Even if a Multi-modal Multi-Objective Evolutionary Algorithm (MMOEA) is designed to find solutions well spread over all locally optimal approximation sets of a Multi-modal Multi-objective Optimization Problem (MMOP), there is a risk that the found set of solutions is not smoothly navigable because the solutions belong to various niches, reducing the insight for decision makers. To tackle this issue, a new MMOEAs is proposed: the Multi-Modal Bézier Evolutionary Algorithm (MM-BezEA), which produces 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. When benchmarked against the MMOEAs MO_Ring_PSO_SCD and MO-HillVallEA on MMOPs with linear Pareto sets, MM-BezEA was found to perform best in terms of best hypervolume.

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Deep learning algorithms have become the golden standard for segmentation of medical imaging data. In most works, the variability and heterogeneity of real clinical data is acknowledged to still be a problem. One way to automatically overcome this is to capture and exploit this variation explicitly. Here, we propose an approach that improves on our previous work in this area and explain how it potentially can improve clinical acceptance of (semi-)automatic segmentation methods. In contrast to a standard neural network that produces one segmentation, we propose to use a multi-path Unet network that produces multiple segmentation variants, presumably corresponding to the variations that reside in the dataset. Different paths of the network are trained on disjoint data subsets. Because a priori it may be unclear what variations exist in the data, the subsets should be automatically determined. This is achieved by searching for the best data partitioning with an evolutionary optimization algorithm. Because each network path can become more specialized when trained on a more homogeneous data subset, better segmentation quality can be achieved. In practical usage, various automatically produced segmentations can be presented to a medical expert, from which the preferred segmentation can be selected. In experiments with a real clinical dataset of CT scans with prostate segmentations, our approach provides an improvement of several percentage points in terms of Dice and surface Dice coefficients compared to when all network paths are trained on all training data. Noticeably, the largest improvement occurs in the upper part of the prostate that is known to be most prone to inter-observer segmentation variation.

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To achieve excellent performance with modern neural networks, having the right network architecture is important. Neural Architecture Search (NAS) concerns the automatic discovery of task-specific network architectures. Modern NAS approaches leverage super-networks whose subnetworks encode candidate neural network architectures. These subnetworks can be trained simultaneously, removing the need to train each network from scratch, thereby increasing the efficiency of NAS. A recent method called Neural Architecture Transfer (NAT) further improves the efficiency of NAS for computer vision tasks by using a multi-objective evolutionary algorithm to find high-quality subnetworks of a supernetwork pretrained on ImageNet. Building upon NAT, we introduce ENCAS - - Evolutionary Neural Cascade Search. ENCAS can be used to search over multiple pretrained supernetworks to achieve a trade-off front of cascades of different neural network architectures, maximizing accuracy while minimizing FLOPs count. We test ENCAS on common computer vision benchmarks (CIFAR-10, CIFAR-100, ImageNet) and achieve Pareto dominance over previous state-of-the-art NAS models up to 1.5 GFLOPs. Additionally, applying ENCAS to a pool of 518 publicly available ImageNet classifiers leads to Pareto dominance in all computation regimes and to increasing the maximum accuracy from 88.6% to 89.0%, accompanied by an 18% decrease in computation effort from 362 to 296 GFLOPs.

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Deep Neural Networks (DNNs) have the potential for making various clinical procedures more time-efficient by automating medical image segmentation. Due to their strong, in some cases human-level, performance, they have become the standard approach in this field. The design of the best possible medical image segmentation DNNs, 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 for various tasks. However, the existing NAS methods for medical image segmentation have explored a quite limited range of types of DNN architectures that can be discovered. In this work, we propose 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 proven to have a strong performance in image classification tasks. The search is performed by looking for the best topology of multiple cells simultaneously with the configuration of each cell within, allowing for interactions between topology and cell-level attributes. From experiments on two publicly available datasets, we find that the networks discovered by our proposed NAS method have better performance 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.

