This thesis utilizes Evolutionary Algorithms (EAs) within the BRIGHT framework for developing breast cancer brachytherapy treatment plans. We use expert knowledge and state-of-the-art EAs to formulate treatment planning as a multi-objective optimization problem whose solutions can be applied to actual patients. We propose four novel 2- and 3-objective formulations of this problem, which we implement within BRIGHT and empirically validate against anonymized data from 9 real-world patient cases. We demonstrate that all four formulations, under reasonable computational and time budgets, are capable of generating plans that match or exceed the properties of reference treatment plans. To verify the clinical relevance of our contributions, we rely on the expertise of a clinical expert who assesses whether the generated plans can be used in clinical treatment planning. The results of our empirical analysis show that 17 of the 18 plans presented to the expert are clinically acceptable and of immediate value to practitioners within the field of breast brachytherapy today.

Cervical cancer affects about half a million women globally every year. The treatment of cervical cancer with the aim of healing mainly consists of surgery, radiation treatment, or a combination of radiation treatment with chemotherapy or hyperthermia. Radiation treatment is a type of treatment wherein a high dose of ionizing radiation is used to kill the tumor cells. The radiation dose is usually delivered in the form of External Beam Radiation Treatment (EBRT) with a linear accelerator followed by internal radiation treatment (brachytherapy) during which a small radioactive source is passed through an applicator and needles that are placed temporarily nearby the cervix. EBRT typically spans several weeks with daily sessions (often referred to as fractions), whereas brachytherapy typically consists of three or four fractions based on one to three implantations. The aim of the radiation treatment is to provide effective radiation to kill the tumor cells while sparing the nearby healthy tissue or Organs At Risk (OARs) as much as possible. This is achieved by treatment planning following the contouring of target volumes and OARs, on medical imaging scans, which typically are Computed Tomography (CT) and/orMagnetic Resonance Imaging (MRI)....@en

Counterfactual explanations are a useful tool to explain trained models. They are based on counterfactual thoughts, which are a natural human thought process that helps us reason about the past. When applied to trained models they show how to make minimal changes to a data point in order to obtain a desired output.
Most methods find these counterfactuals by optimizing a set of objectives. Previously these objectives were often combined into a loss function using an aggregation operator. This operator implicitly decides the priority between the objectives, but this ordering is not always in line with the user’s preferences.
To mitigate this the Multi-Objective Counterfactuals (MOC) method was introduced. MOC turns counterfactual generation into a multi-objective optimization problem and presents the user with a diverse set of counterfactuals that have different trade-offs for the objectives. It optimizes the set of objectives with an evolutionary algorithm called Nondominated Sorting Genetic Algorithm II.
In this thesis we optimize this problem using Multi-Objective Real-Valued Gene-Pool Optimal Mixing Evolutionary Algorithm, which is a different evolutionary algorithm. We present a single-modal method and two multi-modal methods. We compare the performance of our methods to a counterfactual generation method named Diverse Counterfactual Explanations (DiCE), which focusses on feasibility and diversity within a set of generated counterfactuals. Additionally, we also present a visualization tool for sets of counterfactuals.
The single-modal method generates counterfactuals that are realistic, but do not consistently perform well in other areas. The first multi-modal method generates diverse sets of counterfactuals, but overall performs worse. The second multi-modal method generates counterfactuals that perform similarly to the single-modal method, but are more diverse.

Machine learning (ML) models are used increasingly in high-stakes areas such as health and finance because of their strong performance. However, having good performance in metrics such as accuracy or the f1 score alone is not all that is important as trust is also essential in these areas. TalkToModel is a system that addresses this challenge, using a large language model (LLM), by letting the users interact with their models through natural language. However, this system only allows a user to ask black-box questions. Another way to achieve trust is through models that are constructed with interpretability in mind that a human can understand. Genetic programming (GP) models are such models that have the potential to be interpreted. This thesis investigates if GP models can be made even more interpretable
using TalkToModel. To do this an enhanced version of TalkToModel called TalkToGP is created with three main contributions: 1) Integration of GP Models into TalkToModel, 2) the ability to ask GP modelspecific questions and 3) the ability to do a comparative analysis between multiple GP models. This system is built using the feedback from GP users who gave insights on their experience with GP as well as their wishes for this system. In the end, the system is evaluated by GP users in an experiment. The experiments showed that the enhanced version of TalkToModel shows a strong indication that it increases the interpretability of GP models. This means the system could be a useful tool for anyone working with GP models.

