arXiv subjects

Peter Nielsen

Publications and source records attributed to Peter Nielsen.

9 recordsLinked to original sources

arXiv2024

A Semi-Automated Solution Approach Recommender for a Given Use Case: a Case Study for AI/ML in Oncology via Scopus and OpenAI

Nowadays, literature review is a necessary task when trying to solve a given problem. However, an exhaustive literature review is very time-consuming in today's vast literature landscape. It can take weeks, even if looking only for abstracts or surveys. Moreover, choosing a method among others, and targeting searches within relevant problem and solution domains, are not easy tasks. These are especially true for young researchers or engineers starting to work in their field. Even if surveys that provide methods used to solve a specific problem already exist, an automatic way to do it for any use case is missing, especially for those who don't know the existing literature. Our proposed tool, SARBOLD-LLM, allows discovering and choosing among methods related to a given problem, providing additional information about their uses in the literature to derive decision-making insights, in only a few hours. The SARBOLD-LLM comprises three modules: (1: Scopus search) paper selection using a keyword selection scheme to query Scopus API; (2: Scoring and method extraction) relevancy and popularity scores calculation and solution method extraction in papers utilizing OpenAI API (GPT 3.5); (3: Analyzes) sensitivity analysis and post-analyzes which reveals trends, relevant papers and methods. Comparing the SARBOLD-LLM to manual ground truth using precision, recall, and F1-score metrics, the performance results of AI in the oncology case study are 0.68, 0.9, and 0.77, respectively. SARBOLD-LLM demonstrates successful outcomes across various domains, showcasing its robustness and effectiveness. The SARBOLD-LLM addresses engineers more than researchers, as it proposes methods and trends without adding pros and cons. It is a useful tool to select which methods to investigate first and comes as a complement to surveys. This can limit the global search and accumulation of knowledge for the end user. However...

cs.AI↗

arXiv2022

On the Fitness Landscapes of Interdependency Models in the Travelling Thief Problem

Since its inception in 2013, the Travelling Thief Problem (TTP) has been widely studied as an example of problems with multiple interconnected sub-problems. The dependency in this model arises when tying the travelling time of the "thief" to the weight of the knapsack. However, other forms of dependency as well as combinations of dependencies should be considered for investigation, as they are often found in complex real-world problems. Our goal is to study the impact of different forms of dependency in the TTP using a simple local search algorithm. To achieve this, we use Local Optima Networks, a technique for analysing the fitness landscape.

cs.AI↗

arXiv2021

New estimates for convex layer numbers

Starting with a finite point set $X \subset \mathbf{R}^d$, the peeling process repeatedly removes the set of the vertices of the convex hull of the current set. The number of peeling steps required to completely remove $X$ is called the layer number of $X$, denoted by $L(X)$. In the article, we study the layer number of evenly distributed families of point sets contained in $B^d$, the $d$-dimensional unit ball. These sets consist of points in $B^d$ whose minimal distance is asymptotically as large as possible. We show that for a set $X$ belonging to an evenly distributed family, $L(X) \geq Ω(|X|^{1/d})$ holds, with the bound being asymptotically sharp. On the other hand, building on earlier results, we prove that $L(X)\leq O(|X|^{2/d})$ holds for $d\geq 2$, which improves greatly on the current upper bound of $O(|X|^{(d+1)/2d})$ for $d \geq 3$. Finally, we provide a recursive construction of evenly distributed families whose sets satisfy $L(X) = Θ(|X|^{2/d - 1/(d 2^{d-1})})$, showing that our upper bound is nearly tight.

math.MG↗

arXiv2021

MATE: A Model-based Algorithm Tuning Engine

In this paper, we introduce a Model-based Algorithm Turning Engine, namely MATE, where the parameters of an algorithm are represented as expressions of the features of a target optimisation problem. In contrast to most static (feature-independent) algorithm tuning engines such as irace and SPOT, our approach aims to derive the best parameter configuration of a given algorithm for a specific problem, exploiting the relationships between the algorithm parameters and the features of the problem. We formulate the problem of finding the relationships between the parameters and the problem features as a symbolic regression problem and we use genetic programming to extract these expressions. For the evaluation, we apply our approach to configuration of the (1+1) EA and RLS algorithms for the OneMax, LeadingOnes, BinValue and Jump optimisation problems, where the theoretically optimal algorithm parameters to the problems are available as functions of the features of the problems. Our study shows that the found relationships typically comply with known theoretical results, thus demonstrating a new opportunity to consider model-based parameter tuning as an effective alternative to the static algorithm tuning engines.

