Decision trees are accurate and interpretable models that can predict classes or values based on features of a data point, but they are vulnerable to small changes to the data that greatly affect the predictions. Previous work has resulted in methods that can find robust optimal classification trees or robust regression trees, but not robust optimal regression trees. Computing optimal decision trees is already NP-hard, and continuous prediction values make robust regression trees more complex than robust classification trees. We analyze in further detail why this is a difficult problem to solve. We introduce ForTree, a method that uses exhaustive search with pruning to find robust optimal regression trees out of a set of trees with limited prediction values. It evaluates all possible configurations of trees with this limitation and stores the tree with the highest adversarial accuracy. We also introduce the partial accuracy as a lower bound for pruning, which we use to speed up the runtime of ForTree. Our experiments show that ForTree achieves up to 1.23 times the adversarial accuracy of state-of-the-art robust regression tree methods, but that the runtime of ForTree is greatly sensitive to the amount of unique feature values in a dataset. We propose multiple approaches to find robust regression trees with higher adversarial accuracy or within less runtime in the future.

Normative modeling is a promising statistical framework in clinical neuroscience that characterizes individual deviations from population-based reference distributions. While traditional approaches focus on univariate modeling of individual brain measures, multivariate normative modeling using deep generative models, particularly Variational Autoencoders (VAE), has recently emerged as a powerful alternative. These models capture high-dimensional dependencies across brain features and enable the detection of subtle deviations that are difficult to observe with univariate methods. However, current multivariate approaches lack systematic evaluation of covariate modeling methods and remain underexplored in handling batch effects and clinical applicability. For this work, an experimental platform is developed to train and evaluate VAE-based multivariate normative models. The models are trained on structural MRI data from the Generation R Study and the Healthy Brain Network, incorporating key covariates such as age, sex, and acquisition site. A wide set of covariate modeling methods is systematically evaluated in terms of reconstruction quality, latent space covariate invariance, and alignment with normative priors. This work also investigates whether VAE-based multivariate normative models can accommodate batch effects, such as site variation, and compares them to traditional data harmonization techniques, like ComBat. Finally, the model is applied to the clinically relevant task of brain age estimation. The results show that incorporating covariate modeling into the VAE architecture can significantly improve covariate invariance. When examining the influence of batch effects, covariate modeling methods and ComBat data harmonization both reduce site-related information in low-dimensional latent spaces. However, when the latent dimensionality increases, ComBat data harmonization outperforms all covariate modeling methods. In a proof-of-concept application, the model was successfully extended for brain age estimation, capturing age-related deviations while preserving an age-invariant latent space. Altogether, these findings show the potential of VAE-based multivariate normative models for clinical neuroscience applications.

Anomaly detection is a cornerstone of data analysis, aimed at identifying patterns that deviate from expected behaviour. However, conventional anomaly detection methods often fail to differentiate between actionable anomalies and those that, while statistically anomalous, are irrelevant to the user’s goals. Such uninteresting anomalies, originating from distinct, unrelated distributions, contribute to false alarms and resource inefficiencies, particularly in critical domains like cybersecurity and healthcare. This thesis proposes a novel, adaptive framework that retrains anomaly detection models to exclude uninteresting anomalies from being flagged, thereby improving the relevance of detected anomalies.

Central to this framework is the use of the Synthetic Minority Over-sampling Technique for Nominal and Continuous (SMOTE-NC) to artificially augment datasets with labelled uninteresting anomalies, transforming them into regular data. The framework also incorporates user feedback to iteratively refine model performance during deployment. A key finding of this research is that the effectiveness of the framework is highly dependent on the degree of distinguishability between interesting and uninteresting anomalies. Specifically, when the two types of anomalies are clearly distinct in terms of their statistical and categorical features, the framework achieves a significant reduction in false positives without adversely affecting the detection rate of actionable anomalies or the accuracy of regular data.

