed Integer Linear Minimum Multiplicative Programs
We present two new algorithms for a class of single-objective non-linear optimization problems, the so-called Mixed Integer Linear minimum Multiplicative Programs (MIL-mMPs). This class of optimization problems has a desirable characteristic: a MIL-mMP can be viewed as a special case of the problem of optimization over the efficient set in multi-objective optimization. The proposed algorithms … Read more
A bi-level branch-and-bound algorithm for the capacitated competitive facility location problem
Competitive facility location problem is a typical facility locating optimization problem but in a competitive environment. The main characteristic of this problem is the competitive nature of the market. In essence, the problem involves two competitors, i.e., a leader and a follower, who seek to attract customers by establishing new facilities to maximize their own … Read more
Casting light on the hidden bilevel combinatorial structure of the k-Vertex Separator problem
Given an undirected graph, we study the capacitated vertex separator problem which asks to find a subset of vertices of minimum cardinality, the removal of which induces a graph having a bounded number of pairwise disconnected shores (subsets of vertices) of limited cardinality. The problem is of great importance in the analysis and protection of … Read more
On Integer and Bilevel Formulations for the k-Vertex Cut Problem
The family of Critical Node Detection Problems asks for finding a subset of vertices, deletion of which minimizes or maximizes a predefined connectivity measure on the remaining network. We study a problem of this family called the k-vertex cut problem. The problems asks for determining the minimum weight subset of nodes whose removal disconnects a … Read more
Integer Programming, Constraint Programming, and Hybrid Decomposition Approaches to Discretizable Distance Geometry Problems
Given an integer dimension K and a simple, undirected graph G with positive edge weights, the Distance Geometry Problem (DGP) aims to find a realization function mapping each vertex to a coordinate in K-dimensional space such that the distance between pairs of vertex coordinates is equal to the corresponding edge weights in G. The so-called … Read more
A Bilevel Approach for Identifying the Worst Contingencies for Nonconvex Alternating Current Power Systems
We address the bilevel optimization problem of identifying the most critical attacks to an alternating current (AC) power flow network. The upper-level binary maximization problem consists in choosing an attack that is treated as a parameter in the lower-level defender minimization problem. Instances of the lower-level global minimization problem by themselves are NP-hard due to … Read more
Integer Programming Formulations for Minimum Spanning Tree Interdiction
We consider a two-player interdiction problem staged over a graph where the leader’s objective is to minimize the cost of removing edges from the graph so that the follower’s objective, i.e., the weight of a minimum spanning tree in the residual graph, is increased up to a predefined level $r$. Standard approaches for graph interdiction … Read more