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Genetic programming (GP) is one of the best approaches today to discover symbolic regression models. To find models that trade off accuracy and complexity, the non-dominated sorting genetic algorithm II (NSGA-II) is widely used. Unfortunately, it has been shown that NSGA-II can be inefficient: in early generations, low-complexity models over-replicate and take over most of the population. Consequently, studies have proposed different approaches to promote diversity. Here, we study the root of this problem, in order to design a superior approach. We find that the over-replication of low complexity-models is due to a lack of evolvability, i.e., the inability to produce offspring with improved accuracy. We therefore extend NSGA-II to track, over time, the evolvability of models of different levels of complexity. With this information, we limit how many models of each complexity level are allowed to survive the generation. We compare this new version of NSGA-II, evoNSGA-II, with the use of seven existing multi-objective GP approaches on ten widely-used data sets, and find that evoNSGA-II is equal or superior to using these approaches in almost all comparisons. Furthermore, our results confirm that evoNSGA-II behaves as intended: models that are more evolvable form the majority of the population. Code: https://github.com/dzhliu/evoNSGA-II

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We propose a novel surrogate-assisted Evolutionary Algorithm for solving expensive combinatorial optimization problems. We integrate a surrogate model, which is used for fitness value estimation, into a state-of-the-art P3-like variant of the Gene-Pool Optimal Mixing Algorithm (GOMEA) and adapt the resulting algorithm for solving non-binary combinatorial problems. We test the proposed algorithm on an ensemble learning problem. Ensembling several models is a common Machine Learning technique to achieve better performance. We consider ensembles of several models trained on disjoint subsets of a dataset. Finding the best dataset partitioning is naturally a combinatorial non-binary optimization problem. Fitness function evaluations can be extremely expensive if complex models, such as Deep Neural Networks, are used as learners in an ensemble. Therefore, the number of fitness function evaluations is typically limited, necessitating expensive optimization techniques. In our experiments we use five classification datasets from the OpenML-CC18 benchmark and Support-vector Machines as learners in an ensemble. The proposed algorithm demonstrates better performance than alternative approaches, including Bayesian optimization algorithms. It manages to find better solutions using just several thousand fitness function evaluations for an ensemble learning problem with up to 500 variables.

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Anatomical landmark correspondences in medical images can provide additional guidance information for the alignment of two images, which, in turn, is crucial for many medical applications. However, manual landmark annotation is labor-intensive. Therefore, we propose an end-to-end deep learning approach to automatically detect landmark correspondences in pairs of two-dimensional (2D) images. Our approach consists of a Siamese neural network, which is trained to identify salient locations in images as landmarks and predict matching probabilities for landmark pairs from two different images. We trained our approach on 2D transverse slices from 168 lower abdominal Computed Tomography (CT) scans. We tested the approach on 22,206 pairs of 2D slices with varying levels of intensity, affine, and elastic transformations. The proposed approach finds an average of 639, 466, and 370 landmark matches per image pair for intensity, affine, and elastic transformations, respectively, with spatial matching errors of at most 1 mm. Further, more than 99% of the landmark pairs are within a spatial matching error of 2 mm, 4 mm, and 8 mm for image pairs with intensity, affine, and elastic transformations, respectively. To investigate the utility of our developed approach in a clinical setting, we also tested our approach on pairs of transverse slices selected from follow-up CT scans of three patients. Visual inspection of the results revealed landmark matches in both bony anatomical regions as well as in soft tissues lacking prominent intensity gradients.

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Feature construction can substantially improve the accuracy of Machine Learning (ML) algorithms. Genetic Programming (GP) has been proven to be effective at this task by evolving non-linear combinations of input features. GP additionally has the potential to improve ML explainability since explicit expressions are evolved. Yet, in most GP works the complexity of evolved features is not explicitly bound or minimized though this is arguably key for explainability. In this article, we assess to what extent GP still performs favorably at feature construction when constructing features that are (1) Of small-enough number, to enable visualization of the behavior of the ML model; (2) Of small-enough size, to enable interpretability of the features themselves; (3) Of sufficient informative power, to retain or even improve the performance of the ML algorithm. We consider a simple feature construction scheme using three different GP algorithms, as well as random search, to evolve features for five ML algorithms, including support vector machines and random forest. Our results on 21 datasets pertaining to classification and regression problems show that constructing only two compact features can be sufficient to rival the use of the entire original feature set. We further find that a modern GP algorithm, GP-GOMEA, performs best overall. These results, combined with examples that we provide of readable constructed features and of 2D visualizations of ML behavior, lead us to positively conclude that GP-based feature construction still works well when explicitly searching for compact features, making it extremely helpful to explain ML models.

