arXiv subjects

Pierre Hosteins

Publications and source records attributed to Pierre Hosteins.

12 recordsLinked to original sources

arXiv2025

Heuristic approaches for a new variant of the Team Orienteering Problem

In this paper we tackle the Team Orienteering Problem with Service Times, Mandatory Nodes and Incompatibilities, introduced in~\cite{Guastalla2024} and arising from two real-world healthcare applications. We propose two heuristic algorithms in the form of a Variable Descent Neighbourhood algorithm and a matheuristic based on a Cuts Separation approach. For the former, we also provide a multi-thread version exploiting its intrinsic capability to be parallelised. Both algorithms include a specific heuristic routine to provide a starting feasible solution, since finding a feasible solution has been proved to be NP-complete. The results of our heuristic algorithms are compared with an exact cutting plane approach and have complementary strengths and weaknesses. They are also evaluated on existing TOP benchmarks against TOP state-of-the-art algorithms, demonstrating their competitiveness on general grounds.

math.OC↗

arXiv2024

The Team Orienteering Problem with Service Times and Mandatory & Incompatible Nodes

The Team Orienteering Problem with Service Times and Mandatory & Incompatible Nodes (TOP-ST-MIN) is a variant of the classic Team Orienteering Problem (TOP), which includes three novel features that stem from two real-world problems previously studied by the authors. We prove that even finding a feasible solution is NP-complete. Two versions of this variant are considered in our study. For such versions, we proposed two alternative mathematical formulations, a mixed and a compact formulations. Based on the compact formulation, we developed a Cutting-Plane Algorithm (CPA) exploiting five families of valid inequalities. Extensive computational experiments showed that the CPA outperforms CPLEX in solving the new benchmark instances, generated in such a way to evaluate the impact of the three novel features that characterise the problem. The CPA is also competitive for the TOP since it is able to solve almost the same number of instances as the state-of-art algorithms.

math.OC↗

arXiv2024

On the completeness of several fortification-interdiction games in the Polynomial Hierarchy

Fortification-interdiction games are tri-level adversarial games where two opponents act in succession to protect, disrupt and simply use an infrastructure for a specific purpose. Many such games have been formulated and tackled in the literature through specific algorithmic methods, however very few investigations exist on the completeness of such fortification problems in order to locate them rigorously in the polynomial hierarchy. We clarify the completeness status of several well-known fortification problems, such as the Tri-level Interdiction Knapsack Problem with unit fortification and attack weights, the Max-flow Interdiction Problem and Shortest Path Interdiction Problem with Fortification, the Multi-level Critical Node Problem with unit weights, as well as a well-studied electric grid defence planning problem. For all of these problems, we prove their completeness either for the $\Sigma^p_2$ or the $\Sigma^p_3$ class of the polynomial hierarchy. We also prove that the Multi-level Fortification-Interdiction Knapsack Problem with an arbitrary number of protection and interdiction rounds and unit fortification and attack weights is complete for any level of the polynomial hierarchy, therefore providing a useful basis for further attempts at proving the completeness of protection-interdiction games at any level of said hierarchy.

cs.CC↗

arXiv2020

Complexity of the Multilevel Critical Node Problem

In this work, we analyze a sequential game played in a graph called the Multilevel Critical Node problem (MCN). A defender and an attacker are the players of this game. The defender starts by preventively interdicting vertices (vaccination) from being attacked. Then, the attacker infects a subset of non-vaccinated vertices and, finally, the defender reacts with a protection strategy. We provide the first computational complexity results associated with MCN and its subgames. Moreover, by considering unitary, weighted, undirected, and directed graphs, we clarify how the theoretical tractability of those problems vary. Our findings contribute with new NP-complete, $Σ_2^p$-complete and $Σ_3^p$-complete problems. Furthermore, for the last level of the game, the protection stage, we build polynomial time algorithms for certain graph classes.

cs.CC↗

arXiv2019

The Stochastic Critical Node Problem over Trees

We tackle a stochastic version of the Critical Node Problem (CNP) where the goal is to minimize the pairwise connectivity of a graph by attacking a subset of its nodes. In the stochastic setting considered, the attacks on nodes can fail with a certain probability. In our work we focus on trees and demonstrate that over trees the stochastic CNP actually generalizes to the stochastic Critical Element Detection Problem where attacks on edges can also fail with a certain probability. We also prove the NP-completeness of the decision version of the problem when connection costs are one, while its deterministic counterpart was proved to be polynomial. We then derive linear and nonlinear models for the considered CNP version. Moreover, we propose an exact approach based on Benders decomposition and test its effectiveness on a large set of instances. As a side result, we introduce an approximation algorithm for a problem variant of interest.

cs.DS↗

arXiv2010

Searching singlet extensions of the supersymmetric standard model in $ Z_{6-II}$ orbifold compactification of heterotic string