Mixed-integer optimization problems, incorporating both discrete and continuous variables, present unique challenges across various domains such as computer science, finance, logistics, and healthcare. Evolutionary Algorithms (EAs) have emerged as powerful optimization techniques capable of tackling such complex problems in either the discrete or continuous domain. Model-based EAs, integrating machine learning techniques, have further improved the efficiency and scalability of these algorithms. The first algorithm to combine discrete and continuous model-based EAs is the Mixed-Integer Hybrid Evolutionary Algorithm (MIHEA). Despite its potential, MIHEA remains relatively underutilized in research endeavours. This thesis seeks to bridge this gap in research by applying the algorithm to a novel context: structure learning of Bayesian Networks (BNs).

BNs offer a transparent framework for probabilistic reasoning, making them well-suited for various applications. However, learning the structure and discretizations of BNs from data is a challenging task. It is not uncommon for the datasets to contain values of continuous nodes as well. Assuming no normality, these nodes in the data need to be discretized, since BNs are designed for discrete data. The optimal discretizations of these nodes depend on the structure of the BN, meaning that the discretization optimization should happen simultaneously with the structure learning. MIHEA holds promise for addressing this challenge by leveraging its mixed-integer optimization capabilities.

The investigation performed in this thesis starts with a reproduction study. The description of the code for MIHEA is shown to be inconsistent with the experiment results, which prompts a reproduction study resulting in a version of the code that more accurately fits the results.
Subsequently, MIHEA is applied to the structure learning of BNs, where discrete variables represent network structure and continuous variables encode discretizations of continuous nodes. Several solution representations are explored. The experiments show that MIHEA achieves similar or better performance than the state-of-the-art DBN-GOMEA approach on the task of recreating randomly generated BNs from data, at the cost of increased execution time.
These results demonstrate the potential of model-based mixed-integer EAs, particularly MIHEA, for BN structure learning from continuous data. The findings encourage further exploration and utilization of mixed-integer EAs in solving (real-world) problems involving BNs and continuous data.

With the advances in General-Purpose computing on Graphics Processing Units (GPGPU), it is worthwhile to explore whether other areas in the field of Artificial Intelligence (AI) can reap the benefits. One such area is Evolutionary Algorithms (EAs), which—among other processes—involves the repetitive exchange of genes among individuals. This repetitive nature aligns with our intuition for parallel optimisation, precisely what GPGPU is designed for. Currently, the state-of-the-art approach in EA is known as Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA), which capitalises on the information embedded within the population by computing the linkage between genes across the entire population. However, when it comes to parallelising the exchange of complete linkage sets, particularly in the context of our specific problem of interest, the challenge becomes more intricate.

In the case of our problem, known as Max-cut, there are dependencies between genes that must be considered when constructing parallel sets of linkage sets, referred to as packages. We propose three solutions: contamination, revision, and association. Contamination fully utilises parallel capabilities but deviates from the concept of linkage sets. Revision constructs the linkage sets as described by GOMEA, but keeps the dependencies between linkage sets within a package untouched. Association on the other hand attempts to resolve the dependencies by generating a dependency graph to create the set of packages.

From our experiments, we can conclude that parallel acceleration using GPGPU is roughly on par with—and sometimes even outperforms—its non-parallelised counterpart. Out of the three solutions, it is evident that association demonstrates the most promising performance profile in terms of approaching the optimal solution. However, the performance falls significantly short of matching the capabilities exhibited by GOMEA. Furthermore, all of the solutions face a significant burden when evaluating the fitness for each exchanged linkage set. An option to consider as an extension to the current setup is known as partial evaluation, although the performance exhibited by contamination implies that simplicity could be the key to success. Further exploration of the acceleration process using widely employed parallel operators—such as those found in linear algebra—has the potential to yield valuable insights for enhancing performance.

Deformable Image Registration (DIR) is a medical imaging process involving the spatial alignment of two or more images using a transformation model that can account for non-rigid deformations. B-spline-based transformation models have emerged as a common approach to express such spatial alignments. However, without additional measures, their flexibility can lead to physically implausible deformations. This flexibility has motivated the inclusion of penalty terms to improve the smoothness and regularity of the transformation. Determining an appropriate weight for this penalty term is difficult, as each registration problem requires a different trade-off between this penalty term and the quality of the transformed image.

Gradient-based methods are commonly used as optimization methods in medical image registration toolboxes due to their computational efficiency and fast convergence rates. However, due to their gradient-based approach, they may converge prematurely in local minima. In this thesis, we investigate the efficacy of a gradient-less alternative: the Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (RV-GOMEA), a population-based method that can exploit the problem structure of optimization problems through explicit mappings of dependencies between problem variables. To improve the computational efficiency of RV-GOMEA when applied to DIR, we show how to apply partial evaluations for common image similarity metrics and penalty terms when using B-spline-based transformation models.

