Eduardo Uchoa

Cluster branching for vehicle routing problems

  • Joao Marcos P Silva
  • Eduardo Uchoa
  • Anand Subramanian
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Integer Programming Tags , , ,

    This article introduces Cluster Branching, a novel branching strategy for exact algorithms solving Vehicle Routing Problems (VRPs). While branching is crucial for the efficiency of branch-and-bound-based algorithms, existing branching types such as Edge Branching, CutSet Branching, and Ryan&Foster Branching have their limitations. The proposed branching strategy aggregates multiple edge variables into higher-level decision structures corresponding … Read more

    Kantorovich and Zalgaller (1951): the 0-th Column Generation Algorithm

  • Eduardo Uchoa
  • Ruslan Sadykov
    • Categories Other Topics Tags , ,

    This article delves into the early development of the Column Generation technique. It begins with Kantorovich’s classic 1939 work, correcting widespread misconceptions about his contributions to the Cutting Stock Problem. Then, it brings to light Kantorovich and Zalgaller’s lesser-known 1951 book, which is revealed to contain a complete Column Generation algorithm. The article also places … Read more

    A modern POPMUSIC matheuristic for the capacitated vehicle routing problem

  • Eduardo Queiroga
  • Ruslan Sadykov
  • Eduardo Uchoa
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Meta Heuristics

    This work proposes a partial optimization metaheuristic under special intensification conditions (POPMUSIC) for the classical capacitated vehicle routing problem (CVRP). The proposed approach uses a branch-cut-and-price algorithm as a powerful heuristic to solve subproblems whose dimensions are typically between 25 and 200 customers. The whole algorithm can be seen as the application of local search … Read more

    A Generic Exact Solver for Vehicle Routing and Related Problems

  • Artur Alves Pessoa
  • Ruslan Sadykov
  • Eduardo Uchoa
  • François Vanderbeck
    • Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms, Modeling Languages and Systems Tags , ,

    Major advances were recently obtained in the exact solution of Vehicle Routing Problems (VRPs). Sophisticated Branch-Cut-and-Price (BCP) algorithms for some of the most classical VRP variants now solve many instances with up to a few hundreds of customers. However, adapting and reimplementing those successful algorithms for other variants can be a very demanding task. This … Read more

    A Bucket Graph Based Labeling Algorithm with Application to Vehicle Routing

  • Artur Alves Pessoa
  • Ruslan Sadykov
  • Eduardo Uchoa
    • Categories Combinatorial Optimization, Dynamic Programming, Integer Programming

    We consider the Resource Constrained Shortest Path problem arising as a subproblem in state-of-the-art Branch-Cut-and-Price algorithms for vehicle routing problems. We propose a variant of the bi-directional label correcting algorithm in which the labels are stored and extended according to so-called bucket graph. Such organization of labels helps to decrease significantly the number of dominance … Read more

    Comparative Analysis of Capacitated Arc Routing Formulations for Branch-Cut-and-Price Algorithms

  • Diego Pecin
  • Eduardo Uchoa
    • Categories Combinatorial Optimization, Integer Programming, Transportation

    The current best exact algorithms for the Capacitated Arc Routing Problem are based on the combination of cut and column generation. This work presents a deep theoretical investigation of the formulations behind those algorithms, classifying them and pointing similarities and differences, advantages and disadvantages. In particular, we discuss which families of cuts and branching strategies … Read more

    Improved Space-State Relaxation for Constrained Two-Dimensional Guillotine Cutting Problems

  • Eduardo Uchoa
  • André Velasco
    • Categories (Mixed) Integer Linear Programming, Combinatorial Optimization Tags , ,

    Christofides and Hadjiconstantinou introduced a dynamic programming state space relaxation for obtaining upper bounds for the Constrained Two-dimensional Guillotine Cutting Problem. The quality of those bounds depend on the chosen item weights, they are adjusted using a subgradient-like algorithm. This paper proposes Algorithm X, a new weight adjusting algorithm based on integer programming that provably … Read more

    New Benchmark Instances for the Capacitated Vehicle Routing Problem

  • Diego Pecin
  • Artur Alves Pessoa
  • Marcus Poggi de Aragão
  • Anand Subramanian
  • Eduardo Uchoa
  • Thibaut Vidal
    • Categories (Mixed) Integer Linear Programming, Meta Heuristics, Transportation Tags , ,

    The recent research on the CVRP is being slowed down by the lack of a good set of benchmark instances. The existing sets suff er from at least one of the following drawbacks: (i) became too easy for current algorithms; (ii) are too arti cial; (iii) are too homogeneous, not covering the wide range of characteristics found … Read more

    Exact algorithms for the Traveling Salesman Problem with Draft Limits

  • Maria Battarra
  • Artur Alves Pessoa
  • Anand Subramanian
  • Eduardo Uchoa
    • Categories Branch and Cut Algorithms, Integer Programming Tags , , , ,

    This paper deals with the Traveling Salesman Problem (TSP) with Draft Limits (TSPDL), which is a variant of the well-known TSP in the context of maritime transportation. In this recently proposed problem, draft limits are imposed due to restrictions on the port infrastructures. Exact algorithms based on three mathematical formulations are proposed and their performance … Read more

    Cuts over Extended Formulations by Flow Discretization

  • Eduardo Uchoa
    • Categories Branch and Cut Algorithms, Integer Programming Tags ,

    Large-sized extended formulations have the potential for providing high-quality bounds on some combinatorial optimization problems where the natural formulations perform poorly. This chapter discusses the use of some families of cuts that have been recently applied on extended formulations that are obtained by the discretization of the continuous variables occurring in the natural formulation of … Read more