arXiv subjects

Christian Truden

Publications and source records attributed to Christian Truden.

7 recordsLinked to original sources

arXiv2024

Variable Selection Using Nearest Neighbor Gaussian Processes

We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as scalable approximations of classical Gaussian processes. Variable selection is achieved by conditioning the process mean and covariance function on a random set that represents the indices of contributing variables. A priori beliefs regarding this set control the variable selection, while reference priors are assigned to the remaining model parameters, ensuring numerical robustness in the process covariance matrix. We propose a Metropolis-Within-Gibbs algorithm for model inference. Evaluation using simulated data, a computer experiment approximation, and two real-world data sets demonstrate the effectiveness of our approach.

stat.CO↗

arXiv2021

Computational Approaches for Grocery Home Delivery Services

Grocery home delivery services require customers to be present when their deliveries arrive. Hence, the grocery retailer and the customer must mutually agree on a time window during which the delivery can be guaranteed. This concept is referred to as the Attended Home Delivery (AHD) problem. The phase during which customers place orders, usually through a web service, constitutes the computationally most challenging part of the logistical processes behind such services. The system must determine potential delivery time windows that can be offered to incoming customers and incrementally build the delivery schedule as new orders are placed. Typically, a Vehicle Routing Problem with Time Windows forms the underlying optimization problem. This work is concerned with the use case given by an international grocery retailer's online shopping service. We present an analysis of efficient solution methods that can be employed to AHD services. We provide several heuristic approaches for tackling the steps mentioned above. However, the basic framework can be easily be adapted to be used for many similar Vehicle Routing applications. We provide a comprehensive computational study comparing several algorithmic strategies, combining heuristics utilizing Local Search operations and Mixed-Integer Linear Programs, tackling the booking process. Finally, we analyze the scalability and suitability of the approaches.

math.OC↗

arXiv2021

Lower Bounds for the Bandwidth Problem

The Bandwidth Problem seeks for a simultaneous permutation of the rows and columns of the adjacency matrix of a graph such that all nonzero entries are as close as possible to the main diagonal. This work focuses on investigating novel approaches to obtain lower bounds for the bandwidth problem. In particular, we use vertex partitions to bound the bandwidth of a graph. Our approach contains prior approaches for bounding the bandwidth as special cases. By varying sizes of partitions, we achieve a trade-off between quality of bounds and efficiency of computing them. To compute lower bounds, we derive a Semidefinite Programming relaxation. We evaluate the performance of our approach on several data sets, including real-world instances.

math.OC↗

arXiv2021

A Bayesian Approach for Predicting Food and Beverage Sales in Staff Canteens and Restaurants

Accurate demand forecasting is one of the key aspects for successfully managing restaurants and staff canteens. In particular, properly predicting future sales of menu items allows a precise ordering of food stock. From an environmental point of view, this ensures maintaining a low level of pre-consumer food waste, while from the managerial point of view, this is critical to guarantee the profitability of the restaurant. Hence, we are interested in predicting future values of the daily sold quantities of given menu items. The corresponding time series show multiple strong seasonalities, trend changes, data gaps, and outliers. We propose a forecasting approach that is solely based on the data retrieved from Point of Sales systems and allows for a straightforward human interpretation. Therefore, we propose two generalized additive models for predicting the future sales. In an extensive evaluation, we consider two data sets collected at a casual restaurant and a large staff canteen consisting of multiple time series, that cover a period of 20 months, respectively. We show that the proposed models fit the features of the considered restaurant data. Moreover, we compare the predictive performance of our method against the performance of other well-established forecasting approaches.

stat.AP↗

arXiv2019

Optimal allocation of defibrillator drones in mountainous regions

Responding to emergencies in Alpine terrain is quite challenging as air ambulances and mountain rescue services are often confronted with logistics challenges and adverse weather conditions that extend the response times required to provide life-saving support. Among other medical emergencies, sudden cardiac arrest (SCA) is the most time-sensitive event that requires the quick provision of medical treatment including cardiopulmonary resuscitation and electric shocks by automated external defibrillators (AED). An emerging technology called unmanned aerial vehicles (or drones) is regarded to support mountain rescuers in overcoming the time criticality of these emergencies by reducing the time span between SCA and early defibrillation. A drone that is equipped with a portable AED can fly from a base station to the patient's site where a bystander receives it and starts treatment. This paper considers such a response system and proposes an integer linear program to determine the optimal allocation of drone base stations in a given geographical region. In detail, the developed model follows the objectives to minimize the number of used drones and to minimize the average travel times of defibrillator drones responding to SCA patients. In an example of application, under consideration of historical helicopter response times, the authors test the developed model and demonstrate the capability of drones to speed up the delivery of AEDs to SCA patients. Results indicate that time spans between SCA and early defibrillation can be reduced by the optimal allocation of drone base stations in a given geographical region, thus increasing the survival rate of SCA patients.

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arXiv2019

Sweep Algorithms for the Capacitated Vehicle Routing Problem with Structured Time Window

The capacitated Vehicle Routing Problem with structured Time Windows (cVRPsTW) is concerned with finding optimal tours for vehicles with given capacity constraints to deliver goods to customers within assigned time windows. In our problem variant these time windows have a special structure, namely they are non-overlapping and each time window holds several customers. This is a reasonable assumption for Attended Home Delivery services. Sweep algorithms are known as simple, yet effective heuristics for the classical capacitated Vehicle Routing Problem. We propose variants of the sweep algorithm that are not only able to deal with time windows, but also exploit the additional structure of the time windows in a cVRPsTW. Afterwards we suggest local improvement heuristics to decrease our objective function even further. A carefully constructed benchmark set that resembles real-world data is used to prove the efficacy of our algorithms in a computational study.

math.OC↗

arXiv2018

An Optimization Approach to the Ordering Phase of an Attended Home Delivery Service

Attended Home Delivery (AHD) systems are used whenever a supplying company offers online shopping services that require that customers must be present when their deliveries arrive. Therefore, the supplying company and the customer must both agree on a time window, which ideally is rather short, during which delivery is guaranteed. Typically, a capacitated Vehicle Routing Problem with Time Windows forms the underlying optimization problem of the AHD system. In this work, we consider an AHD system that runs the online grocery shopping service of an international grocery retailer. The ordering phase, during which customers place their orders through the web service, is the computationally most challenging part of the AHD system. The delivery schedule must be built dynamically as new orders are placed. We propose a solution approach that allows to (non-stochastically) determine which delivery time windows can be offered to potential customers. We split the computations of the ordering phase into four key steps. For performing these basic steps we suggest both a heuristic approach and a hybrid approach employing mixed-integer linear programs. In an experimental evaluation we demonstrate the efficiency of our approaches.

math.OC↗