The framework was evaluated using four state-of-the-art anomaly detection models: Isolation Forest, One-Class Support Vector Machines, Autoencoders, and Variational Autoencoders. It was then tested using two datasets: one in cybersecurity, involving various attack types, and another in healthcare, where anomalies represent different diagnostic categories. The results demonstrate that the framework can effectively identify and suppress uninteresting anomalies, achieving over 90\% accuracy in classifying these cases as regular data under favourable conditions. Notably, when the distinction between interesting and uninteresting anomalies was substantial, the models retained their ability to detect actionable anomalies, with minimal degradation in overall accuracy. Furthermore, it was seen that a significant number of samples are needed to be able to successfully represent the uninteresting anomalies class, a minimum of around 50. When not using the framework, it takes many more samples for the algorithm to successfully no longer detect these uninteresting anomalies as anomalies. This class then needs to make up a significant amount of the training data, so depending on the size of the training data set, this can mean thousands of samples. Gathering around 50 samples poses no problem for the framework, as it is meant to be especially relevant when we have too many uninteresting anomalies, where it is constantly giving false alerts, so there is usually a sufficient number of samples available.

Graphs and richer property graphs are common models for real-world data. We typically run algorithms on such data to extract meaningful information. Using domainspecific programming languages (DSLs) is a common approach to expressing such algorithms, contrasting to general-purpose programming languages and declarative graph query languages. On one hand, algorithms in general-purpose languages are verbose and conceptually far removed from from the algorithm theory, as is the case for some community detection algorithms in DSLs. On the other hand, the DSLs that are available are insufficient to express all common graph analysis algorithms. The Green-Marl Intermediate Representation (GMIR) is such a graph algorithm DSL. As it has been built from the ground up, it only provides a minimal feature to support the algorithms it initially needed to support, similar to how other DSLs are developed. This specifically prevents frontier exploration algorithms and community detection algorithms to be expressed, such as Dijkstra’s shortest path and the Louvain clustering method. We use GMIR as a vehicle to introduce new domain-specific abstractions for algorithmic graph processing, targeting those algorithms. We evaluate our abstractions by implementing them in the commercial GMIR compiler, which we then use to compile various new algorithms to existing commercial graph processing platforms. This shows that we have successfully enabled more graph algorithms to be expressed in GMIR, even though there are still many algorithms that remain inexpressible.

The Shunt Routing Problem (SRP) is an important logistic problem at nearly every railway station. It is a subproblem of an even bigger train scheduling problem, the Train Unit Shunting Problem (TUSP). The objective of SRP is to schedule conflict-free routes between the platforms and the yards, for currently non-operational trains that have completed their current journeys and have not yet commenced the next one.
We developed a Constraint Programming (CP) model for the Shunt Routing Problem at NS. The model is intended to replace the current algorithm for constructing the initial solution for the Local Search, addressing the TUSP at NS. The model incorporates all essential feasibility requirements and produces conflict-free solutions, in contrast to its forerunner. Moreover, it can be applied to any instance and station layout.

Initially, the model exhibited an average performance of 7-8 minutes on a real-life instance at Enkhuizen station. We managed to enhance the model and reduce the computation time to less than a second. The key improvements were achieved by changing the solver search strategy, imposing additional search guidelines, or further restricting the domains of influential variables. During experimentation, an optimized second version of the model was proposed.
The evaluation undoubtedly confirmed that it outperforms the first version.

Both versions of the model, without any additional enhancements, perform exceptionally well on a second real-life instance at Amersfoort station, solving it in milliseconds. Even with a considerable number of additional routes, the performance of the second version remained reasonable, with a computation time of 18 seconds.

A final experiment revealed the remarkable performance of Gecode, achieving computation time in milliseconds with the second version of the model implemented for Enkhuizen in MiniZinc. This performance is an order of magnitude faster compared to the default performance of Google OR-Tools on Enkhuizen with the second version.

The process of using formal verification, in order to ensure that a piece of software meets it functional requirements consists of three main steps: designing a model of the given piece of software, translating the functional requirements, which the piece of software must satisfy, into properties of said model and verifying that the model satisfies those properties. Traditionally, regardless of whether the piece of software is developed based on a predesigned model or the piece of software is developed first and its model is designed after that, the piece of software and its model are two separate entities. Therefore, aside from checking that the model satisfies its properties, it must also be verified that the model accurately represents the given piece of software. While this task may initially seem simple, it gets progressively more difficult, as the piece of software becomes more complex. And, if it turns out that the model is not accurate, then the entire formal verification process is invalid, since it does not provide any guarantees about the actual piece of software. In this thesis we present a solution to this problem: a way of modelling sequential effectful programs, such that the resulting models can be directly translated into runnable programs, thereby guaranteeing the models' accuracy. We achieve this by using algebraic effects, in order to model sequential effectful programs as instances of the coinductive free monad, that could then be translated into runnable pieces of software by applying the necessary effect handlers. Furthermore, we demonstrate that it is possible to express functional requirements as properties of such models using the first-order modal μ-calculus, a fixed-point dynamic logic which has previously been used to reason about labelled transition systems (e.g. in mCRL2).