cs.NE↗

arXiv2018

Instance Scale, Numerical Properties and Design of Metaheuristics: A Study for the Facility Location Problem

Metaheuristics are known to be strong in solving large-scale instances of computationally hard problems. However, their efficiency still needs exploration in the context of instance structure, scale and numerical properties for many of these problems. In this paper, we present an in-depth computational study of two local search metaheuristics for the classical uncapacitated facility location problem. We investigate four problem instance models, studied for the same problem size, for which the two metaheuristics exhibit intriguing and contrasting behaviours. The metaheuristics explored include a local search (LS) algorithm that chooses the best moves in the current neighbourhood, while a randomised local search (RLS) algorithm chooses the first move that does not lead to a worsening. The experimental results indicate that the right choice between these two algorithms depends heavily on the distribution of coefficients within the problem instance. This is also put further into context by finding optimal or near-optimal solutions using a mixed-integer linear programming problem solver. Since the facility location problem is a relatively simple example of a choice-and-assignment problem, similar phenomena are likely to be discovered in a number of other, possibly more complex computational problems in science and engineering.

cs.CE↗

arXiv2017

The impact of stochastic lead times on the bullwhip effect under correlated demand and moving average forecasts

We quantify the bullwhip effect (which measures how the variance in replenishment orders is amplified as the orders move up the supply chain) when random demands and random lead times are estimated using the industrially popular moving average forecasting method. We assume that the lead times constitute a sequence of independent identically distributed random variables and correlated demands are described by a first order autoregressive process. We obtain an expression that reveals the impact of demand and lead time forecasting on the bullwhip effect. We draw a number of conclusions on the behavior of the bullwhip effect with respect to the demand auto-correlation and the number of past lead times and demands used in the forecasts. Furthermore we find the maxima and minima of the bullwhip measure as a function of the demand auto-correlation.

stat.AP↗

arXiv2015

The impact of lead time forecasting on the bullwhip effect

In this article we quantify the bullwhip effect (the variance amplification in replenishment orders) when demands and lead times are predicted in a simple two-stage supply chain with one supplier and one retailer. In recent research the impact of stochastic order lead time on the bullwhip effect is investigated, but the effect of needing to predict / estimate the lead time is not considered in the supply chain models. Under uncertainty conditions it is necessary to estimate the lead time for a member of the supply chain to place an order. We find a new cause of the bullwhip effect in the form of lead time forecasting and we give an exact form of the bullwhip effect measure (the ratio of variances) when demands and lead times are predicted by moving averages. In the bullwhip effect measure we discover two terms amplifying the effect which are the result of lead time estimation

math.PR↗

arXiv2015

The impact of stochastic lead times on the bullwhip effect

In this article we want to review the research state on the bullwhip effect in supply chains with stochastic lead times and give a contribution to quantifying the bullwhip effect. We analyze the models quantifying the bullwhip effect in supply chains with stochastic lead times and find advantages and disadvantages of their approaches to the bullwhip problem. Using real data we confirm that real lead times are stochastic and can be modeled by a sequence of independent identically distributed random variables. Moreover we modify a model where stochastic lead times and lead time demand forecasting are considered and give an analytical expression for the bullwhip effect measure which indicates that the distribution of a lead time and the delay parameter of the lead time demand prediction are the main factors of the bullwhip phenomenon. Moreover we analyze a recent paper of Michna and Nielsen adding simulation results.

stat.AP↗

arXiv2013

Lévy processes in storage and inventory problems

In this paper we consider storage and inventory systems. Our aim is to apply and review main results of the fluctuation theory of stochastic processes in the context of storage and inventory modeling. We describe systems where the inflow is due to a Lévy process and the outflow is linear and conversely systems where the inflow is linear and the outflow is due to a Lévy process. For such systems we investigate the process of a storage (inventory) level. We give formulas for the probability that the storage level exceeds a certain value. This probability is crucial in the management of storage and inventory systems.

math.PR↗