This manuscript makes the claim of having computed the \(9\) th Dedekind number, D(9). This was done by accelerating the core operation of the process with an efficient FPGA design that outperforms an optimized 64-core CPU reference by 95 \(\times\) . The FPGA execution was parallelized on the Noctua 2 supercomputer at Paderborn University. The resulting value for D(9) is 286386577668298411128469151667598498812366. This value can be verified in two steps. We have made the data file containing the 490 M results available, each of which can be verified separately on CPU, and the whole file sums to our proposed value. The paper explains the mathematical approach in the first part, before putting the focus on a deep dive into the FPGA accelerator implementation followed by a performance analysis. The FPGA implementation was done in Register-Transfer Level using a dual-clock architecture and shows how we achieved an impressive FMax of 450 MHz on the targeted Stratix 10 GX 2,800 FPGAs. The total compute time used was 47,000 FPGA hours.

Patient scheduling is a difficult task involving stochastic factors, such as the unknown arrival times of patients. Similarly, the scheduling of radiotherapy for cancer treatments needs to handle patients with different urgency levels when allocating resources. High-priority patients may arrive at any time, and there must be resources available to accommodate them. A common solution is to reserve a flat percentage of treatment capacity for emergency patients. However, this solution can result in overdue treatments for urgent patients, a failure to fully exploit treatment capacity, and delayed treatments for low-priority patients. This problem is especially severe in large and crowded hospitals. In this paper, we propose a prediction-based approach for online dynamic radiotherapy scheduling that dynamically adapts the present scheduling decision based on each incoming patient and the current allocation of resources. Our approach is based on a regression model trained to recognize the links between patients’ arrival patterns and their ideal waiting time in optimal off-line solutions when all future arrivals are known in advance. When our prediction-based approach is compared with flat-reservation policies, it does a better job of preventing overdue treatments for emergency patients and also maintains comparable waiting times for the other patients. We also demonstrate how our proposed approach supports explainability and interpretability in scheduling decisions using Shapley additive explanation values. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Funding: Mitacs Accélération IT26995 and Canada Research Chair in Analytics and Logistics in Healthcare (HANALOG). Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.1289 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0342 ) at ( http://dx.doi.org/10.5281/zenodo.7579533 ).

Many problems in operations research require that constraints be specified in the model. Determining right constraints is a hard and laborsome task. We propose an approach to automate this process using artificial intelligence and machine learning principles. We focus on personnel rostering and scheduling problems in which there are often past schedules available and show that it is possible to automatically learn constraints from such examples. To realize this, we adapted some techniques from the constraint programming community and extended them in order to cope with multidimensional examples. The method uses a tensor representation of the example, which helps in capturing the dimensionality as well as the structure of the example, and applies tensor operations to find the constraints that are satisfied by the example. The algorithm also identifies inherent clusters in the data and uses it as background knowledge to learn more detailed constraints. To evaluate the proposed algorithm, we used constraints from the Nurse Rostering Competition and generated solutions that satisfy these constraints; these solutions were then used as examples to learn constraints. Experiments demonstrate that the proposed algorithm is capable of producing human readable constraints that capture the underlying characteristics of the examples.

Observation requests for autonomous observation satellites are dynamically generated. Considering the limited computing resources, a data-driven onboard scheduling method combining AI techniques and polynomial-time heuristics is proposed in this work. To construct observation schedules, a framework with offline learning and onboard scheduling is adopted. A neural network is trained offline in ground stations to assign the scheduling priority to observation requests in the onboard scheduling, based on the optimized historical schedules obtained by genetic algorithms which are computationally demanding to run onboard. The computational simulations show that the performance of the scheduling heuristic is enhanced using the data-driven framework.

Algorithm selection approaches have achieved impressive performance improvements in many areas of AI. Most of the literature considers the offline algorithm selection problem, where the initial selection model is never updated after training. However, new data from running algorithms on instances becomes available when algorithms are selected and run. We investigate how this online data can be used to improve the selection model over time. This is especially relevant when insufficient training instances were used, but potentially improves the performance of algorithm selection in all cases. We formally define the online algorithm selection problem and model it as a contextual multi-armed bandit problem, propose a methodology for solving it, and empirically demonstrate performance improvements. We also show that our online algorithm selection method can be used when no training data whatsoever is available, a setting where offline algorithm selection cannot be used. Our experiments indicate that a simple greedy approach achieves the best performance.

Over the recent years, several tools for the automated configuration of parameterized algorithms have been developed. These tools, also called configurators, have themselves parameters that influence their search behavior and make them malleable to different kinds of configuration tasks. The default values of these parameters are set manually based on the experience of the configurator's developers. Studying the impact of these parameters or configuring them is very expensive as it would require many executions of these tools on configuration tasks, each taking often many hours or days of computation. In this work, we tackle this problem using a meta-tuning process, based on the use of surrogate benchmarks that are much faster to evaluate. This paper studies the feasibility of this process using the popular irace configurator as the method to be meta-configured. We first study the consistency between the real and surrogate benchmarks using three measures: the prediction accuracy of the surrogate models, the homogeneity of the benchmarks and the list of important algorithm parameters. Afterwards, we use irace to configure irace on those surrogates. Experimental results indicate the feasibility of this process and a clear potential improvement of irace over its default configuration.

The reach of an arc in a network can intuitively be described as an indication of the maximum length of the shortest paths of the digraph that pass through this arc. This concept captures the natural hierarchy of any type of network, in an accurate and comprehensive manner. Traditional reach approximation algorithms compute upper bounds to these reaches and require computation of a partial shortest path tree rooted in all vertices of the network. Tailored for route computation enhancement, these methods yield exact reaches in the low reach spectrum, whereas higher reaches are kept set to infinity.