Survival analysis predicts survival functions that give the probability of survival until a given time. Many applications of survival analysis involve health care, which requires interpretability of the models used to predict the survival function. Provably optimal decision trees have shown to be an interpretable alternative to so-called black box models. However, these algorithms often choose estimators that are fast, yet not necessarily most accurate. Moreover, the objective functions of optimal decision tree algorithms tend to make (possibly incorrect) assumptions about the survival function. In this paper, we tackle both problems. We implement the iterative Breslow estimator in an already existing optimal survival tree algorithm in order to iteratively improve the Nelson-Aalen estimator. This approach has great potential, as we show by using it on artificial datasets, but we do not see an improvement in accuracy on real world data. To eliminate the assumptions made by the objective function, we implement the Integrated Brier Score objective, which causes a significant improvement on training accuracy. However, we see no improvement on out-of-sample accuracy

In this paper, we combine image denoising and classification, aiming to enhance human perception of noisy images captured by edge devices, like security cameras. Since edge devices have little computational power, we also optimize for efficiency by proposing a novel architecture that integrates the two tasks. Additionally, we alter a Neural Architecture Search (NAS) method, which searches for classifiers, to search for the integrated model while optimizing for a target latency, classification accuracy, and denoising performance. Our NAS architectures outperform our manually designed alternatives in both denoising and classification, offering a significant improvement to human perception. Moreover, our approach empowers users to construct architectures tailored to domains like medical imaging, surveillance systems, and industrial inspections.

Decision trees are integral to machine learning, with their robustness being a critical measure of effectiveness against adversarial data manipulations. Despite advancements in algorithms, current solutions are either optimal but lack scalability or scale well, but do not guarrantee optimality. This paper presents a novel adaptation of the Murtree algorithm to address these challenges in the pursuit of optimal robust decision trees. We introduce a new method for modeling an adversary as a network flow problem, and provide a dynamic programming approach to solve optimal robust decision trees beyond a depth of two. The performance of our proposed algorithm is compared with bruteforce solutions across varying decision tree depths, feature numbers, and data sizes. This research contributes a significant advancement towards obtaining efficient and effective solutions for optimal robust decision trees, potentially setting a new performance benchmark in this area.

The goal of quantum application scheduling is to enable the execution of applications on a quantum network. As the final step in the application scheduling process, program scheduling locally schedules execution of blocks of instructions on each node by defining so-called node schedules. In this thesis, we present a formal definition of program scheduling and propose success metrics to evaluate the quality of node schedules. We implement program scheduling using the framework of Resource-Constrained Project Scheduling Problem (RCPSP) and and simulate the execution of node schedules. By evaluating the performance of program scheduling on datasets with diverse quantum applications including quantum key distribution and blind quantum computing, we observe that heuristic-driven approaches achieve comparable results to optimal program scheduling while requiring fewer computational resources. Our work offers valuable insights into the translation of classical scheduling problems into the quantum domain, contributing to the advancement of quantum application scheduling.

Accurate and trustworthy short-term traffic prediction is crucial in the modern world for the comfort of drivers and decision-makers as it is used to improve the performance of traffic management systems, lessen congestion, increase safety, and shorten journey times. It is possible to discover useful information for network transportation planning, such as forecasting demand, finding bottlenecks, and prioritizing infrastructure improvements, by concentrating on network-wide traffic prediction.

Scholars have developed a variety of methods that can be generally divided into model-based and data-based methods in order to accurately predict network-wide traffic. However, while studies have demonstrated the capability of deep learning methods, particularly convolutional neural networks (CNNs), in predicting traffic states, the complex nonlinear spatial and temporal traffic characteristics, the time-consuming model creation and training, and the unexplained methodology and predictions continue to pose challenges to the task.

This thesis seeks to address these issues by analyzing how deep neural networks identify spatiotemporal traffic patterns for network-wide traffic predictions. To this end, a hybrid CNN-RNN model utilizing a pretrained Inception ResNet v2 feature extractor and a long short-term memory encoder-decoder is constructed to forecast network traffic speeds. A pretrained Inception ResNet v2-based image classifier is built based on the predictions to identify traffic patterns, and Grad-CAM is used to explore how the model identifies them. A freeway network in Amsterdam, Netherlands, is used as a case study.

