Uncrowded Hypervolume-Based Multiobjective Optimization with Gene-Pool Optimal Mixing.

Domination-based multiobjective (MO) evolutionary algorithms (EAs) are today arguably the most frequently used type of MOEA. These methods, however, stagnate when the majority of the population becomes nondominated, preventing further convergence to the Pareto set. Hypervolume-based MO optimization has shown promising results to overcome this. Direct use of the hypervolume, however, results in no selection pressure for dominated solutions. The recently introduced Sofomore framework overcomes this by solving multiple interleaved single-objective dynamic problems that iteratively improve a single approximation set, based on the uncrowded hypervolume improvement (UHVI). It thereby however loses many advantages of population-based MO optimization, such as handling multimodality. Here, we reformulate the UHVI as a quality measure for approximation sets, called the uncrowded hypervolume (UHV), which can be used to directly solve MO optimization problems with a single-objective optimizer. We use the state-of-the-art gene-pool optimal mixing evolutionary algorithm (GOMEA) that is capable of efficiently exploiting the intrinsically available grey-box properties of this problem. The resulting algorithm, UHV-GOMEA, is compared with Sofomore equipped with GOMEA, and the domination-based MO-GOMEA. In doing so, we investigate in which scenarios either domination-based or hypervolume-based methods are preferred. Finally, we construct a simple hybrid approach that combines MO-GOMEA with UHV-GOMEA and outperforms both.

Improving Model-Based Genetic Programming for Symbolic Regression of Small Expressions.

The Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) is a model-based EA framework that has been shown to perform well in several domains, including Genetic Programming (GP). Differently from traditional EAs where variation acts blindly, GOMEA learns a model of interdependencies within the genotype, that is, the linkage, to estimate what patterns to propagate. In this article, we study the role of Linkage Learning (LL) performed by GOMEA in Symbolic Regression (SR). We show that the non-uniformity in the distribution of the genotype in GP populations negatively biases LL, and propose a method to correct for this. We also propose approaches to improve LL when ephemeral random constants are used. Furthermore, we adapt a scheme of interleaving runs to alleviate the burden of tuning the population size, a crucial parameter for LL, to SR. We run experiments on 10 real-world datasets, enforcing a strict limitation on solution size, to enable interpretability. We find that the new LL method outperforms the standard one, and that GOMEA outperforms both traditional and semantic GP. We also find that the small solutions evolved by GOMEA are competitive with tuned decision trees, making GOMEA a promising new approach to SR.

Surrogate-free machine learning-based organ dose reconstruction for pediatric abdominal radiotherapy.

To study radiotherapy-related adverse effects, detailed dose information (3D distribution) is needed for accurate dose-effect modeling. For childhood cancer survivors who underwent radiotherapy in the pre-CT era, only 2D radiographs were acquired, thus 3D dose distributions must be reconstructed from limited information. State-of-the-art methods achieve this by using 3D surrogate anatomies. These can however lack personalization and lead to coarse reconstructions. We present and validate a surrogate-free dose reconstruction method based on Machine Learning (ML). Abdominal planning CTs (n = 142) of recently-treated childhood cancer patients were gathered, their organs at risk were segmented, and 300 artificial Wilms' tumor plans were sampled automatically. Each artificial plan was automatically emulated on the 142 CTs, resulting in 42,600 3D dose distributions from which dose-volume metrics were derived. Anatomical features were extracted from digitally reconstructed radiographs simulated from the CTs to resemble historical radiographs. Further, patient and radiotherapy plan features typically available from historical treatment records were collected. An evolutionary ML algorithm was then used to link features to dose-volume metrics. Besides 5-fold cross validation, a further evaluation was done on an independent dataset of five CTs each associated with two clinical plans. Cross-validation resulted in mean absolute errors ≤ 0.6 Gy for organs completely inside or outside the field. For organs positioned at the edge of the field, mean absolute errors ≤ 1.7 Gy for [Formula: see text], ≤ 2.9 Gy for [Formula: see text], and ≤ 13% for [Formula: see text] and [Formula: see text], were obtained, without systematic bias. Similar results were found for the independent dataset. To conclude, we proposed a novel organ dose reconstruction method that uses ML models to predict dose-volume metric values given patient and plan features. Our approach is not only accurate, but also efficient, as the setup of a surrogate is no longer needed.

Automatic bi-objective parameter tuning for inverse planning of high-dose-rate prostate brachytherapy.

We present an automatic bi-objective parameter-tuning approach for inverse planning methods for high-dose-rate prostate brachytherapy, which aims to overcome the difficult and time-consuming manual parameter tuning that is currently required to obtain patient-specific high-quality treatment plans. We modelled treatment planning as a bi-objective optimization problem, in which dose-volume-based planning criteria related to target coverage are explicitly separated from organ-sparing criteria. When this model is optimized, a large set of high-quality plans with different trade-offs can be obtained. This set can be visualized as an insightful patient-specific trade-off curve. In our parameter-tuning approach, the parameters of inverse planning methods are automatically tuned, aimed to maximize the two objectives of the bi-objective planning model. By generating trade-off curves for different inverse planning methods, their maximally achievable plan quality can be insightfully compared. Automatic parameter tuning furthermore allows to construct standard parameter sets (class solutions) representing different trade-offs in a principled way, which can be directly used in current clinical practice. In this work, we considered the inverse planning methods IPSA and HIPO. Thirty-nine previously treated prostate cancer patients were included. We compared automatic parameter tuning, random parameter sampling, and the maximally achievable plan quality obtained by directly optimizing the bi-objective planning model with the state-of-the-art optimization software GOMEA. We showed that for each patient, a set of plans with a wide range of trade-offs could be obtained using automatic parameter tuning for both IPSA and HIPO. By tuning HIPO, better trade-offs were obtained than by tuning IPSA. For most patients, automatic tuning of HIPO resulted in plans close to the maximally achievable plan quality obtained by optimizing the bi-objective planning model directly. Automatic parameter tuning was shown to improve plan quality significantly compared to random parameter sampling. Finally, from the automatically-tuned plans, three class solutions were successfully constructed representing different trade-offs.