In the single-objective automated algorithm configuration problem, given an algorithm with a set of parameters that need to be configured and a distribution of problem instances, the automated algorithm configurator will try to search for a good parameter configuration based on a pre-defined performance measure. In this paper, we point out two motivations for the development of a multi-objective algorithm configurator, in which more than one performance measure are considered at the same time. The first motivation is a parameter configuration case study for a deterministic single machine scheduling algorithm with two performance measures: minimization of the average running time and maximization of the total number of optimal solutions. The second one is the configuration problem for non-exact multi-objective optimization algorithms. In addition, a discussion of solving approach for the first motivating problem is also presented.

MOTIVATION: Gene prioritization aims at identifying the most promising candidate genes among a large pool of candidates-so as to maximize the yield and biological relevance of further downstream validation experiments and functional studies. During the past few years, several gene prioritization tools have been defined, and some of them have been implemented and made available through freely available web tools. In this study, we aim at comparing the predictive performance of eight publicly available prioritization tools on novel data. We have performed an analysis in which 42 recently reported disease-gene associations from literature are used to benchmark these tools before the underlying databases are updated. RESULTS: Cross-validation on retrospective data provides performance estimate likely to be overoptimistic because some of the data sources are contaminated with knowledge from disease-gene association. Our approach mimics a novel discovery more closely and thus provides more realistic performance estimates. There are, however, marked differences, and tools that rely on more advanced data integration schemes appear more powerful. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Collaboration in Digital Ecosystems can be very complex due to varying types and numbers of actors and artifacts, and the many possible interactions between these entities. Hereby, network visualizations are useful for analyzing networked collaboration and consequently for supporting cognitive processes, like fostering reflection, enabling awareness in students' learning. In this paper, we examine different techniques for visualizing ICT-enabled interactions in Digital Ecosystems. After giving a brief overview of related work, we argue for the application of two-mode networks for visualizing patterns of networked collaboration and discuss different issues by comparing this technique to traditional visualizations.

The mashup era has emerged in response to the challenge of integrating existing services, data sources, and tools to generate new applications. Mashups are usually realized either through a seamless integration, in which only the resulting application is known by the end-users, or through integration of original applications, data sources, and tools, particularly in terms of widgets, into the same graphical space, in which participating applications and data sources are identifiable by the end-users. The former composes a unified functionality or data presentation/source from the original sources. The latter generates a digital environment in which participating sources exist as individual entities, but the true integration can only be realized through enabling widgets to be responsive to the events happening in each other. We call such an integration widget orchestration. In this paper, we provide a holistic view on the mashup era and a theoretical grounding for widget-based digital environments, we elaborate on key challenges for realizing such environments and (semi-)automatic widget orchestration, and we introduce our solution strategies. We identified following challenges: widget interoperability, user-behavior mining, and infrastructure. We introduce functional interfaces (FWI) for application interoperability, exploit semantic web technologies for data interoperability, and investigate the possibility of employing workflow/process mining techniques, along with Petri nets as a formal ground, for user-behavior mining. We outline a reference platform and architecture, compliant with our strategies, to foster re-usability of widgets and development of standardized widget-based environments. We have implemented a prototype for a Widget-based Personal Learning Environment (WIPLE) for foreign language learning in order to demonstrate the feasibility of our solution strategies, framework, and architecture.

Finding the most promising genes among large lists of candidate genes has been defined as the gene prioritization problem. It is a recurrent problem in genetics in which genetic conditions are reported to be associated with chromosomal regions. In the last decade, several different computational approaches have been developed to tackle this challenging task. In this study, we review 19 computational solutions for human gene prioritization that are freely accessible as web tools and illustrate their differences. We summarize the various biological problems to which they have been successfully applied. Ultimately, we describe several research directions that could increase the quality and applicability of the tools. In addition we developed a website (http://www.esat.kuleuven.be/gpp) containing detailed information about these and other tools, which is regularly updated. This review and the associated website constitute together a guide to help users select a gene prioritization strategy that suits best their needs.

A hyper-heuristic performs search over a set of other search mechanisms. During the search, it does not require any problem-dependent data. This structure makes hyper-heuristics problem-independent indirect search mechanisms. In this study, we propose a learning strategy to explore elite heuristic subsets for different phases of a search. For that purpose, we apply a number of hyper-heuristics with the proposed approach to a set of home care scheduling problem instances. The results show that the learning strategy increases the performance of the different hyper-heuristics by excluding some heuristics from the heuristic set over the tested problem instances.

Users of hospital personnel planning software cope with the complex task of translating their needs into several constraints of a very different nature and with differing cost parameters. We present a multi criteria evolutionary approach, which overcomes some of the practical difficulties that personnel schedulers in hospitals often face.

When applying evolutionary algorithms to difficult real-world problems, the fitness function routinely needs evaluating for a very high number of intermediary cases. The paper is concerned with real-world nurse rostering problems with highly constrained resources. We consider a particular approach, which allows for a quick evaluation and is general enough to deal with other kinds of resource planning problems with time-related constraints. The model developed for this approach handles the constraints in a modular way and the addition of new constraints is relatively straightforward. Simple constraints (such as those affecting the personal wishes of employees) and global constraints (such as balancing the workload among people) can be formulated easily using this approach. Our approach can also handle very complex time-related constraints as well as conditions that are related to previously planned work. Moreover, it provides clear feedback about violation of constraints. The approach has been implemented successfully in a nurse rostering program entitled "Plane" which is used in hospitals all over Belgium. It can tackle a high number of specific and modifiable constraints of a very different nature. The benefits from this approach (in terms of software requirements) are small memory use and a computationally simple, single evaluation function allowing for the simultaneous rostering of several hospital wards at the same time.