While it is expected that the hybrid CNN-RNN model can give comparable performance to the state-of-the-art methods, e.g. the DGCN proposed by Li et al., results indicate that it cannot fully capture the
dynamic characteristics of the traffic, nor can it accurately provide predictions. The image classifier failed to identify the distinct traffic patterns as well, despite Grad-CAM's success in indicating locations with rapid changes of values.

Overall, the findings highlight the influence of inductive bias on deep learning models, and the importance of fine-tuning and model-data compatibility. Although further research is required, the conclusions are still beneficial to make informed decisions when choosing appropriate models for future network-wide traffic speed prediction tasks.

Quantum networks offer more capabilities than classical networks. For example, quantum networks can solve certain problems faster than classical networks and they can even solve problems which cannot be solved with classical networks. One well-known quantum network application is blind quantum computing (BQC). In a BQC application a client node sends a computation to a server node in the network. The server node performs this computation without knowing the details about the actual input or computation being performed and returns the result of the computation to the client node. Quantum applications are often repeated many times, due to randomness that is involved in the result of executing a quantum application. When a server node performs BQC repeatedly with multiple client nodes, there follows an interesting problem how all corresponding instructions can be scheduled for the server optimally, given that certain types of instructions referred to as entanglement instructions can only be scheduled at given moments by a so called network schedule. One classical metric used to assess the quality of a schedule is makespan, which is the time that it takes to complete all instructions. A quantum oriented metric involved is success probability, which indicates what fraction of executions yield a desired result when repeatedly executing an application. In this thesis, an experimental demonstration is given of the use of constraint programming (CP) for the scheduling of instructions of quantum network applications. This demonstration focuses on scheduling instructions that the server node should execute when performing BQC repeatedly with a small number of client nodes at the same time. Different CP models are presented that assign start times to tasks that the server node should execute. By comparing the CP models to a baseline scheduler that schedules tasks as soon as possible, it was found that CP can be used to reduce the makespan when BQC is performed by the server node with multiple clients at the same time, while preserving a similar success probability. A main drawback that followed from the CP approach is scalability. Future work is to be done on studying how CP can be used for larger quantum networks.

The superoptimizer STOKE has previously been shown to be effective at optimizing programs containing floating-point numbers. The STOKE optimizer obtains these results by running a stochastic search over the set of all programs and selecting the best-optimized one. This study aims to find more clearly what floating-point programs STOKE optimizes particularly well and for which ones it fails to find significant rewrites. To answer the research question, STOKE and GCC optimized multiple small programs, and I compared these on execution speed. The results showed numerous cases where STOKE failed to obtain a better optimization than GCC. The results suggest that for specific floating-point functions, there exist limitations in both the test case generator and the STOKE search algorithm that prevent it from finding good optimizations. The findings of this paper suggest further research on the STOKEs test case generator to improve its performance.

STOKE is one of the Superoptimizers which are programs that given a function and a set of instructions of a processor, traverse through a space of programs that compute a given function and try to find the optimal usually in terms of execution speed or size of the binary. Authors of STOKE make some extraordinary claims. They suggest that it is able to produce programs that are multiple times faster than programs without any optimization, and programs which are at least as efficient as programs produced by gcc -O3 and sometimes expert handwritten assembly. The goal of this paper is to check these claims. In this paper classes of programs that STOKE may handle particularly well and any class of programs that stochastic optimization might not be able to handle will be identified. We conclude from the experiments described in this paper that STOKE is able to fulfill that statement in some cases. The searching algorithm of STOKE is not always able to find programs that are at least as efficient as programs optimized by gcc -O3. STOKE works particularly well in programs where a lot consecutive logical and mathematical operations are calculating (e.g. counting bits). It is often not that successful with programs containing loops where it sometimes can’t find a solution at all.

