54 research outputs found
Learning to Optimize Computational Resources: Frugal Training with Generalization Guarantees
Algorithms typically come with tunable parameters that have a considerable
impact on the computational resources they consume. Too often, practitioners
must hand-tune the parameters, a tedious and error-prone task. A recent line of
research provides algorithms that return nearly-optimal parameters from within
a finite set. These algorithms can be used when the parameter space is infinite
by providing as input a random sample of parameters. This data-independent
discretization, however, might miss pockets of nearly-optimal parameters: prior
research has presented scenarios where the only viable parameters lie within an
arbitrarily small region. We provide an algorithm that learns a finite set of
promising parameters from within an infinite set. Our algorithm can help
compile a configuration portfolio, or it can be used to select the input to a
configuration algorithm for finite parameter spaces. Our approach applies to
any configuration problem that satisfies a simple yet ubiquitous structure: the
algorithm's performance is a piecewise constant function of its parameters.
Prior research has exhibited this structure in domains from integer programming
to clustering
Dynamic lot size MIPs for multiple products and ELSPs with shortages, capacity and changeover limits
Scheduling multiple products with limited resources and varying demands
remain a critical challenge for many industries. This work presents mixed
integer programs (MIPs) that solve the Economic Lot Sizing Problem (ELSP) and
other Dynamic Lot-Sizing (DLS) models with multiple items. DLS systems are
classified, extended and formulated as MIPs. Especially, logical constraints
are a key ingredient in succeeding in this endeavour. They were used to
formulate the setup/changeover of items in the production line. Minimising the
holding, shortage and setup costs is the primary objective for ELSPs. This is
achieved by finding an optimal production schedule taking into account the
limited manufacturing capacity. Case studies for a production plants are used
to demonstrate the functionality of the MIPs. Optimal DLS and ELSP solutions
are given for a set of test-instances. Insights into the runtime and solution
quality are given.Comment: 14 pages, 6 figure
Optimising halting station of passenger railway lines
In many real life passenger railway networks, the types of stations and lines characterisethe halting stations of the train lines. Common types are Regional, Interregional or Intercity.This paper considers the problem of altering the halts of lines by both upgrading and downgrading stations, such that this results in less total travel time. We propose a combination of reduction methods, Lagrangian relaxation, and a problem-specific multiplier adjustment algorithm to solve the presented mixed integer linear programming formulation. A computational study of several real-life instances based on problem data of the Dutch passenger railway operator NS Reizigers is included.mathematical economics and econometrics ;
Exact Combinatorial Optimization with Graph Convolutional Neural Networks
Combinatorial optimization problems are typically tackled by the
branch-and-bound paradigm. We propose a new graph convolutional neural network
model for learning branch-and-bound variable selection policies, which
leverages the natural variable-constraint bipartite graph representation of
mixed-integer linear programs. We train our model via imitation learning from
the strong branching expert rule, and demonstrate on a series of hard problems
that our approach produces policies that improve upon state-of-the-art
machine-learning methods for branching and generalize to instances
significantly larger than seen during training. Moreover, we improve for the
first time over expert-designed branching rules implemented in a
state-of-the-art solver on large problems. Code for reproducing all the
experiments can be found at https://github.com/ds4dm/learn2branch.Comment: Accepted paper at the NeurIPS 2019 conferenc
Branch-and-Bound Solves Random Binary IPs in Polytime
Branch-and-bound is the workhorse of all state-of-the-art mixed integer
linear programming (MILP) solvers. These implementations of branch-and-bound
typically use variable branching, that is, the child nodes are obtained by
fixing some variable to an integer value in one node and to in the
other node. Even though modern MILP solvers are able to solve very large-scale
instances efficiently, relatively little attention has been given to
understanding why the underlying branch-and-bound algorithm performs so well.
In this paper our goal is to theoretically analyze the performance of the
standard variable branching based branch-and-bound algorithm. In order to avoid
the exponential worst-case lower bounds, we follow the common idea of
considering random instances. More precisely, we consider random integer
programs where the entries of the coefficient matrix and the objective function
are randomly sampled.
Our main result is that with good probability branch-and-bound with variable
branching explores only a polynomial number of nodes to solve these instances,
for a fixed number of constraints. To the best of our knowledge this is the
first known such result for a standard version of branch-and-bound. We believe
that this result provides a compelling indication of why branch-and-bound with
variable branching works so well in practice
Hybrid Models for Learning to Branch
A recent Graph Neural Network (GNN) approach for learning to branch has been
shown to successfully reduce the running time of branch-and-bound algorithms
for Mixed Integer Linear Programming (MILP). While the GNN relies on a GPU for
inference, MILP solvers are purely CPU-based. This severely limits its
application as many practitioners may not have access to high-end GPUs. In this
work, we ask two key questions. First, in a more realistic setting where only a
CPU is available, is the GNN model still competitive? Second, can we devise an
alternate computationally inexpensive model that retains the predictive power
of the GNN architecture? We answer the first question in the negative, and
address the second question by proposing a new hybrid architecture for
efficient branching on CPU machines. The proposed architecture combines the
expressive power of GNNs with computationally inexpensive multi-linear
perceptrons (MLP) for branching. We evaluate our methods on four classes of
MILP problems, and show that they lead to up to 26% reduction in solver running
time compared to state-of-the-art methods without a GPU, while extrapolating to
harder problems than it was trained on.Comment: Preprint. Under revie
Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies
Branch and Bound (B&B) is the exact tree search method typically used to
solve Mixed-Integer Linear Programming problems (MILPs). Learning branching
policies for MILP has become an active research area, with most works proposing
to imitate the strong branching rule and specialize it to distinct classes of
problems. We aim instead at learning a policy that generalizes across
heterogeneous MILPs: our main hypothesis is that parameterizing the state of
the B&B search tree can aid this type of generalization. We propose a novel
imitation learning framework, and introduce new input features and
architectures to represent branching. Experiments on MILP benchmark instances
clearly show the advantages of incorporating an explicit parameterization of
the state of the search tree to modulate the branching decisions, in terms of
both higher accuracy and smaller B&B trees. The resulting policies
significantly outperform the current state-of-the-art method for "learning to
branch" by effectively allowing generalization to generic unseen instances.Comment: AAAI 2021 camera-ready version with supplementary materials, improved
readability of figures in main article. Code, data and trained models are
available at https://github.com/ds4dm/branch-search-tree
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