The Gene-pool Optimal Mixing EA (GOMEA) family of EAs offers a specific means to exploit problem-specific knowledge through linkage learning, i.e., inter-variable dependency detection, expressed using subsets of variables, that should undergo joint variation. Such knowledge can be exploited if faster fitness evaluations are possible when only a few variables are changed in a solution, enabling large speed-ups. The recent-most version of Real-Valued GOMEA (RV-GOMEA) can learn a conditional linkage model during optimization using fitness-based linkage learning, enabling fine-grained dependency exploitation in learning and sampling a Gaussian distribution. However, while the most efficient Gaussian-based EAs, like NES and CMA-ES, employ incremental learning of the Gaussian distribution rather than performing full re-estimation every generation, the recent-most RV-GOMEA version does not employ such incremental learning. In this paper, we therefore study whether incremental distribution estimation can lead to efficiency enhancements of RV-GOMEA. We consider various benchmark problems with varying degrees of overlapping dependencies. We find that, compared to RV-GOMEA and VKD-CMA-ES, the required number of evaluations to reach high-quality solutions can be reduced by a factor of up to 1.5 if population sizes are tuned problem-specifically, while a reduction by a factor of 2–3 can be achieved with generic population-sizing guidelines.

The publisher regrets that one of the authors is missing in the PDF and web version of the article. Namely, Anton Bouter, who is affiliated with the Centrum Wiskunde & Informatica as described above in this erratum. In table 1, a space is missing after the character “<” in the line `Cervix -> Sigmoid' in column `Sparing criteria'. In table 3, the `%' signs in first column (DVI) should also be in subscript, similar to how it is written in the first column of Table 4. The supplementary material should state that needle contribution is limited to up to 40% of the total given dwell time (in applicator and needles). Lastly, the article should be seen as a research article and the authors would like to be cited as “L.R.M. Dickhoff and R.J. Scholman et al”.

The publisher would like to apologise for any inconvenience caused.

PURPOSE: Without a clear definition of an optimal treatment plan, no optimization model can be perfect. Therefore, instead of automatically finding a single “optimal” plan, finding multiple, yet different near-optimal plans, can be an insightful approach to support radiation oncologists in finding the plan they are looking for. METHODS AND MATERIALS: BRIGHT is a flexible AI-based optimization method for brachytherapy treatment planning that has already been shown capable of finding high-quality plans that trade-off target volume coverage and healthy tissue sparing. We leverage the flexibility of BRIGHT to find plans with similar dose-volume criteria, yet different dose distributions. We further describe extensions that facilitate fast plan adaptation should planning aims need to be adjusted, and straightforwardly allow incorporating hospital-specific aims besides standard protocols. RESULTS: Results are obtained for prostate (n = 12) and cervix brachytherapy (n = 36). We demonstrate the possible differences in dose distribution for optimized plans with equal dose-volume criteria. We furthermore demonstrate that adding hospital-specific aims enables adhering to hospital-specific practice while still being able to automatically create cervix plans that more often satisfy the EMBRACE-II protocol than clinical practice. Finally, we illustrate the feasibility of fast plan adaptation. CONCLUSIONS: Methods such as BRIGHT enable new ways to construct high-quality treatment plans for brachytherapy while offering new insights by making explicit the options one has. In particular, it becomes possible to present to radiation oncologists a manageable set of alternative plans that, from an optimization perspective are equally good, yet differ in terms of coverage-sparing trade-offs and shape of the dose distribution.

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.