Superoptimization is the idea of creating the most optimal program possible from a given input program. Equality saturation is a method of superoptimization using rewrite rules and e-graphs. A rewrite rule defines a piece of code that can be rewritten as another part while keeping equal behavior. This is added to an e-graph, a data structure which is able to express a lot of equal programs efficiently using e-nodes and e-classes. Egg is a general equality saturation superoptimizer developed in Rust, which has been the basis of multiple extensions. This research first aimed to validate claims made by the creators of egg which stated that rebuilding improved equality saturation. Secondly, the research aimed to evaluate the performance of egg when supplying a different amount of rewrite rules. The research found that egg indeed does improve equality saturation, with an 88× speedup for a part of the algorithm as claimed by the creators, but a claim of 21× overall speedup is an overestimate, as an overall speedup of between 16.4× and 17.4× was achieved. The second part shows that providing egg with extra unused rewrite rules slows the algorithm down, although the slowdown seems to decrease when the size of the program increases. The second part also tried to draw a conclusion on adding rewrite rules which will be applied indirectly via multiple other rewrite rules, called implied rewrite rules. Two tests indicated a speedup, but another indicated a slowdown. This means it is unknown if adding implied rewrite rules is beneficial, as no general conclusion could be drawn. Therefore, egg seems to benefit from removing unused rewrite rules, and might benefit from adding implied rewrite rules.

Modern compilers exploit syntax \& semantics to optimize input programs.
Often such optimization rules are arduous to get right and the output is not guaranteed to be globally optimal.
Superoptimizers take a different approach to this problem by traversing the program space.
This study focuses on Souper, a synthesizing superoptimizer which makes use of an enhanced counter-example-guided inductive synthesis loop to find optimizations.
We first detail the working mechanism of the superoptimizer and its components, then we explain our attempts at reproducing the results mentioned by Souper's authors.
Finally, we give three program classes each exercising different aspects of the superoptimizer and how these are useful in gaining insight into Souper's optimization capabilities and use cases.

Explainable artificial intelligence has in recent years allowed us to investigate how many machine learning methods are creating its predictions. This is especially useful in scenarios where the goal is not to predict a variable, but to explain what influences that variable. However, the methods that have been created thus far do not focus on specific domains and only give scientific relations between variables. In the case of a production process, there exist a multitude of related variables, constrained in different ways, thus requiring a more sophisticated method than those which are universally applicable. The target of this research is a bottle filling machine at a large carbonated drink manufacturer, of which a great amount of data has been stored. The product quality, in this case the amount of CO2 in the filled bottles, is subject to high amounts of fluctuation, leading to a lot of waste. To further contextualize the problem of bottle filling, an artificial dataset is created to serve as a basis for visualization and evaluation. Using literature on carbonated drink filling, multiple hypotheses were then formulated, independently from the thesis company, as a target for the evaluation process. To address the problem of determining what factors influence bottle CO2, a methodology is proposed which aims to provide explainable quality prediction of production process output, while using available domain knowledge to increase the plausibility of explanations. The methodology makes use of counterfactual explanations for tree ensembles and process state forecasting to show how a process state can be changed to yield better product quality. Evaluation on the artificial and real datasets show that the methodology is able to effectively predict the amount of CO2 in a bottle, while giving changes to the current process state which improve the product quality. It is also shown that the results produced by the methodology are in line with the formulated hypotheses. Bottle CO2 is influenced greatly by temperature changes in the filler and these temperature changes are caused by flow of cooled lemonade through the process. As these flows are dependent on the filling speed, irregular filling is suspected to be the root cause for the bottle CO2 fluctuations.

In general, costs are an important aspect long before the construction of a civil project starts. In the conceptual phase, which is the first phase of a civil construction project, little cost information is available, and the cost estimate is at that stage of project development less accurate than when the project is almost completed. When a cost estimate is made with a conventional method, such as SSK, in the conceptual phase of a civil construction project, the Association for the Advancement of Cost Engineering, AACE, argues that the error of a cost estimate compared to the real price can be 15-50%. The lower accuracy in the conceptual phase is caused by several obstacles: a lack of estimating experience, lack of information, and a method that cannot calculate an accurate cost estimate. Besides, the conventional approach is time-consuming. Machine learning models can overcome these obstacles. This research is initiated by a practical problem within the company Witteveen+Bos. Witteveen+Bos uses a conventional approach for cost estimates and wants to improve the accuracy and calculation time of cost estimates of road bridges in the conceptual phase of a project. This research aims to improve the cost estimates of bridges in the conceptual phase of bridge projects by use of the machine learning model called FALCON. This model is already successful applied in the field of cost estimates for construction project types. Improvement that should be realized in the reduction of the calculation time from hours to minutes. Besides the research aims to reduce the maximum deviation of estimates for road bridge projects to 30%. The FALCON model is not the only model to solve an estimation problem. Standard models, suitable for estimation problems, are multiple linear regression, K nearest neighbors (KNN), and decision trees. The results show that the average absolute deviation is 34% for the KNN model, 36% for the decision tree regression model, 57% for the multiple linear regression model, and 24% for the FALCON model. All 4 models are able to calculate results within a couple of minutes. FALCON is the most accurate model The error of the individual predictions of the FALCON model roughly corresponds to the bandwidth of the AACE (15-50%) for the conceptual phase of a project. The validation of the FALCON model is realized through interviews with cost estimators of Witteveen+Bos. These interviews showed that the realized results meet the expectations of the interviewees. Besides, the interviewees are willing to implement the model in practice. In the end, it must be concluded that the FALCON model can calculate a cost estimate, of bridge projects in the conceptual phase, more quickly, and with a comparable accuracy level as with conventional methods that are used today. For future research, it is recommended to use a larger dataset that has less variation. The used dataset consists of 39 bridge projects. Besides, it is recommended to use international standards for data structuring instead of national standards.

