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: 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.

We present a pricing method based on Shannon wavelet expansions for early-exercise and discretely-monitored barrier options under exponential Lévy asset dynamics. Shannon wavelets are smooth, and thus approximate the densities that occur in finance well, resulting in exponential convergence. Application of the Fast Fourier Transform yields an efficient implementation and since wavelets give local approximations, the domain boundary errors can be naturally resolved, which is the main improvement over existing methods.