@inproceedings{TurnerBertholdBesanconetal., author = {Turner, Mark and Berthold, Timo and Besan{\c{c}}on, Mathieu and Koch, Thorsten}, title = {Cutting Plane Selection with Analytic Centers and Multiregression}, series = {Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2023.}, volume = {13884}, booktitle = {Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2023.}, publisher = {Springer}, doi = {10.1007/978-3-031-33271-5_4}, pages = {52 -- 68}, abstract = {Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of a cut by quantifying the extent to which it separates relevant parts of the relaxed feasible set. For this purpose, we use the analytic centers of the relaxation polytope or of its optimal face, as well as alternative optimal solutions of the linear programming relaxation. We assess the impact of the choice of distance measure on root node performance and throughout the whole branch-and-bound tree, comparing our measures against those prevalent in the literature. Finally, by a multi-output regression, we predict the relative performance of each measure, using static features readily available before the separation process. Our results indicate that analytic center-based methods help to significantly reduce the number of branch-and-bound nodes needed to explore the search space and that our multiregression approach can further improve on any individual method.}, language = {en} } @inproceedings{MexiShamsiBesanconetal., author = {Mexi, Gioni and Shamsi, Somayeh and Besan{\c{c}}on, Mathieu and Bodic, Pierre}, title = {Probabilistic Lookahead Strong Branching via a Stochastic Abstract Branching Model}, series = {Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2024}, volume = {14743}, booktitle = {Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2024}, doi = {10.1007/978-3-031-60599-4_4}, abstract = {Strong Branching (SB) is a cornerstone of all modern branching rules used in the Branch-and-Bound (BnB) algorithm, which is at the center of Mixed-Integer Programming solvers. In its full form, SB evaluates all variables to branch on and then selects the one producing the best relaxation, leading to small trees, but high runtimes. State-of-the-art branching rules therefore use SB with working limits to achieve both small enough trees and short run times. So far, these working limits have been established empirically. In this paper, we introduce a theoretical approach to guide how much SB to use at each node within the BnB. We first define an abstract stochastic tree model of the BnB algorithm where the geometric mean dual gains of all variables follow a given probability distribution. This model allows us to relate expected dual gains to tree sizes and explicitly compare the cost of sampling an additional SB candidate with the reward in expected tree size reduction. We then leverage the insight from the abstract model to design a new stopping criterion for SB, which fits a distribution to the dual gains and, at each node, dynamically continues or interrupts SB. This algorithm, which we refer to as Probabilistic Lookahead Strong Branching, improves both the tree size and runtime over MIPLIB instances, providing evidence that the method not only changes the amount of SB, but allocates it better.}, language = {en} } @article{BolusaniBesanconGleixneretal., author = {Bolusani, Suresh and Besan{\c{c}}on, Mathieu and Gleixner, Ambros and Berthold, Timo and D'Ambrosio, Claudia and Mu{\~n}oz, Gonzalo and Paat, Joseph and Thomopulos, Dimitri}, title = {The MIP workshop 2023 computational competition on reoptimization}, series = {Mathematical Programming Computation}, volume = {16}, journal = {Mathematical Programming Computation}, doi = {10.1007/s12532-024-00256-w}, pages = {255 -- 266}, abstract = {This paper describes the computational challenge developed for a computational competition held in 2023 for the 20th anniversary of the Mixed Integer Programming Workshop. The topic of this competition was reoptimization, also known as warm starting, of mixed integer linear optimization problems after slight changes to the input data for a common formulation. The challenge was to accelerate the proof of optimality of the modified instances by leveraging the information from the solving processes of previously solved instances, all while creating high-quality primal solutions. Specifically, we discuss the competition's format, the creation of public and hidden datasets, and the evaluation criteria. Our goal is to establish a methodology for the generation of benchmark instances and an evaluation framework, along with benchmark datasets, to foster future research on reoptimization of mixed integer linear optimization problems.}, language = {en} } @article{CardereraBesanconPokutta, author = {Carderera, Alejandro and Besan{\c{c}}on, Mathieu and Pokutta, Sebastian}, title = {Scalable Frank-Wolfe on generalized self-concordant functions via simple steps}, series = {SIAM Journal on Optimization}, volume = {34}, journal = {SIAM Journal on Optimization}, number = {3}, doi = {10.1137/23M1616789}, language = {en} } @inproceedings{HendrychBesanconPokutta, author = {Hendrych, Deborah and Besan{\c{c}}on, Mathieu and Pokutta, Sebastian}, title = {Solving the optimal experiment design problem with mixed-integer convex methods}, series = {22nd International Symposium on Experimental Algorithms (SEA 2024)}, volume = {301}, booktitle = {22nd International Symposium on Experimental Algorithms (SEA 2024)}, doi = {10.4230/LIPIcs.SEA.2024.16}, pages = {16:1 -- 16:22}, abstract = {We tackle the Optimal Experiment Design Problem, which consists of choosing experiments to run or observations to select from a finite set to estimate the parameters of a system. The objective is to maximize some measure of information gained about the system from the observations, leading to a convex integer optimization problem. We leverage Boscia.jl, a recent algorithmic framework, which is based on a nonlinear branch-and-bound algorithm with node relaxations solved to approximate optimality using Frank-Wolfe algorithms. One particular advantage of the method is its efficient utilization of the polytope formed by the original constraints which is preserved by the method, unlike alternative methods relying on epigraph-based formulations. We assess our method against both generic and specialized convex mixed-integer approaches. Computational results highlight the performance of our proposed method, especially on large and challenging instances.}, language = {en} }