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Session A
Downtime of industrial
assets such as wind turbines and medical imaging devices is costly. To avoid
such downtime costs, companies seek to initiate maintenance just before
failure, which is challenging because: (i) Asset
failures are notoriously difficult to predict, even in the presence of
real-time monitoring devices which signal degradation; and (ii) Limited
resources are available to serve a network of geographically dispersed assets.
In this work, we study the dynamic traveling multi-maintainer problem with
alerts ($K$-DTMPA) under perfect condition
information with the objective to devise scalable solution approaches to
maintain large networks with $K$ maintenance engineers. Since such large-scale
$K$-DTMPA instances are computationally intractable,
we propose an iterative DRL algorithm optimizing long-term discounted
maintenance costs that potentially improves upon any heuristic solution. We
extend existing heuristics to devise both quality benchmarks for specific
instances and suitable initial policies for the DRL algorithm. In our numerical
experiments, we show that DRL can solve single maintainer instances up to
optimality, regardless of the chosen initial solution. Moreover, DRL can be
successfully applied to improve state-of-the-art dispatching heuristics.
Experiments with hospital networks containing up to $35$ assets show that the
proposed DRL algorithm is scalable and it is cost-efficient
to share resources over the network, as opposed to subdividing the network into
smaller regions.
The increasing availability
of condition monitoring data for aircraft components has incentivized the
development of Remaining Useful Life (RUL)
prognostics in the past years. In this presentation, I will present a
predictive maintenance scheduling framework for a fleet of aircraft taking into account imperfect RUL
prognostics. These prognostics are periodically updated. Based on the evolution
of the prognostics over time, alarms are triggered. The scheduling of
maintenance tasks is initiated only after these alarms are triggered. Alarms
ensure that maintenance tasks are not rescheduled multiple times. A maintenance
task is scheduled using a safety factor, to account for potential errors in the
RUL prognostics and thus avoid component failures. We
illustrate our approach for a fleet of 20 aircraft, each equipped with 2
turbofan engines. A Convolution Neural Network is proposed to obtain RUL prognostics. An integer linear program is used to
schedule aircraft for maintenance.
A sampling-based method is introduced to approximate
the Gittins index index for general families of
alternative bandit processes. The approximation consists of truncation of the
horizon and support for the optimized discounted reward, an optimal stopping
value approximation and a stochastic approximation procedure to find the root
of the mean of a stochastic function. Finite-time error bounds are given for
the three approximations, leading to a procedure to construct a confidence
interval for the Gittins index using a finite number of Monte Carlo samples. Furthermore, results are proven on almost sure
convergence and convergence in distribution of the samples generated from the
stochastic approximation procedure. In a numerical study, the approximation
quality of the proposed method is verified for the Bernoulli and Gaussian
bandit with known variance. Finally, the proposed strategy is applied in a
non-standard Bayesian bandit setting where each arm consists of a random effects
model where it is shown to significantly outperform Thompson sampling and the
Bayesian Upper Confidence Bound algorithms. The approximation method can be
applied to any family of alternative bandit processes and can hence be easily
applied to more elaborate Bayesian experimental setups than those usually
considered in the Bayesian multi-armed bandit literature.
In order to use warehouse capacity in an optimal way,
ensure customers next day delivery, and use warehouses in a cost
efficient way we investigate stochastic optimisation
approaches to improve existing ways of steering and planning capacity. In this talk we present results from several projects
and share ideas for further investigation. Session B
Handling symmetries in
optimization problems is essential for devising efficient solution methods. In
this article, we present a general framework that captures many of the already
existing symmetry handling methods (SHMs). While
these SHMs are mostly discussed independently from
each other, our framework allows to apply different SHMs
simultaneously and thus outperforming their individual effect. Moreover, most
existing SHMs only apply to binary variables. Our
framework allows to easily generalize these methods to general variable types.
Numerical experiments confirm that our novel framework is superior to the state-of-the-art
SHMs implemented in the solver SCIP.
The goal of hierarchical
clustering (HC) methods is to
build a hierarchy of nested clusters, which is often visualised in a dendrogram. For certain scientific applications, such as finding phylogenetic (evolutionary)
trees, it takes a long time to
collect the data and the samples are often small. For
these applications it makes sense that more computation time could be spend on finding
good dendrograms. In practice, agglomerative
(bottom-up) and divisive
(top-down) clustering approaches are used, which are not guaranteed
to find an
optimal solution. Since
2016, a lot of research has been devoted on defining a suitable objective function for HC, which has led to several proposed
objective functions and corresponding approximation results. However, exact methods have received little attention. We propose several exact methods for HC, which are based on insights from the
partition based clustering
(e.g. k-means clustering) literature. We propose mixed-integer programming
formulations as well as a branch-and-price
approach, which can easily be adapted
to include other objective functions or constraints. In our computational study, we investigate the performance of commonly used heuristics and approximation algorithms.
We establish a broad methodological foundation
for mixed-integer optimization with learned constraints. We propose an
end-to-end pipeline for data-driven decision making in which constraints and
objectives are directly learned from data using machine learning, and the
trained models are embedded in an optimization formulation. We exploit the
mixed-integer optimization-representability of many machine
learning methods, including linear models, decision trees, ensembles, and
multi-layer perceptrons. The consideration of
multiple methods allows us to capture various underlying relationships between
decisions, contextual variables, and outcomes. We also characterize a decision
trust region using the convex hull of the observations, to ensure credible
recommendations and avoid extrapolation. We efficiently incorporate this
representation using column generation and clustering. In combination with
domain-driven constraints and objective terms, the embedded models and trust
region define a mixed-integer optimization problem for prescription generation.
We implement this framework as a Python package (OptiCL)
for practitioners. We demonstrate the method in both chemotherapy optimization
and World Food Programme planning. The case studies illustrate the benefit of
the framework in generating high-quality prescriptions, the value added by the
trust region, the incorporation of multiple machine learning methods, and the
inclusion of multiple learned constraints. |
