Robust optimization incorporating weekly predicted anatomical CTs in IMPT of nasopharyngeal cancer.

Objective.This study proposes a robust optimization (RO) strategy utilizing virtual CTs (vCTs) predicted by an anatomical model in intensity-modulated proton therapy (IMPT) for nasopharyngeal cancer (NPC).Methods and Materials.For ten NPC patients, vCTs capturing anatomical changes at different treatment weeks were generated using a population average anatomy model. Two RO strategies of a 6 beams IMPT with 3 mm setup uncertainty (SU) and 3% range uncertainty (RU) were compared: conventional robust optimization (cRO) based on a single planning CT (pCT), and anatomical RO incorporating 2 and 3 predicted anatomies (aRO2 and aRO3). The robustness of these plans was assessed by recalculating them on weekly CTs (week 2-7) and extracting the voxel wise-minimum and maximum doses with 1 mm SU and 3% RU (voxmin\voxmax1mm3%).Results.The aRO plans demonstrated improved robustness in high-risk CTV1 and low-risk CTV 2 coverage compared to cRO plans. The weekly evaluation showed a lower plan adaptation rate for aRO3 (40%) vs. cRO (70%). The weekly nominal and voxmax1mm3%doses to OARs, especially spinal cord, are better controlled relative to their baseline doses at week 1 with aRO plans. The accumulated dose analysis showed that CTV1&2 had adequate coverage and serial organs (spinal cord and brainstem) were within their dose tolerances in the voxmin\voxmax1mm3%, respectively.Conclusion.Incorporating predicted weekly CTs from a population based average anatomy model in RO improves week-to-week target dose coverage and reduces false plan adaptations without increasing normal tissue doses. This approach enhances IMPT plan robustness, potentially facilitating reduced SU and further lowering OAR doses.

Effect of breathing phase number on the 4D robust optimization for pancreatic cancer intensity modulated proton therapy.

PURPOSE: Respiratory movement, as one of the main challenges in proton therapy for pancreatic cancer patients, could not only lead to harm to normal tissues but also lead to failure of the tumor control, resulting in irreversible consequences. Including respiratory movements into the plan optimization, i.e. 4D robust optimization, may mitigate the interplay effect. However, 4D robust optimization considering images of all breathing phases is time-consuming and less efficient. This work aims to investigate the effect of the breathing phase number on the 4D robust optimization for pancreatic cancer intensity modulated proton therapy (IMPT) by examining plan quality and computational efficiency. METHODS: A total of 15 pancreatic cancer patients were retrospectively analyzed. In this study, both anterior-fields and posterior-fields plans were created for each patient. For each plan, six four-dimensional (4D) robust treatment planning strategies with different numbers of respiratory phases and one three-dimensional (3D) treatment plan were created. Optimization of the plans were performed on all ten phases (10phase plan), two extreme phases (2phase plan), two extreme phases plus an intermediate state (3phase plan), two extreme phases plus the 3D CT (3Aphase plan), six phases during the exhalation stage (6Exphase plan), six phases during the inhalation stage (6Inphase plan) and 3D Computed Tomography (CT) scan image (3D plan), respectively. 4D dynamic dose (4DDD) was then calculated to access the interplay effect by considering respiratory motion and dynamic beam delivery. Plan quality and dosimetric parameters for the target and organs at risk (OARs) were then analyzed. RESULTS: Compared to the 4D plans, 3D plan performed terribly in terms of target coverage and organs at risk. Target dose in anterior-fields plan varied slightly among all six 4D treatment planning strategies. Both the 6Exphase and 6Inphase plans demonstrated performance that was comparable to the 10phase plan in target coverage, outperforming the other five plans for anterior-fields plan. It's basically the same for the posterior-fields plan. The six strategies showed similar OARs sparing effect for both anterior-fields and posterior-fields plan. Compared with the 10phase plan, the average decline rates of the optimization time of the six plans of 2phase, 3phase, 3Aphase, 6Exphase, 6Inphase, and 3D were 73.26 ± 6.54% vs. 74.48 ± 6.63%, 65.80 ± 7.89% vs. 65.81 ± 9.58%, 54.67 ± 11.52% vs. 65.75 ± 9.58%, 42.14 ± 13.57% vs. 39.63 ± 16.93%, 37.72 ± 11.70% vs. 40.79 ± 13.62% and 75.52 ± 8.21% vs. 80.67 ± 5.62%, respectively (anterior vs. posterior). With the decrease of the number of phases selected for optimization, the decline rates increased, while the other dosimetry parameters generally showed a deterioration trend. CONCLUSION: In this study, a comprehensive evaluation of six 4D robust treatment planning strategies and one 3D treatment planning strategy for pancreatic cancer patients receiving IMPT was performed. The results showed that six 4D robust optimization strategies were comparable in common posterior field therapy. 2phase and 3phase (including 3Aphase) treatment planning strategies could replace the 10phase treatment planning strategy. It should be noted that patients with large motion amplitudes should receive special attention. The dosimetric performance of the 6Exphase and 6Inphase plans closely aligned with that of the 10phase plan in anterior fields. These plans offered a feasible alternative to 10phase treatment planning strategy by reducing optimization time while maintaining dose coverage of the target and protection of OARs. This research provides guidelines to reduce optimization time and improve clinical efficiency for pancreatic cancer IMPT.