We test RV-GOMEA on a synthetic registration problem to better understand its performance in the context of DIR. Based on our findings, we propose several methods that hybridize RV-GOMEA with a gradient-based method and impose specific constraints on the B-spline-based transformation model. We validate the performance of these methods on clinical registration problems and find that RV-GOMEA with a gradient-based local search operator can provide significant benefits over purely gradient-based methods for DIR problems. Additionally, placing specific constraints on the transformation model can increase the regularity of transformations without requiring a penalty term.

The Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (RV-GOMEA) is a state-of-the-art algorithm for single-objective, real-valued optimization. As many practical applications are inherently constrained, evolutionary algorithms are equipped with constraint handling techniques to allow optimizing constrained problems. The approach currently in use with RV-GOMEA prioritizes solution feasibility over the objective value in all cases, pressuring the algorithm to find feasible solutions. However, this can be inefficient if the constrained optimum is located at the constraint boundary, as search is discouraged from exploring the search space close to infeasible solutions.

In this thesis, several well-known constraint handling techniques from literature are adapted for use with RV-GOMEA and evaluated on different benchmark problems, identifying the strengths and limitations of the various techniques. Furthermore, the inefficiency of the current technique is investigated in detail. Based on the insights gained, modifications to the existing techniques are proposed, leading to promising preliminary results.

Even if a Multi-modal Multi-Objective Evolutionary Algorithm (MMOEA) is designed to find all locally optimal approximation sets of a Multi-modal Multi-objective Optimization Problem (MMOP), there is a risk that the found approximation sets are not smoothly navigable because the solutions belong to various niches, which reduces the insight for decision makers. Moreover, when the multi-modality of MMOPs increases, this risk grows and the trackability of finding all locally optimal approximation sets decreases. One example where this issue occurs is that of High-Dose-Rate (HDR) brachytherapy for prostate cancer. In HDR brachytherapy a treatment plan is to be optimized that irradiates a tumour with a prescribed dose, whilst sparing all of the healthy organs surrounding the tumour. The radiation is administered through a radioactive source that is stopped at certain dwell positions within a set of hollow catheters that have been implanted into the patient. In a treatment plan, each of the dwell positions is given a specific dwell time for which the source is kept at that location in order to irradiate the surrounding tissue.
To tackle the navigability issues, two new MMOEAs are proposed: Multi-Modal Bézier Evolutionary Algorithm (MM-BezEA) and Set Bézier Evolutionary Algorithm (Set-BezEA). Both MMOEAs produce approximation sets that cover individual niches and exhibit inherent decision-space smoothness as they are parameterized by Bézier curves. MM-BezEA combines the concepts behind the recently introduced BezEA and MO-HillVallEA to find all locally optimal approximation sets. Set-BezEA employs a novel multi-objective fitness function formulation to find limited numbers of diverse, locally optimal, approximation sets for MMOPs of high multi-modality.
Both algorithms, but especially MM-BezEA, are found to outperform the MMOEAs MO_Ring_PSO_SCD and MO-HillVallEA on MMOPs of moderate multi-modality with linear Pareto sets. Moreover, for MMOPs of high multi-modality, Set-BezEA is found to indeed be able to produce high-quality approximation sets, each pertaining to a single niche. Set-BezEA is also shown to be comparable to the current BRIGHT approach used in the Amsterdam UMC for the optimization of treatment plans for prostate cancer HDR brachytherapy, which opens the way for it to be introduced in the clinical practice in the future.

Neural networks (NNs) have, in recent years, become a major part of modern pattern recognition, and both theoretical and applied research evolve at an astounding pace. NNs are usually trained via gradient descent (GD), but research has shown that GD is not always capable of training very small networks. As a result, networks trained via GD are often significantly larger than necessary, demanding more computing power and energy to evaluate, and thereby hampering adoption on lower- power devices. This thesis investigates whether evolutionary algorithms (EAs) can successfully train NNs and if these networks can be smaller than those required by GD. Four algorithms, namely the GD-based Adam, Adam with cold restarts, and the EAs GOMEA and BIPOP-CMA-ES, were used to train various configurations of multilayer perceptrons (MLPs) with one hidden layer for the Exclusive-OR (XOR) problem. Their relative performance was gauged by comparing the rates at which each algorithm attained an acceptable loss for a given number of hidden nodes. The main findings are that EAs could find smaller ReLU-activated networks than GD could, while, oppositely, the GD could generally find smaller networks for sigmoid- activated networks. However, GOMEA in particular was able to successfully train XOR networks using the highly discrete Heaviside activation function, whereas GD could not due gradient erasure. Problem-specific knowledge in the form of a soft symmetry breaking constraint was found to be effective to increase success rates in a limited number of cases. These findings indicate that using EAs is a viable strategy for training NNs, yielding smaller, and therefore more efficient networks than those trained via GD, provided that the network topology is suitable for the chosen EA. This opens up future research into, including but not limited to, the many ways EAs can be scaled up to training larger NNs, hybridization with GD, and niche network topologies.

