When it comes to solving optimization problems with evolutionary algorithms (EAs) in a reliable and scalable manner, detecting and exploiting linkage information, that is, dependencies between variables, can be key. In this paper, we present the latest version of, and propose substantial enhancements to, the gene-pool optimal mixing evolutionary algorithm (GOMEA): an EA explicitly designed to estimate and exploit linkage information. We begin by performing a large-scale search over several GOMEA design choices to understand what matters most and obtain a generally best-performing version of the algorithm. Next, we introduce a novel version of GOMEA, called CGOMEA, where linkage-based variation is further improved by filtering solution mating based on conditional dependencies. We compare our latest version of GOMEA, the newly introduced CGOMEA, and another contending linkage-aware EA, DSMGA-II, in an extensive experimental evaluation, involving a benchmark set of nine black-box problems that can be solved efficiently only if their inherent dependency structure is unveiled and exploited. Finally, in an attempt to make EAs more usable and resilient to parameter choices, we investigate the performance of different automatic population management schemes for GOMEA and CGOMEA, de facto making the EAs parameterless. Our results show that GOMEA and CGOMEA significantly outperform the original GOMEA and DSMGA-II on most problems, setting a new state of the art for the field.

The transformation model is an essential component of any deformable image registration approach. It provides a representation of physical deformations between images, thereby defining the range and realism of registrations that can be found. Two types of transformation models have emerged as popular choices: B-spline models and mesh models. Although both models have been investigated in detail, a direct comparison has not yet been made, since the models are optimized using very different optimization methods in practice. B-spline models are predominantly optimized using gradient-descent methods, while mesh models are typically optimized using finite-element method solvers or evolutionary algorithms. Multi-objective optimization methods, which aim to find a diverse set of high-quality trade-off registrations, are increasingly acknowledged to be important in deformable image registration. Since these methods search for a diverse set of registrations, they can provide a more complete picture of the capabilities of different transformation models, making them suitable for a comparison of models. In this work, we conduct the first direct comparison between B-spline and mesh transformation models, by optimizing both models with the same state-of-the-art multi-objective optimization method, the Multi-Objective Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (MO-RV-GOMEA). The combination with B-spline transformation models, moreover, is novel. We experimentally compare both models on two different registration problems that are both based on pelvic CT scans of cervical cancer patients, featuring large deformations. Our results, on three cervical cancer patients, indicate that the choice of transformation model can have a profound impact on the diversity and quality of achieved registration outcomes.

The recently introduced real-valued gene-pool optimal mixing evolutionary algorthm (RV-GOMEA) has been shown to be among the state of the art for solving gray-box optimization problems where partial evaluations can be leveraged. A core strength is its ability to effectively exploit the linkage structure of a problem, which often is unknown a priori and has to be learned online. Previously published work on RV-GOMEA, however, demonstrated excellent scalability when the linkage structure is prespecified appropriately. A mutual information-based metric to learn linkage structure online, as commonly adopted in EDA's and the original discrete version of the gene-pool optimal mixing evolutionary algorithm, did not lead to similarly excellent results, especially in a black-box setting. In this article, the strengths of RV-GOMEA are combined with a new fitness-based linkage learning approach that is inspired by differential grouping that 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, outperforming also, for the first time, the EDA AMaLGaM upon which it is partially based in a black-box setting where partial evaluations cannot be leveraged.11This article is extended from the MSc thesis of Chantal Olieman, available at https://repository.tudelft.nl/ [24].

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.

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.