In the m-Peripatetic Salesman Problem (m-PSP) the aim is to determine m edge disjoint Hamiltonian cycles of minimum total cost on a graph. This article describes exact branch-and-cut solution procedures for the undirected m-PSP. Computational results are reported on random and Euclidean graphs.

In [1], we proposed a graph-based formulation that links and clusters person hypotheses over time by solving a minimum cost subgraph multicut problem. In this paper, we modify and extend [1] in three ways: 1) We introduce a novel local pairwise feature based on local appearance matching that is robust to partial occlusion and camera motion. 2) We perform extensive experiments to compare differe...

One method which has been used very successfully for finding optimal and provably good solutions for large instances of the Symmetric Travelling Salesman Problem (ST SP) is the branch and cut method. This method requires knowledge of classes of useful valid inequalities for the polytope associated with the ST SP, as well as efficient separation routines for these classes of inequalities. Recent...

We report and analyze the results of our computational testing of branchand-cut for the complementarity-constrained optimization problem (CCOP). Besides the MIP cuts commonly present in commercial optimization software, we used inequalities that explore complementarity constraints. To do so, we generalized two families of cuts proposed earlier by de Farias, Johnson, and Nemhauser that had never...

Date approved: To my parents Maria and Stoyan To my wife Dilyana Acknowledgments This dissertation would not be possible without those whose love, understanding, experience , and knowledge have inspired and supported me during my Ph.D. study. First of all, I would like to thank my advisor, Prof. Gérard Cornuéjols, for his advice and guidance. As a skilled researcher and excellent teacher, he pr...

Many real-life scheduling, routing and location problems can be formulated as combinatorial optimization problems whose goal is to find a linear layout of an input graph in such a way that the number of edge crossings is minimized. In this paper, we study a restricted version of the linear layout problem where the order of vertices on the line is fixed, the so-called fixed linear crossing numbe...

A short introduction to Integer Programming (IP). Problems leading to IP models. Some modelling tricks and reformulations. Geometry of linear IP. TUM matrices. Brief notes on polyhedral analysis. Separation theory. Chvatal cut hierarchy, Gomory cuts, Disjunctive cuts, RLT cut hierarchy. Iterative methods: Branch-and-Bound, Cutting Plane, Branch-and-Cut, Branch-and-Price. Lower bounds: Lagrangia...

Many relevant applications from diverse areas such as marketing, wildlife conservation, or defending critical infrastructure can be modeled interdiction games. In this work, we introduce games whose objective is a monotone and submodular set function. Given ground of items, the leader interdicts usage some items follower in order to minimize value achievable by follower, who seeks maximize func...