Solutions to many real-life optimization problems take a long time to evaluate. This limits the number of solutions we can evaluate. When optimizing with an Evolutionary Algorithm (EA) a frequently used approach is to approximate the objective using a surrogate function, replacing the time-consuming real evaluation. This surrogate model is combined with a so-called acquisition function, to select promising candidate solutions. The acquisition function balances the trade-off between exploration of parameter space and the exploitation of the surrogate. These candidates are subject to an expensive evaluation with the true objective function and are used to update the surrogate model. Iteratively applying this process can effectively optimize global optimization problems. In this work, we propose a new multi-objective optimization algorithm with inverse distance weighting as surrogate function, which we call IDW-SAEA (inverse distance weighting surrogate assisted evolutionary algorithm). We introduce a new objective to the optimization problem to improve exploration and reduce the complexity of the acquisition function. We show this algorithm is competitive with state-of-the-art kriging-based surrogate-assisted EAs on certain benchmark problems. Additionally, we use the algorithm to optimize a practical problem: a Finite Element Method simulation of the cervix region with applications in radiotherapy for cervical cancer.

Deep Neural Networks (DNNs) have the potential to make various clinical procedures more time-efficient by automating medical image segmentation; largely due to their strong, in some cases human-level, performance. The design of the best possible medical image segmentation DNN, however, is task-specific. Neural Architecture Search (NAS), i.e., the automation of neural network design, has been shown to have the capability to outperform manually designed networks. However, the existing NAS methods for medical image segmentation have explored a quite limited range of types of DNN architectures that can be discovered, and, more importantly, do not evaluate the accuracy of performance estimation methods.

In this thesis, various performance estimation methods for DNNs are analysed for medical image segmentation tasks. Due to the use of different metrics, small datasets, and inter-physician variability, DNN performance values are susceptible to considerable noise. Through experiments on multiple datasets, it is shown that performance estimation needs to be more elaborate than proposed in previous literature on NAS for medical image segmentation. Only then can the noise induced by the problem be overcome. Based on evaluations of NAS performance with different levels of noise, a method is put forward to evaluate this noise, such that a more informed decision on performance estimation can be made.

The second contribution of this thesis, is the proposal of a novel NAS search space for medical image segmentation networks. This search space combines the strength of a generalised encoder-decoder structure, well known from U-Net, with network blocks that have been proven to have a strong performance in image classification tasks. The search is performed by looking for the best topology of the network, and simultaneously searching the configuration of each cell. This allows for interactions between topology- and cell-level attributes to be found. Experiments were performed on two publicly available datasets. The networks discovered by the proposed NAS method perform better than well-known handcrafted segmentation networks, and outperform networks found with other NAS approaches that perform only topology search, and topology-level search followed by cell-level search.

Finally, three search algorithms are compared for different performance estimation methods on a realistic clinical medical image segmentation task. The results show that the performance of these algorithms is very similar in noisy environments for initial runs, and show deterioration of performance for all algorithms when correlation with the validation performance values are low. This supports the findings that not adapting performance estimation to the task at hand will lead to poor NAS performance, no matter the chosen search algorithm.

In this thesis BRIGHT, a multi-objective evolutionary algorithm for the creation of treatment plans for high-dose rate brachytherapy for prostate cancer, is extended with a new objective to mitigate the formation of high dose contiguous volumes, i.e. hotspots. Multiple new objectives are tested on their performance to reduce hotspots, while minimally impacting existing objectives.

