Plenary Speakers
Marianna De Santis
K-adaptability for two-stage stochastic optimization
Abstract: Two-stage stochastic programs provide a powerful framework for decision-making under uncertainty. In these models, a decision maker first selects the values of the first-stage variables, then observes the realization of uncertain parameters, and finally determines the second-stage decisions. A widely used approach for handling two-stage problems under uncertainty is K-adaptability, in which a small set of K candidate second-stage solutions is computed already in the first stage, and one of them is selected after the uncertainty is revealed. While K-adaptability has been extensively studied in the context of two-stage robust optimization, its role in two-stage stochastic optimization has received comparatively little attention.
In this talk, we present a K-adaptability framework for two-stage stochastic optimization, focusing on the case where uncertainty can be modeled by a finite number of scenarios. We derive approximation guarantees for the resulting K-adaptable solutions with respect to the exact two-stage stochastic problem and identify conditions under which K-adaptability is optimal. Furthermore, we introduce an exact partition-based branch-and-bound algorithm capable of solving the stochastic K-adaptability problem to optimality. Computational experiments on linear and quadratic knapsack and facility location problems are presented.
Leo Liberti
Random projections in mathematical programming: recent advances
Abstract: In this talk I will briefly survey previous work about the application of random projections to mathematical programming, and then talk about recent advances, specifically about quadratically constrained quadratic programs, as well as on a specific MINLP problem, i.e.~the minimum sum-of-squares clustering. Joint work with Benedetto Manca and Pierre-Louis Poirion
Martine Labbé
TBA
Fabio Furini
Hidden Bilevel Structures in Graph Disconnection Problems
Abstract: Many fundamental graph disconnection problems hide an underlying bilevel structure that can be exploited for stronger formulations and algorithms. In this talk, we reveal and formalize this hidden structure for two key problems: the capacitated vertex separator and the k-vertex cut. Both are modeled as two-phase bilevel games, where a leader strategically deletes vertices and a follower reacts by optimizing over the disconnected graph. We present new integer programming formulations naturally capturing this bilevel interaction, supported by families of strengthening valid inequalities and polynomial-time separation procedures. Our computational studies demonstrate that these approaches significantly improve the state-of-the-art, yielding better solutions and faster convergence on benchmark instances. Beyond these two problems, the bilevel perspective opens promising directions for a broader class of graph modification and partitioning problems.
Invited Speakers
Giulia Caselli
Exact formulations and a kernel search heuristic for the fleet allocation scheduling problem with soft precedence constraints
Abstract: In the Block Relocation Problem (BRP), a sequence of items stored vertically in stacks or yard blocks must be unloaded while minimizing the total number of relocations. In this work, we propose a new variant of the BRP, called the Fleet Allocation Problem with Soft Precedence Constraints, in which a set of items must be assigned to a fleet of heterogeneous vehicles with limited capacities, where each vehicle can load only available items belonging to the same destination family. During the unloading of items, any blocking item can be relocated to an unlimited storage area, each producing a single unproductive move. The primary objective is to maximize the number of items unloaded from the yard and assigned to vehicles, while the secondary objective is to minimize the number of unproductive moves. The problem finds applications in logistic operations in steel plants and container terminals, as well as in humanitarian supply operations in the context of natural or industrial disasters. We provide two compact formulations, two reformulations, and a family of valid inequalities. The models providing the best dual bounds serve as the backbone of a Kernel Search heuristic. Computational results show that the tested models are able to reach proven optimality for 70 out of 80 test instances, starting to find difficulty in closing the gaps as the number of items increases from 100 to 900. The heuristic matches or improves the best-known bounds in 70% of the instances, with an average gap of 0.02% from best-known bounds.
Matteo Lapucci
Exploiting line searches in overparametrized models training
Abstract: The training of modern artificial intelligence systems is by now well established and relies on optimizers based on stochastic gradient descent. In fact, recent literature has shown how these overparameterized models operate in a data interpolation regime where SGD algorithms proceed with provably very efficient convergence rates. In this setting, it is actually possible to soundly employ (stochastic) line search strategies - inspired by classical methods in nonlinear optimization - for the calibration of step sizes, making the whole process even faster and more robust.
In this talk, we discuss several aspects related to the convergence and computational efficiency of algorithms combining line searches and aggressive choices for search directions or base step sizes. Tailored solutions for specific architectures or parameterizations are also taken into account.
