arXiv subjects

Emiliano Traversi

Publications and source records attributed to Emiliano Traversi.

10 recordsLinked to original sources

arXiv2026

An Integer Programming Approach to Compute Lower Bounds for Ramsey Numbers Using Circulant Graphs

The Ramsey number $R(m,n)$ is the smallest order at which every red-blue edge coloring of a complete graph must contain a blue clique (a complete subgraph) of size $m$ or a red clique of size $n$. Determining these numbers exactly is extremely hard, and even certifying a lower bound requires exhibiting an explicit coloring that avoids both cliques. We develop an integer programming framework for certifying such lower bounds, restricting the search to circulant graphs, whose rotational symmetry lets us reformulate the problem in a projected distance space, reducing the number of binary variables from quadratic to linear in the graph order. We strengthen this projected model through coefficient reduction and solve it with a branch-and-cut algorithm whose separation routine exploits the common neighborhood structure of circulant graphs, combining heuristic and exact maximum-clique algorithms. In an extensive computational campaign on circulant graphs with up to 410 vertices, we improve the best lower bounds previously obtained by other methods by up to 11 points for 25 values of $R(3,n)$ with $24\le n\le49$ and $n\neq27$, each backed by an explicit graph certificate that can be independently verified with a stand-alone exact clique solver. To the best of our knowledge, our method also provides the first reproducible optimization-based procedure for certifying circulant Ramsey numbers $R_C(m,n)$, which we use to establish eight new values of $R_C(3,n)$ with $13\le n\le20$. Our framework, graph certificates, and stand-alone checker are provided as supplementary material to support independent verification and reuse.

math.OC↗

arXiv2025

Bundle Network: a Machine Learning-Based Bundle Method

This paper presents Bundle Network, a learning-based algorithm inspired by the Bundle Method for convex non-smooth minimization problems. Unlike classical approaches that rely on heuristic tuning of a regularization parameter, our method automatically learns to adjust it from data. Furthermore, we replace the iterative resolution of the optimization problem that provides the search direction-traditionally computed as a convex combination of gradients at visited points-with a recurrent neural model equipped with an attention mechanism. By leveraging the unrolled graph of computation, our Bundle Network can be trained end-to-end via automatic differentiation. Experiments on Lagrangian dual relaxations of the Multi-Commodity Network Design and Generalized Assignment problems demonstrate that our approach consistently outperforms traditional methods relying on grid search for parameter tuning, while generalizing effectively across datasets.

math.OC↗

arXiv2025

Alleviating the quantum Big-$M$ problem

A major obstacle for quantum optimizers is the reformulation of constraints as a quadratic unconstrained binary optimization (QUBO). Current QUBO translators exaggerate the weight $M$ of the penalty terms. Classically known as the "Big-$M$" problem, the issue becomes even more daunting for quantum solvers, since it affects the physical energy scale. We take a systematic, encompassing look at the quantum big-$M$ problem, revealing NP-hardness in finding the optimal $M$ and establishing bounds on the Hamiltonian spectral gap $Δ$, inversely related to the expected run-time of quantum solvers. We propose a practical translation algorithm, based on SDP relaxation, that outperforms previous methods in numerical benchmarks. Our algorithm gives values of $Δ$ orders of magnitude greater, e.g. for portfolio optimization instances. Solving such instances with an adiabatic algorithm on 6-qubits of an IonQ device, we observe significant advantages in time to solution and average solution quality. Our findings are relevant to quantum and quantum-inspired solvers alike.

quant-ph↗

arXiv2023

Branch and Price for Submodular Bin Packing

The Submodular Bin Packing (SMBP) problem asks for packing unsplittable items into a minimal number of bins for which the capacity utilization function is submodular. SMBP is equivalent to chance-constrained and robust bin packing problems under various conditions. SMBP is a hard binary nonlinear programming optimization problem. In this paper, we propose a branch-and-price algorithm to solve this problem. The resulting price subproblems are submodular knapsack problems, and we propose a tailored exact branch-and-cut algorithm based on a piece-wise linear relaxation to solve them. To speed up column generation, we develop a hybrid pricing strategy to replace the exact pricing algorithm with a fast pricing heuristic. We test our algorithms on instances generated as suggested in the literature. The computational results show the efficiency of our branch-and-price algorithm and the proposed pricing techniques.

math.OC↗

arXiv2022

Deep Reinforcement Learning for Combined Coverage and Resource Allocation in UAV-aided RAN-slicing