Computer vision tasks, like supervised image classification, are effectively tackled by convolutional neural networks, provided that the architecture, which defines the structure of the network, is set correctly. Neural Architecture Search (NAS) is a relatively young and increasingly popular field that is concerned with automatically optimizing the architecture of neural networks. Previously known work shows that even though a recent trend has been to develop increasingly complex search strategies for NAS, several search strategies do not significantly outperform simple approaches like randomly sampling from the search space on single-objective NAS tasks. Additionally, proper ablation studies are often missing. Therefore, it is currently uncertain at best which mechanisms are key for an algorithm to have to achieve excellent NAS performance. In the first part of this thesis, Local Search (LS) and a differently biased form of random search, are proposed for multi-objective (MO) NAS. The multi-objective version of NAS is studied less and understanding the trade-off between between multiple objectives for architectures is arguably more interesting. We find that very simple algorithms can achieve search performance close to that of state-of-the-art evolutionary algorithms (EAs), while outperforming plain random search. Additionally, we find that the quality of the set of architectures found by LS is similar to the those found by the EAs, if compared with respect to test accuracy. Nevertheless, from the compared search strategies the Multi-Objective Gene-pool Optimal Mixing Evolutionary Algorithm (MO-GOMEA), a state-of-the-art model-based EA, achieves the best performance. In the second part of this thesis, it is explored which mechanisms are essential for MO-GOMEA to achieve an excellent search performance for NAS spaces. We find that the automatic population-sizing scheme of MO-GOMEA offers a welcome anytime-performance, but objective space clustering has only a small beneficial impact. The number of clusters can be set arbitrarily. Special (extreme) clusters that optimize for one objective only can be enabled to the practitioner’s preference, resulting in different search behaviors. The improvement in performance gained by automatically detecting and exploiting dependencies within architectures is limited: this model-based aspect of MO-GOMEA seems only helpful for finding highly accurate networks.

The recently introduced Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (RV-GOMEA) has been shown to be among the state-of-the-art for solving grey-box optimization problems where partial evaluations can be leveraged. A core strength is its ability to effectively exploit the linkage structure of a problem. For many real-world optimization problems, the linkage structure is unknown a priori and has to be learned online. Previously published work on RV-GOMEA however demonstrated excellent scalability only when the linkage structure is pre-specified appropriately. The commonly used mutual-information-based metric that is used to a learn linkage structure online in the discrete version of GOMEA did not show as effective in the real-valued domain and did not result in similarly excellent results, especially in a black-box setting.
In this thesis, the strengths of RV-GOMEA are combined with a new fitness-based linkage learning approach that is inspired by differential grouping but reduces its computational overhead by an order of magnitude for problems with fewer interactions. The resulting new version of RV-GOMEA achieves scalability similar to when a predefined linkage model is used. Additionally, for the first time, the EDA AMaLGaM, that served as a foundation for RV-GOMEA is outperformed in a black-box setting, where partial evaluations cannot be leveraged.

Model-based evolutionary algorithms (MBEAs) are praised for their broad applicability to black-box optimization problems. In practical applications however, they are mostly used to repeatedly optimize different instances of a single problem class, a setting in which specialized algorithms generally perform better. In this paper, we introduce the concept of a new type of MBEA that can automatically specialize its behavior to a given problem class using tabula rasa self-learning. For this, reinforcement learning (RL) is a naturally fitting paradigm. A proof-of-principle framework, called SL-ENDA, based on estimation of normal distribution algorithms in combination with reinforcement learning is defined. SL-ENDA uses an RL-agent to decide upon the next population mean while approaching the rest of the algorithm as the environment. A comparison of SL-ENDA to AMaLGaM and CMA-ES on unimodal noiseless functions shows mostly comparable performance and scalability to the broadly used and carefully manually crafted algorithms. This result, in combination with the inherent potential of self-learning model-based evolutionary algorithms with regard to specialization, opens the door to a new research direction with great potential impact on the field of model-based evolutionary algorithms.

Cancer is a deadly disease which occurs when cells divide uncontrollably. In the battle against cancer, many types of treatments exist to preferably cure the disease. Brachytherapy is one such type of treatment, a form of radiotherapy where the radiation source is internally placed through implanted catheters. A research team consisting of researchers from Centrum Wiskunde \& Informatica (CWI) and Academisch Medisch Centrum (AMC) have developed a solution that generates a wide range of near-optimal brachytherapy treatment plans for treating prostate cancer, which they have named the brachy automated treatment-planning system (BATS). However, the generated plans can currently not be viewed in any tangible way. Physicians must be able to oversee and look into the generated plans before they can act upon it. In addition, the physician must be able to compare multiple treatment plans and must be able to select the most optimal treatment plan.We have developed a front-end solution that works in tandem with BATS that provides the necessary features to create a working environment suited to the needs of the research team. Multiple plans can be viewed and compared through visualization and plan properties. Additionally, the application has DICOM compatibility and can operate on Windows and Linux operating systems.While not all requirements are met, we are satisfied with the resulting application. Recommendations for future iterations include improved navigation through icon-based buttons, and more control options through hotkeys and the like. Additional 3D treatment plan visualizations and multi-plane views would provide opportunities for 3D planning.