A low blood pressure (hypotension, as mean arterial pressure < 65 mmHg) in patients on the intensive care unit (ICU) is associated with adverse outcomes and death. Proactive treatment with the use of a predictive alarm could improve patient outcome. The Hypotension Prediction Index (HPI) is a machinelearning algorithm that uses arterial blood pressure waveforms to calculate the probability of impending hypotension. Prior to clinical implementation, the HPI model needs to be validated. In previously published validation protocols of the HPI, possible sources of bias were identified. Therefore, the primary objectives were to assess HPI performance on the ICU population by using a clinically relevant validation protocol and to evaluate the differences between previous protocols. Secondary objectives included evaluation of subgroup performance and the effect of individual validation protocol settings on the subsequent results. The three applied validation protocols used conceptually different methods to classify predictions (e.g. as a true or false alarm). The primary forward sliding window (FSW) protocol labels each single prediction based on hypotension occurrence thereafter. The forward tumbling window (FTW) groups predictions in nonoverlapping time windows to only classify the window based on hypotension occurrence thereafter. The backward (BW) protocol labels the onsets of hypotension based on alarm occurrence at ’t’ minutes prior to onset, hence ’backward’ in time. Identical metrics were used to quantify performance. For secondary analyses the FSW protocol was used. Performance for the FSW protocol was reduced compared to the FTW and BW protocol. Using the FDAapproved alarm settings for FSW, FTW and BW (t=10min) protocols, sensitivity was 0.59, 1.00 and 0.83, respectively. Positive predictive values were 0.41. 0.83 and 1.00, respectively. For the FSW protocol the median [IQR] timetohypotension was 3.3 [1.0 to 7.3] min, for an alarm defined as the last of consecutive alarms prior to hypotension. Reducing the minimal mean arterial pressure in the definition of nonhypotension from 75 to 65 mmHg reduced the area under the precision recall curve from 0.82 to 0.31. Omission of a washout period of 30 min increased the positive predictive value from 0.41 to 0.64. This thesis demonstrates the importance of validation methodology and the generalizability of the Hypotension Prediction Index to the intensive care unit population. The definition of nonhypotension and a washout period strongly influenced the results. Overall, the results demonstrate the ability of the HPI to predict hemodynamic instability in ICU patients. Therefore, validation results support the introduction of the HPI to the ICU for clinical use. However, the optimal alarm threshold and clinical benefit remain to be evaluated in future clinical studies.

In the field of cooperative multi-agent pathfinding (MAPF) the optimal set of non-conflicting paths must be found for a set of agents in a graph. The addition of waypoints to this problem (MAPFW) gives rise to the possibility of more complex applications, such as in vehicle routing, aviation, computer games or robotics. Yet no algorithms have been proposed that can provide optimal solutions efficiently in practice. Starting with an established algorithm for multi-agent pathfinding, A* with operator decomposition and independence detection, this paper provides an extension to find optimal results when waypoints are present that the agents need to visit. This is achieved by altering the heuristic to make use of a solver of an adapted version of the traveling salesperson problem, to calculate the shortest path to visit all the waypoints for each agent individually. It is then empirically shown that this algorithm can solve problem instances of decent sizes, and it is compared to another algorithms that were developed at the same time based by others based on different pre-existing MAPF solvers. While the extension of A* is less performant than alternatives, the difference in performance can be small depending on the type of problem. Together with the relative ease of implementation, this means that A* can be an effective algorithm to optimally solve multi-agent pathfinding problems with waypoints. Additionally, the extension techniques used to adapt A* to MAPFW can also be useful to other algorithms that utilise A* in the context of waypoints.