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There has recently been great progress in automatic segmentation of medical images with deep learning algorithms. In most works observer variation is acknowledged to be a problem as it makes training data heterogeneous but so far no attempts have been made to explicitly capture this variation. Here, we propose an approach capable of mimicking different styles of segmentation, which potentially can improve quality and clinical acceptance of automatic segmentation methods. In this work, instead of training one neural network on all available data, we train several neural networks on subgroups of data belonging to different segmentation variations separately. Because a priori it may be unclear what styles of segmentation exist in the data and because different styles do not necessarily map one-on-one to different observers, the subgroups should be automatically determined. We achieve this by searching for the best data partition with a genetic algorithm. Therefore, each network can learn a specific style of segmentation from grouped training data. We provide proof of principle results for open-sourced prostate segmentation MRI data with simulated observer variations. Our approach provides an improvement of up to 23% (depending on simulated variations) in terms of Dice and surface Dice coefficients compared to one network trained on all data.

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Often, real-world problems are of the gray-box type. It has been shown that the Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (RV-GOMEA) is in principle capable of exploiting such a Gray-Box Optimization (GBO) setting using linkage models that capture dependencies between problem variables, resulting in excellent performance and scalability on both benchmark and real-world problems that allow for partial evaluations. However, linkage models proposed for RV-GOMEA so far cannot explicitly capture overlapping dependencies. Consequently, performance degrades if such dependencies exist. In this paper, we therefore introduce various ways of using conditional linkage models in RV-GOMEA. Their use is compared to that of non-conditional models, and to VkD-CMA, whose performance is among the state of the art, on various benchmark problems with overlapping dependencies. We find that RV-GOMEA with conditional linkage models achieves the best scalability on most problems, with conditional models leading to similar or better performance than non-conditional models. We conclude that the introduction of conditional linkage models to RV-GOMEA is an important contribution, as it expands the set of problems for which optimization in a GBO setting results in substantially improved performance and scalability. In future work, conditional linkage models may prove to benefit the optimization of real-world problems.

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Performing large-scale three-dimensional radiation dose reconstruction for patients requires a large amount of manual work. We present an image processing-based pipeline to automatically reconstruct radiation dose. The pipeline was designed for childhood cancer survivors that received abdominal radiotherapy with anterior-to-posterior and posterior-to-anterior field set-up. First, anatomical landmarks are automatically identified on two-dimensional radiographs. Second, these landmarks are used to derive parameters to emulate the geometry of the plan on a surrogate computed tomography. Finally, the plan is emulated and used as input for dose calculation. For qualitative evaluation, 100 cases of automatic and manual plan emulations were assessed by two experienced radiation dosimetrists in a blinded comparison. The two radiation dosimetrists approved 100%/100% and 92%/91% of the automatic/manual plan emulations, respectively. Similar approval rates of 100% and 94% hold when the automatic pipeline is applied on another 50 cases. Further, quantitative comparisons resulted in on average <5 mm difference in plan isocenter/borders, and <0.9 Gy in organ mean dose (prescribed dose: 14.4 Gy) calculated from the automatic and manual plan emulations. No statistically significant difference in terms of dose reconstruction accuracy was found for most organs at risk. Ultimately, our automatic pipeline results are of sufficient quality to enable effortless scaling of dose reconstruction data generation.@en