Evaluating the Impact of the Level of Robustness in Operating Room Scheduling Problems.

Managing uncertainty in surgery times presents a critical challenge in operating room (OR) scheduling, as it can have a significant impact on patient care and hospital efficiency. Objectives: By incorporating robustness into the decision-making process, we can provide a more reliable and adaptive solution compared to traditional deterministic approaches. Materials and methods: In this paper, we consider a cardinality-constrained robust optimization model for OR scheduling, addressing uncertain surgery durations. By accounting for patient waiting times, urgency levels and delay penalties in the objective function, our model aims to optimise patient-centred outcomes while ensuring operational resilience. However, to achieve an appropriate balance between resilience and robustness cost, the robustness level must be carefully tuned. In this paper, we conduct a comprehensive analysis of the model's performance, assessing its sensitivity to robustness levels and its ability to handle different uncertainty scenarios. Results: Our results show significant improvements in patient outcomes, including reduced waiting times, fewer missed surgeries and improved prioritisation of urgent cases. Key contributions of this research include an evaluation of the representativeness and performance of the patient-centred objective function, a comprehensive analysis of the impact of robustness parameters on OR scheduling performance, and insights into the impact of different robustness levels. Conclusions: This research offers healthcare providers a pathway to increase operational efficiency, improve patient satisfaction, and mitigate the negative effects of uncertainty in OR scheduling.

Clinical advantages of incorporating predicted weekly anatomy in IMPT optimization with reduced setup error.

BACKGROUND: In head and neck (H&N) cancer treatment, a conventional setup error (SE) of 3mm is often used in robust optimization (cRO3mm). However, cRO3mm may lead to excessive radiation doses to organs at risk (OARs) and does not purposefully compensate for interfractional anatomy variations. PURPOSE: This study introduces a method using predicted images from an anatomical model and a reduced 1mm SE uncertainty for robust optimization (aRO1mm), aiming to decrease the dose to OARs without affecting the coverage of the clinical target volume (CTV). METHODS: This retrospective study involved 10 nasopharynx radiotherapy patients. Validation CT scans (vCT) from treatment weeks 1 to 6 were analyzed. A predictive anatomical model, designed to capture the average anatomical changes over time, provided predicted CT images for weeks 1, 3, and 5. We compared three optimization scenarios: (1) aRO1mm, using three predicted images with 1mm setup shift and 3% range uncertainty, (2) cRO3mm, with a robust 3mm setup shift and 3% range uncertainty, and (3) cRO1mm, a robust 1mm setup shift and 3% range uncertainty. The accumulated dose to CTVs and serial organs was evaluated under these uncertainties, while parallel OARs were assessed using the accumulated nominal dose (without errors). RESULTS: The accumulated volume receiving 94% of the prescribed dose (V94) for CTVs in cRO3mm exceeded 98%, meeting the clinical goal. For high-risk CTV, the minimum V94 was 96.44% in aRO1mm and 94.05% in cRO1mm. For low-risk CTV, these values were 97.68% in aRO1mm and 97.15% in cRO1mm. When comparing aRO1mm to cRO3mm on OARs, aRO1mm reduced normal tissue complication probability (NTCP) for grade ≥ $\ge$ 2 xerostomia and dysphagia by averages of 3.67% and 1.54%, respectively. CONCLUSION: aRO1mm lowers the radiation dose to OARs compared to the traditional approach, while maintaining adequate dose coverage on the target area. This method offers an improved strategy for managing uncertainties in radiation therapy planning for H&N cancer, enhancing treatment effectiveness.