We search for supersymmetric standard model realizations with extra singlets and extra $ U(1)$ using the heterotic string compactification on the $ Z_{6-II}$ orbifold with two Wilson lines. We analyze the vacuum restabilization mechanism for three representative Pati-Salam string models obtained in the literature and present detailed results for the effective superpotential compatible with the string selection rules. An automated selection of semi-realistic vacua along flat directions in the non-Abelian singlet modes field space is performed by requiring the presence of massless pairs of electroweak Higgs bosons having trilinear superpotential couplings with massless singlet modes and the decoupling of color triplet exotic modes needed to suppress $B $ and $ L $ number violating processes.

hep-ph↗

arXiv2009

Gauge-top unification

Higher-dimensional models of grand unification allow us to relate the top Yukawa coupling y_t to the gauge coupling g. The tree level relation y_t=g at the scale of grand unification implies, in the framework of the MSSM, a rather small ratio of Higgs expectation values tan beta. We find that, in the presence of localized Fayet-Iliopoulos terms, y_t is suppressed against g because the bulk fields acquire non-trivial profiles whose overlap is smaller than in the case of flat profiles. This increases the prediction for tan beta to moderately large values. Thus tan beta is related to the geometry of compact space. We also discuss explicit realizations of such settings in orbifold compactifications of the heterotic string. It turns out that anisotropic compactifications, allowing for an orbifold GUT interpretation, are favored.

hep-ph↗

arXiv2008

Successful Leptogenesis in SO(10) Unification with a Left-Right Symmetric Seesaw Mechanism

We study thermal leptogenesis in a broad class of supersymmetric SO(10) models with a left-right symmetric seesaw mechanism, taking into account flavour effects and the contribution of the next-to-lightest right-handed neutrino supermultiplet. Assuming M_D = M_u and a normal hierarchy of light neutrino masses, we show that four out of the eight right-handed neutrino mass spectra reconstructed from low-energy neutrino data can lead to successful leptogenesis with a reheating temperature in the (10^9 - 10^10) GeV range. In the remaining four solutions, leptogenesis is dominated by N_2 decays, as in the type I seesaw case. We find that some of these spectra can generate the observed baryon asymmetry for reheating temperatures above 10^10 GeV, in contrast to the type I case. Together with flavour effects, an accurate description of charged fermion masses turns out to be a crucial ingredient in the analysis.

hep-ph↗

arXiv2008

A new, direct link between the baryon asymmetry and neutrino masses

We point out that, in a class of SO(10) models with matter fields in 16 and 10 representations and type II realization of the seesaw mechanism, the light neutrino masses and the CP asymmetry needed for leptogenesis are controlled by one and the same set of couplings. The generated baryon asymmetry then directly depends on the low-energy neutrino parameters, with no unknown seesaw-scale flavour parameters involved; in particular, the necessary CP violation is provided by the CP-violating phases of the lepton mixing matrix. We compute the CP asymmetry in triplet decays for this scenario and show that it can lead to successful leptogenesis.

hep-ph↗

arXiv2007

Quantum corrections to the effective neutrino mass operator in 5D MSSM

We discuss in detail a five-dimensional Minimal Supersymmetric Standard Model compactified on $S^1/Z_2$ extended by the effective Majorana neutrino mass operator. We study the evolution of neutrino masses and mixings. Masses and angles, in particular the atmospheric mixing angle $θ_{23}$, can be significantly lowered at high energies with respect to their value at low energy.

hep-ph↗

arXiv2006

Quark-Lepton Unification and Eight-Fold Ambiguity in the Left-Right Symmetric Seesaw Mechanism

In many extensions of the Standard Model, including a broad class of left-right symmetric and Grand Unified theories, the light neutrino mass matrix is given by the left-right symmetric seesaw formula $M_ν= f v_L - \frac{v^2}{v_R} Y_νf^{-1} Y_ν$, in which the right-handed neutrino mass matrix and the $SU(2)_L$ triplet couplings are proportional to the same matrix f. We propose a systematic procedure for reconstructing the $2^n$ solutions (in the n-family case) for the matrix f as a function of the Dirac neutrino couplings $(Y_ν)_{ij}$ and of the light neutrino mass parameters, which can be used in both analytical and numerical studies. We apply this procedure to a particular class of supersymmetric SO(10) models with two 10-dimensional and a pair of $126 + \bar{126}$ representations in the Higgs sector, and study the properties of the corresponding 8 right-handed neutrino spectra. Then, using the reconstructed right-handed neutrino and triplet parameters, we study leptogenesis and lepton flavour violation in these models, and comment on flavour effects in leptogenesis in the type I limit. We find that the mixed solutions where both the type I and the type II seesaw mechanisms give a significant contribution to neutrino masses provide new opportunities for successful leptogenesis in SO(10) GUTs.

hep-ph↗

arXiv2006

Reconstructing the Right-Handed Neutrino Masses in Left-Right Symmetric Theories

We introduce a method to extract the right-handed neutrino mass matrix from the Left-Right symmetric seesaw formula and apply it to the study of a simple SUSY SO(10) theory. We find 8 possible solutions for the heavy neutrino spectrum and a richer phenomenology than in the pure type I or type II seesaw mechanism. Leptogenesis is studied in SO(10) and can be accomodated more easily than with the type I dominance.

hep-ph↗