The advent of Machine Learning (ML) is proving extremely beneficial in many healthcare applications. In pediatric oncology, retrospective studies that investigate the relationship between treatment and late adverse effects still rely on simple heuristics. To capture the effects of radiation treatment, treatment plans are typically simulated on virtual surrogates of patient anatomy called phantoms. Currently, phantoms are built to represent categories of patients based on reasonable yet simple criteria. This often results in phantoms that are too generic to accurately represent individual anatomies. We present a novel approach that combines imaging data and ML to build individualized phantoms automatically. We design a pipeline that, given features of patients treated in the pre-3D planning era when only 2D radiographs were available, as well as a database of 3D Computed Tomography (CT) imaging with organ segmentations, uses ML to predict how to assemble a patient-specific phantom. Using 60 abdominal CTs of pediatric patients between 2 to 6 years of age, we find that our approach delivers significantly more representative phantoms compared to using current phantom building criteria, in terms of shape and location of two considered organs (liver and spleen), and shape of the abdomen. Furthermore, as interpretability is often central to trust ML models in medical contexts, among other ML algorithms we consider the Gene-pool Optimal Mixing Evolutionary Algorithm for Genetic Programming (GP-GOMEA), that learns readable mathematical expression models. We find that the readability of its output does not compromise prediction performance as GP-GOMEA delivered the best performing models.@en

Purpose: Current phantoms used for the dose reconstruction of long-term childhood cancer survivors lack individualization. We design a method to predict highly individualized abdominal three-dimensional (3-D) phantoms automatically. Approach: We train machine learning (ML) models to map (2-D) patient features to 3-D organ-at-risk (OAR) metrics upon a database of 60 pediatric abdominal computed tomographies with liver and spleen segmentations. Next, we use the models in an automatic pipeline that outputs a personalized phantom given the patient's features, by assembling 3-D imaging from the database. A step to improve phantom realism (i.e., avoid OAR overlap) is included. We compare five ML algorithms, in terms of predicting OAR left-right (LR), anterior-posterior (AP), inferior-superior (IS) positions, and surface Dice-Sørensen coefficient (sDSC). Furthermore, two existing human-designed phantom construction criteria and two additional control methods are investigated for comparison. Results: Different ML algorithms result in similar test mean absolute errors: ∼8 mm for liver LR, IS, and spleen AP, IS; ∼5 mm for liver AP and spleen LR; ∼80 % for abdomen sDSC; and ∼60 % to 65% for liver and spleen sDSC. One ML algorithm (GP-GOMEA) significantly performs the best for 6/9 metrics. The control methods and the human-designed criteria in particular perform generally worse, sometimes substantially (+5-mm error for spleen IS,-10 % sDSC for liver). The automatic step to improve realism generally results in limited metric accuracy loss, but fails in one case (out of 60). Conclusion: Our ML-based pipeline leads to phantoms that are significantly and substantially more individualized than currently used human-designed criteria.

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3D dose reconstruction for radiotherapy (RT) is the estimation of the 3D radiation dose distribution patients received during RT. Big dose reconstruction data is needed to accurately model the relationship between the dose and onset of adverse effects, to ultimately gain insights and improve today's treatments. Dose reconstruction is often performed by emulating the original RT plan on a surrogate anatomy for dose estimation. This is especially essential for historically treated patients with long-Term follow-up, as solely 2D radiographs were used for RT planning, and no 3D imaging was acquired for these patients. Performing dose reconstruction for a large group of patients requires a large amount of manual work, where the geometry of the original RT plan is emulated on the surrogate anatomy, by visually comparing the latter with the original 2D radiograph of the patient. This is a labor-intensive process that for practical use needs to be automated. This work presents an image-processing pipeline to automatically emulate plans on surrogate computational tomography (CT) scans. The pipeline was designed for childhood cancer survivors that historically received abdominal RT with anterior-To-posterior and posterior-To-Anterior RT field set-up. First, anatomical landmarks are automatically identified on 2D radiographs. Next, these landmarks are used to derive parameters needed to finally emulate the plan on a surrogate CT. Validation was performed by an experienced RT planner, visually assessing 12 cases of automatic plan emulations. Automatic emulations were approved 11 out of 12 times. This work paves the way to effortless scaling of dose reconstruction data generation.