Network slicing is a well assessed approach enabling virtualization of the mobile core and radio access network (RAN) in the emerging 5th Generation New Radio. Slicing is of paramount importance when dealing with the emerging and diverse vertical applications entailing heterogeneous sets of requirements. 5G is also envisioning Unmanned Aerial Vehicles (UAVs) to be a key element in the cellular network standard, aiming at their use as aerial base stations and exploiting their flexible and quick deployment to enhance the wireless network performance. This work presents a UAV-assisted 5G network, where the aerial base stations (UAV-BS) are empowered with network slicing capabilities aiming at optimizing the Service Level Agreement (SLA) satisfaction ratio of a set of users. The users belong to three heterogeneous categories of 5G service type, namely, enhanced mobile broadband (eMBB), ultra-reliable low-latency communication (URLLC), and massive machine-type communication (mMTC). A first application of multi-agent and multi-decision deep reinforcement learning for UAV-BS in a network slicing context is introduced, aiming at the optimization of the SLA satisfaction ratio of users through the joint allocation of radio resources to slices and refinement of the UAV-BSs 2-dimensional trajectories. The performance of the presented strategy have been tested and compared to benchmark heuristics, highlighting a higher percentage of satisfied users (at least 27% more) in a variety of scenarios.

cs.NI↗

arXiv2021

A Semidefinite Optimization-based Branch-and-Bound Algorithm for Several Reactive Optimal Power Flow Problems

The Reactive Optimal Power Flow (ROPF) problem consists in computing an optimal power generation dispatch for an alternating current transmission network that respects power flow equations and operational constraints. Some means of action on the voltage are modelled in the ROPF problem such as the possible activation of shunts, which implies discrete variables. The ROPF problem belongs to the class of nonconvex MINLPs (Mixed-Integer Nonlinear Problems), which are NP-hard problems. In this paper, we solve three new variants of the ROPF problem by using a semidefinite optimization-based Branch-and-Bound algorithm. We present results on MATPOWER instances and we show that this method can solve to global optimality most instances. On the instances not solved to optimality, our algorithm is able to find solutions with a value better than the ones obtained by a rounding algorithm. We also demonstrate that applying an appropriate clique merging algorithm can significantly speed up the resolution of semidefinite relaxations of ROPF large instances.

cs.RO↗

arXiv2019

Improving Clique Decompositions of Semidefinite Relaxations for Optimal Power Flow Problems

Semidefinite Programming (SDP) provides tight lower bounds for Optimal Power Flow problems. However, solving large-scale SDP problems requires exploiting sparsity. In this paper, we experiment several clique decomposition algorithms that lead to different reformulations and we show that the resolution is highly sensitive to the clique decomposition procedure. Our main contribution is to demonstrate that minimizing the number of additional edges in the chordal extension is not always appropriate to get a good clique decomposition.

math.OC↗

arXiv2019

A Julia Module for Polynomial Optimization with Complex Variables applied to Optimal Power Flow

Many optimization problems in power transmission networks can be formulated as polynomial problems with complex variables. A polynomial optimization problem with complex variables consists in optimizing a real-valued polynomial whose variables and coefficients are complex numbers subject to some complex polynomial equality or inequality constraints. These problems are usually directly converted to real variables, either using the polar form or the rectangular form. In this work, we propose a Julia module allowing the representation of polynomial problems in their original complex formulation. This module is applied to power systems optimization and its generic design enables the description of several variants of power system problems. Results for the Optimal Power Flow in Alternating Current problem and for the Preventive-Security Constrained Optimal Power Flow problem are presented.

math.OC↗

arXiv2018

Optimal Solution of Vehicle Routing Problems with Fractional Objective Function

This work proposes a first extensive analysis of the Vehicle Routing Problem with Fractional Objective Function (vrpfof). We investigate how the principal techniques used either in the context of fractional programming or in the context of vehicle routing problems interact. We present new dual and primal bounding procedures which have been incorporated in an exact method. The method proposed allows to extend specific variants of \vrp\ to their counterpart with a fractional objective function. Extensive numerical experiments prove the validity of our approach.

math.OC↗

arXiv2017

A simplicial decomposition framework for large scale convex quadratic programming

In this paper, we analyze in depth a simplicial decomposition like algorithmic framework for large scale convex quadratic programming. In particular, we first propose two tailored strategies for handling the master problem. Then, we describe a few techniques for speeding up the solution of the pricing problem. We report extensive numerical experiments on both real portfolio optimization and general quadratic programming problems, showing the efficiency and robustness of the method when compared to Cplex.

math.OC↗