Elena Rener
Flowshop Rescheduling for New Orders with a Time Disruption Constraint
Abstract: Rescheduling problems arise when an existing production schedule must be updated due to unexpected changes in the workload. Such disruptions provide an opportunity to improve an initial schedule that was created under different assumptions, making re‑optimization worthwhile whenever the operational scenario changes. This work focuses on rescheduling for new orders, a setting in which additional jobs arrive after the original schedule has been constructed. The original and newly arrived jobs must then be jointly scheduled on the machines. The challenge is twofold: optimizing overall system performance while limiting deviations from the initial schedule, which may be tied to other operational or planning decisions. Many approaches address this trade‑off by combining an optimization objective with a disruption constraint that restricts the allowable deviation from the original solution. This talk presents new theoretical results and an efficient exact algorithm for the permutation flowshop rescheduling problem. The objective is to minimize the total completion time of all jobs subject to a disruption constraint defined by the maximum absolute deviation of completion times.
Antonio Consolo
Soft decision trees for survival analysis
Abstract: Decision trees are widely used in survival analysis for their interpretability and ability to capture complex relationships. Survival trees, which estimate the timing of singular events from censored historical data, are typically built using heuristic methods. Recently, there has been growing interest in globally optimized trees, where the entire tree is trained by minimizing an error function over all its parameters. We propose a new soft survival tree model (SST), with a soft splitting rule at each branch node, trained via a nonlinear optimization formulation amenable to decomposition. Since SSTs map each input vector to a single leaf node and its associated survival function, they satisfy the conditional computation property. SST combines flexibility with interpretability: any smooth maximum-likelihood survival function can be used (parametric, semiparametric, or nonparametric), and each leaf represents a cluster of distinct survival curves for the routed data points. Experiments on 15 well-known datasets show that SSTs, with parametric and spline-based semiparametric survival functions, trained via an adaptation of the node-based decomposition algorithm of Consolo et al. (2024) for soft regression trees, outperform three benchmark survival trees on four widely used discrimination and calibration metrics. SSTs can also be extended to consider group fairness.
Martina Luzzi
Smart Upgrades: when upgrading boosts revenue and when it doesn’t
Abstract: In competitive markets, firms frequently adopt product upgrade mechanisms to improve revenue performance and resource utilization under capacity constraints. Such mechanisms enable customers to receive higher-tier products than initially purchased and can take different forms: automatic or secret upgrades integrated into allocation rules, desk upgrades offered at the point of service, and standby upgrades proposed at the time of purchase with conditional acceptance.
While upgrades are widely used across industries, their economic implications and strategic interactions with pricing and inventory decisions remain underexplored.
This study develops a quantitative framework to analyze when, how, and why it is profitable to apply upgrades to specific product classes, and under which operational and behavioral conditions one mechanism dominates another. By comparing alternative upgrade policies and their revenue effects, we explore their impact on pricing decisions, effective capacity allocation, and customer choice behavior. The results highlight the structural conditions under which upgrades enhance total system revenue and identify cases where they may instead erode profitability, providing insights for both theoretical modeling and managerial practice.
Carmine Sorgente
Exact approaches for colorful components problems
Abstract: We present exact solution approaches for three optimization problems, with applications in community detection, cybersecurity, and bioinformatics, in which a node-colored graph must be partitioned into colorful components. A colorful component is a connected subgraph whose nodes have pairwise distinct colors. The three problems have different objectives: (i) minimizing the number of removed edges; (ii) minimizing the number of connected components; and (iii) maximizing the number of edges in the transitive closure of the output graph.
First, we present integer non-linear formulations based on classical assignment variables, which are then linearized using standard techniques and solved through exact branch-and-cut algorithms embedding valid inequalities, bounds limiting the number of variables, as well as warm-start and preprocessing techniques. Then, we provide compact integer programming formulations, where each component is identified by a representative, and we alternatively enforce connectivity of the components by using additional flow variables and constraints. Finally, we develop a preprocessing procedure reducing the number of variables in the representative formulations.
The performances of the proposed approaches are compared through computational experiments on benchmark instances. The results show that representative formulations with flow-based connectivity constraints currently constitute the most efficient exact approach for colorful components problems, being able to solve all benchmark instances to optimality within negligible computational time.
Anna Livia Croella
Strong MILP Formulations for Train Single-Routing Selection Problem
Abstract: Efficient railway traffic management requires selecting feasible and cost-effective routes for trains in congested areas. We study the Train Single-Routing Selection Problem (TSRSP), which assigns exactly one route to each train while minimizing route and interaction costs under pairwise compatibility constraints. The problem can be modeled as a minimum-weight clique problem in a weighted k-partite graph and is NP-hard. We propose an exact formulation based on Binary Quadratic Programming and a linearization derived from Glover's technique. By exploiting the k-partite structure of the problem, we strengthen the LP relaxation through dedicated bounding strategies. A theoretical comparison with existing formulations and computational experiments on real-world instances from the French railway network confirm the effectiveness of the approach.