combinatorial optimization

Robust combinatorial optimization problems under locally budgeted interdiction uncertainty against the objective function and covering constraints

  • Alejandro Crema
    • Categories Combinatorial Optimization, Robust Optimization Tags ,

    Recently robust combinatorial optimization problems with budgeted interdiction uncertainty affecting cardinality-based constraints or objective were considered by presenting, comparing and experimenting with compact formulations. In this paper we present a compact formulation for the case in which locally budgeted interdiction uncertainty affects the objective function and covering constraints simultaneously. ArticleDownload View PDF

    Machine Learning Algorithms for Assisting Solvers for Decision Optimization Problems

  • Morteza Kimiaei
  • Vyacheslav Kungurtsev
    • Categories Applications - OR and Management Sciences, Integer Programming, Optimization in Data Science Tags , , , , , , , ,

    Combinatorial decision problems lie at the intersection of Operations Research (OR) and Artificial Intelligence (AI), encompassing structured optimization tasks such as submodular selection, dynamic programming, planning, and scheduling. These problems exhibit exponential growth in decision complexity, driven by interdependent choices coupled through logical, temporal, and resource constraints.  Classical optimization frameworks—including integer programming, submodular optimization, and … Read more

    Strength of the Upper Bounds for the Edge-Weighted Maximum Clique Problem

  • Fabio Ciccarelli
  • Valerio Dose
  • Fabio Furini
  • Marta Monaci
    • Categories Graphs and Matroids, Integer Programming Tags , ,

    We theoretically and computationally compare the strength of the two main upper bounds from the literature on the optimal value of the Edge-Weighted Maximum Clique Problem (EWMCP). We provide a set of instances for which the ratio between either of the two upper bounds and the optimal value of the EWMCP is unbounded. This result … Read more

    Stable Set Polytopes with Rank |V(G)|/3 for the Lovász-Schrijver SDP Operator

  • Yu Hin (Gary) Au
    • Categories Combinatorial Optimization, Convex Optimization, Semi-definite Programming Tags , , , ,

    We study the lift-and-project rank of the stable set polytope of graphs with respect to the Lovász–Schrijver SDP operator \( \text{LS}_+ \) applied to the fractional stable set polytope. In particular, we show that for every positive integer \( \ell \), the smallest possible graph with \( \text{LS}_+ \)-rank \( \ell \) contains \( 3\ell … Read more

    A Generalized Voting Game for Categorical Network Choices

  • Lin Yueh
  • Stefano Nasini
  • Martine Labbé
    • Categories Combinatorial Optimization, Data Science Algorithms, Game Theory Tags , , ,

    This paper presents a game-theoretical framework for data classification and network discovery, focusing on pairwise influences in multivariate choices. The framework consists of two complementary games in which individuals, connected through a signed weighted graph, exhibit network similarity. A voting rule captures the influence of an individual’s neighbors, categorized as attractive (friend-like) or repulsive (enemy-like), … Read more

    Spanning and Splitting: Integer Semidefinite Programming for the Quadratic Minimum Spanning Tree Problem

  • Frank de Meijer
  • Melanie Siebenhofer
  • Renata Sotirov
  • Angelika Wiegele
    • Categories (Mixed) Integer Nonlinear Programming, Network Optimization, Semi-definite Programming Tags , , , ,

    In the quadratic minimum spanning tree problem (QMSTP) one wants to find the minimizer of a quadratic function over all possible spanning trees of a graph. We present a formulation of the QMSTP as a mixed-integer semidefinite program exploiting the algebraic connectivity of a graph. Based on this formulation, we derive a doubly nonnegative relaxation … Read more

    Robust combinatorial optimization problems with knapsack constraints under interdiction uncertainty

  • Alejandro Crema
    • Categories Approximation Algorithms, Combinatorial Optimization, Robust Optimization Tags , , , ,

    We present an algorithm for finding near-optimal solutions to robust combinatorial optimization problems with knapsack constraints under interdiction uncertainty. We incorporate a heuristic for generating feasible solutions in a standard row generation approach. Experimental results are presented for set covering, simple plant location, and min-knapsack problems under a discrete-budgeted interdiction uncertainty set introduced in this … Read more

    On the integrality gap of the Complete Metric Steiner Tree Problem via a novel formulation

  • Ambrogio Maria Bernardelli
  • Eleonora Vercesi
  • Stefano Gualandi
  • Monaldo Mastrolilli
  • Luca Maria Gambardella
    • Categories Combinatorial Optimization, Graphs and Matroids, Linear Programming Tags , ,

    In this work, we study the metric Steiner Tree problem on graphs focusing on computing lower bounds for the integrality gap of the bi-directed cut (BCR) formulation and introducing a novel formulation, the Complete Metric (CM) model, specifically designed to address the weakness of the BCR formulation on metric instances. A key contribution of our … Read more

    New cuts and a branch-cut-and-price model for the Multi Vehicle Covering Tour Problem

  • Bruno Oliveira
  • Artur Alves Pessoa
  • Marcos Roboredo
    • Categories Combinatorial Optimization, Cutting Plane Approaches, Integer Programming Tags , , , ,

    The Multi-Vehicle Covering Tour Problem (m-CTP) involves a graph in which the set of vertices is partitioned into a depot and three distinct subsets representing customers, mandatory facilities, and optional facilities. Each customer is linked to a specific subset of optional facilities that define its coverage set. The goal is to determine a set of … Read more