Combinatorial Optimization

Discovering Heuristics with Large Language Models (LLMs) for Mixed-Integer Programs: Single-Machine Scheduling

  • I. Esra Buyuktahtakin Toy
    • Categories (Mixed) Integer Linear Programming, Combinatorial Optimization, Meta Heuristics Tags , , , , , , ,

    TitleDiscovering Heuristics with Large Language Models (LLMs) for Mixed-Integer Programs: Single-Machine Scheduling Authorsİbrahim Oğuz Çetinkaya^1; İ. Esra Büyüktahtakın^1*; Parshin Shojaee^2; Chandan K. Reddy^2 Affiliations^1 Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA, USA^2 Department of Computer Science, Virginia Tech, Arlington, VA, USA Abstract: Our study contributes to the scheduling and combinatorial optimization … Read more

    Consolidation in Crowdshipping with Scheduled Transfer Lines: A Surrogate-Based Network Design Framework

  • Ramazan Çevik
  • Ali Şardağ
  • Barış Yıldız
    • Categories Combinatorial Optimization, Optimization in Data Science, Transportation Tags , , ,

    Abstract: Crowdshipping has gained attention as an emerging delivery model thanks to advantages such as flexibility and an asset-light structure. Yet, it chronically suffers from a lackof mechanisms to create and exploit consolidation opportunities, limiting its efficiency and scalability. This work contributes to the literature in two ways: first, by introducing a novel consolidation concept … Read more

    On vehicle routing problems with stochastic demands — Generic integer L-shaped formulations

  • Matheus Jun Ota
  • Ricardo Fukasawa
    • Categories Branch and Cut Algorithms, Stochastic Programming, Transportation Tags , , ,

    We study a broad class of vehicle routing problems in which the cost of a route is allowed to be any nonnegative rational value computable in polynomial time in the input size. To address this class, we introduce a unifying framework that generalizes existing integer L-shaped (ILS) formulations developed for vehicle routing problems with stochastic … Read more

    Approximating value functions via corner Benders’ cuts

  • Matheus Jun Ota
  • Ricardo Fukasawa
  • Aleksandr M. Kazachkov
    • Categories Branch and Cut Algorithms, Integer Programming, Stochastic Programming Tags , , , , ,

    We introduce a novel technique to generate Benders’ cuts from a conic relaxation (“corner”) derived from a basis of a higher-dimensional polyhedron that we aim to outer approximate in a lower-dimensional space. To generate facet-defining inequalities for the epigraph associated to this corner, we develop a computationally-efficient algorithm based on a compact reverse polar formulation … Read more

    Solution of Stochastic Facility Location Problems with Combinatorially many Decision-Dependent Distributions

  • Giovanni Pantuso
    • Categories Combinatorial Optimization, Facility Planning and Design, Stochastic Programming

    This article describes a model and an exact solution method for facility location problems with decision-dependent uncertainties. The model allows characterizing the probability distribution of the random elements as a function of the choice of open facilities. This, in turn, generates a combinatorial number of potential distributions of the random elements. Though general in the … Read more

    Consistent and unbiased estimation of the hypervolume of an unknown true Pareto front

  • Xavier Gandibleux
  • Andrzej Jaszkiewicz
    • Categories Combinatorial Optimization, Meta Heuristics, Multi-Criteria Optimization Tags , ,

    Hypervolume is most likely the most often used set quality indicator in (evolutionary) multi-objective optimization. It may be used to compare the quality of solution sets whose images in the objective space are approximations of the true Pareto front. Although in this way we may compare two or more approximations, our knowledge is limited without … Read more

    Visiting exactly once all the vertices of {0,1,2}^3 with a 13-segment path that avoids self-crossing

  • Marco Ripà
    • Categories Bound-constrained Optimization, Combinatorial Optimization, Graphs and Matroids Tags , , , , , ,

    In the Euclidean space \(\mathbb{R}^3\), we ask whether one can visit each of the \(27\) vertices of the grid \(G_3:=\{0,1,2\}^3\) exactly once using as few straight-line segments, connected end to end, as possible (an optimal polygonal chain). We give a constructive proof that there exists a \(13\)-segment perfect simple path (i.e., an optimal chain that … Read more

    A Traveling Salesman Problem with Drone Stations and Speed-Optimized Drones

  • Chun Cheng
    • Categories Meta Heuristics, Transportation Tags

    With e-commerce expanding rapidly, last-mile delivery challenges have been exacerbated, necessitating innovative logistics to reduce operational costs and improve delivery speed. This paper investigates a traveling salesman problem with drone stations, where a truck collaborates with multiple drones docked at candidate drone stations to serve customers. In contrast to existing studies that typically assume fixed … Read more

    Greedy Algorithms with Imprecise Oracles for Submodular Knapsack Problems

  • Sabine Münch
    • Categories Approximation Algorithms, Combinatorial Optimization Tags , , ,

    We consider the problem of maximizing a monotone increasing, normalized, and submodular function defined on a set of weighted items under a knapsack constraint. A well-known greedy algorithm, analyzed by Wolsey (1982), achieves an approximation factor of \(0.357\) for this problem. This greedy algorithm starts with an empty solution set and iteratively generates a feasible … Read more