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Purpose: Bi-objective treatment planning for high-dose-rate prostate brachytherapy is a novel treatment planning method with two separate objectives that represent target coverage and organ-at-risk sparing. In this study, we investigated the feasibility and plan quality of this method by means of a retrospective observer study. Methods and Materials: Current planning sessions were recorded to configure a bi-objective optimization model and to assess its applicability to our clinical practice. Optimization software, GOMEA, was then used to automatically generate a large set of plans with different trade-offs in the two objectives for each of 18 patients treated with high-dose-rate prostate brachytherapy. From this set, five plans per patient were selected for comparison to the clinical plan in terms of satisfaction of planning criteria and in a retrospective observer study. Three brachytherapists were asked to evaluate the blinded plans and select the preferred one. Results: Recordings demonstrated applicability of the bi-objective optimization model to our clinical practice. For 14/18 patients, GOMEA plans satisfied all planning criteria, compared with 4/18 clinical plans. In the observer study, in 53/54 cases, a GOMEA plan was preferred over the clinical plan. When asked for consensus among observers, this ratio was 17/18 patients. Observers highly appreciated the insight gained from comparing multiple plans with different trade-offs simultaneously. Conclusions: The bi-objective optimization model adapted well to our clinical practice. GOMEA plans were considered equal or superior to the clinical plans. In addition, presenting multiple high-quality plans provided novel insight into patient-specific trade-offs.

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We introduce a novel surrogate-assisted Genetic Algorithm (GA) for expensive optimization of problems with discrete categorical variables. Specifically, we leverage the strengths of the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA), a state-of-the-art GA, and, for the first time, propose to use a convolutional neural network (CNN) as a surrogate model. We propose to train the model on pairwise fitness differences to decrease the number of evaluated solutions that is required to achieve adequate surrogate model training. In providing a proof of principle, we consider relatively standard CNNs, and demonstrate that their capacity is already sufficient to accurately learn fitness landscapes of various well-known benchmark functions. The proposed CS-GOMEA is compared with GOMEA and the widely-used Bayesian-optimization-based expensive optimization frameworks SMAC and Hyperopt, in terms of the number of evaluations that is required to achieve the optimum. In our experiments on binary problems with dimensionalities up to 400 variables, CS-GOMEA always found the optimum, whereas SMAC and Hyperopt failed for problem sizes over 16 variables. Moreover, the number of evaluated solutions required by CS-GOMEA to find the optimum was found to scale much better than GOMEA.

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Purpose: To investigate the variation in computed dose-volume (DV) indices for high-dose-rate (HDR) prostate brachytherapy that can result from typical differences in computation settings in treatment planning systems (TPSs). Methods: Five factors were taken into account: number of dose-calculation points, radioactive source description, interpolation between delineated contours, intersections between delineated organ contours, and organ shape at the top and bottom contour using either full or partial slice thickness. Using in-house developed software, the DV indices of the treatment plans of 26 patients were calculated with different settings, and compared to a baseline setting that closely followed the default settings of the TPS used in our medical center. Studied organs were prostate and seminal vesicles, denoted as targets, and bladder, rectum, and urethra, denoted as organs at risk (OARs), which were delineated on MRI scans with a 3.3 mm slice thickness. Results: When sampling a fixed number of points in each organ, in order to achieve a width of the 95% confidence interval over all patients of the DV indices of 1% or less, only 32,000 points had to be sampled per target, but 256,000 points had to be sampled per OAR. For the remaining factors, DV indices changed up to 0.4% for rectum, 1.3% for urethra, and 2.6% for prostate. DV indices of the bladder changed especially if the high-dose-region was (partly) located at the most caudal contour, up to 8.5%, and DV indices of the vesicles changed especially if there were few delineated contours, up to 9.8%, both due to the use of full slice thickness for the top and bottom contour. Conclusions: The values of DV indices used in prostate HDR brachytherapy treatment planning are influenced by the computation settings in a TPS, especially at the most caudal part of the bladder, as well as in the seminal vesicles.

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In retrospective radiation treatment (RT) dosimetry, a surrogate anatomy is often used for patients without 3D CT. To gain insight in what the crucial aspects in a surrogate anatomy are to enable accurate dose reconstruction, we investigated the relation of patient characteristics and internal anatomical features with deviations in reconstructed organ dose using surrogate patient's CT scans. Abdominal CT scans of 35 childhood cancer patients (age: 2.1-5.6 yr; 17 boys, 18 girls) undergoing RT during 2004-2016 were included. Based on whether an intact right or left kidney is present in the CT scan, two groups were formed each containing 24 patients. From each group, four CTs associated with Wilms' tumor RT plans with an anterior-posterior - posterior-anterior field setup were selected as references. For each reference, a 2D digitally reconstructed radiograph was computed from the reference CT to simulate a 2D radiographic image and dose reconstruction was performed on the other CTs in the respective group. Deviations in organ mean dose (DE _mean ) of the reconstructions versus the references were calculated, as were deviations in patient characteristics (i.e. age, height, weight) and in anatomical features including organ volume, location (in 3D), and spatial overlaps. Per reference, the Pearson's correlation coefficient between deviations in DE _mean and patient characteristics/features were studied. Deviation in organ locations and DE _mean for the liver, spleen, and right kidney were moderately correlated (R ²

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Semantic Backpropagation (SB) is a recent technique that promotes effective variation in tree-based genetic programming. The basic idea of SB is to provide information on what output is desirable for a specified tree node, by propagating the desired root-node output back to the specified node using inversions of functions encountered along the way. Variation operators then replace the subtree located at the specified node with a tree for which the output is closest to the desired output, by searching in a pre-computed library. In this paper, we propose two contributions to enhance SB specifically for symbolic regression, by incorporating the principles of Keijzer's Linear Scaling (LS). In particular, we show how SB can be used in synergy with the scaled mean squared error, and we show how LS can be adopted within library search. We test our adaptations using the well-known variation operator Random Desired Operator (RDO), comparing to its baseline implementation, and to traditional crossover and mutation. Our experimental results on real-world datasets show that SB enhanced with LS substantially improves the performance of RDO, resulting in overall the best performance among all tested GP algorithms.

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Purpose: The purpose of this study is to improve upon a recently introduced bi-objective treatment planning method for prostate high-dose-rate (HDR) brachytherapy (BT), both in terms of resulting plan quality and runtime requirements, to the extent that its execution time is clinically acceptable. Methods: Bi-objective treatment planning is done using a state-of-the-art multiobjective evolutionary algorithm, which produces a large number of potential treatment plans with different trade-offs between coverage of the target volumes and sparing organs at risk. A graphics processing unit (GPU) is used for large-scale parallelization of dose calculations and the calculation of the dose-volume (DV) indices of potential treatment plans. Moreover, the objectives of the previously used bi-objective optimization model are modified to produce better results. Results: We applied the GPU-accelerated bi-objective treatment planning method to a set of 18 patients, resulting in a set containing a few hundred potential treatment plans with different trade-offs for each of these patients. Due to accelerations introduced in this article, results previously achieved after 1 hour are now achieved within 30 seconds of optimization. We found plans satisfying the clinical protocol for 15 of 18 patients, whereas this was the case for only 4 of 18 clinical plans. Higher quality treatment plans are obtained when the accuracy of DV index calculation is increased using more dose calculation points, requiring still no more than 3 minutes of optimization for 100 000 points. Conclusions: Large sets of high-quality treatment plans that trade-off coverage and sparing are now achievable within 30 seconds, due to the GPU-acceleration of a previously introduced bi-objective treatment planning method for prostate HDR brachytherapy. Higher quality plans can be achieved when optimizing for 3 minutes, which we still consider to be clinically acceptable. This allows for more insightful treatment plan selection in a clinical setting.

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