Clinical implementation of deep learning robust IMPT planning in oropharyngeal cancer patients: A blinded clinical study.

BACKGROUND AND PURPOSE: This study aimed to evaluate the plan quality of our deep learning-based automated treatment planning method for robustly optimized intensity-modulated proton therapy (IMPT) plans in patients with oropharyngeal carcinoma (OPC). The assessment was conducted through a retrospective and prospective study, blindly comparing manual plans with deep learning plans. MATERIALS AND METHODS: A set of 95 OPC patients was split into training (n = 60), configuration (n = 10), test retrospective study (n = 10), and test prospective study (n = 15). Our deep learning optimization (DLO) method combines IMPT dose prediction using a deep learning model with a robust mimicking optimization algorithm. Dosimetrists manually adjusted the DLO plan for individual patients. In both studies, manual plans and manually adjusted deep learning (mDLO) plans were blindly assessed by a radiation oncologist, a dosimetrist, and a physicist, through visual inspection, clinical goal evaluation, and comparison of normal tissue complication probability values. mDLO plans were completed within an average time of 2.5 h. In comparison, the manual planning process typically took around 2 days. RESULTS: In the retrospective study, in 10/10 (100%) patients, the mDLO plans were preferred, while in the prospective study, 9 out of 15 (60%) mDLO plans were preferred. In 4 out of the remaining 6 cases, the manual and mDLO plans were considered comparable in quality. Differences between manual and mDLO plans were limited. CONCLUSION: This study showed a high preference for mDLO plans over manual IMPT plans, with 92% of cases considering mDLO plans comparable or superior in quality for OPC patients.

Robust Optimization Research of Cyber-Physical Power System Considering Wind Power Uncertainty and Coupled Relationship.

To mitigate the impact of wind power uncertainty and power-communication coupling on the robustness of a new power system, a bi-level mixed-integer robust optimization strategy is proposed. Firstly, a coupled network model is constructed based on complex network theory, taking into account the coupled relationship of energy supply and control dependencies between the power and communication networks. Next, a bi-level mixed-integer robust optimization model is developed to improve power system resilience, incorporating constraints related to the coupling strength, electrical characteristics, and traffic characteristics of the information network. The upper-level model seeks to minimize load shedding by optimizing DC power flow using fuzzy chance constraints, thereby reducing the risk of power imbalances caused by random fluctuations in wind power generation. Furthermore, the deterministic power balance constraints are relaxed into inequality constraints that account for wind power forecasting errors through fuzzy variables. The lower-level model focuses on minimizing traffic load shedding by establishing a topology-function-constrained information network traffic model based on the maximum flow principle in graph theory, thereby improving the efficiency of network flow transmission. Finally, a modified IEEE 39-bus test system with intermittent wind power is used as a case study. Random attack simulations demonstrate that, under the highest link failure rate and wind power penetration, Model 2 outperforms Model 1 by reducing the load loss ratio by 23.6% and improving the node survival ratio by 5.3%.

Impact of interplay effects on spot scanning proton therapy with motion mitigation techniques for lung cancer: SFUD versus robustly optimized IMPT plans utilizing a four-dimensional dynamic dose simulation tool.

BACKGROUND: The interaction between breathing motion and scanning beams causes interplay effects in spot-scanning proton therapy for lung cancer, resulting in compromised treatment quality. This study investigated the effects and clinical robustness of two types of spot-scanning proton therapy with motion-mitigation techniques for locally advanced non-small cell lung cancer (NSCLC) using a new simulation tool (4DCT-based dose reconstruction). METHODS: Three-field single-field uniform dose (SFUD) and robustly optimized intensity-modulated proton therapy (IMPT) plans combined with gating and re-scanning techniques were created using a VQA treatment planning system for 15 patients with locally advanced NSCLC (70 GyRBE/35 fractions). In addition, gating windows of three or five phases around the end-of-expiration phase and two internal gross tumor volumes (iGTVs) were created, and a re-scanning number of four was used. First, the static dose (SD) was calculated using the end-of-expiration computed tomography (CT) images. The four-dimensional dynamic dose (4DDD) was then calculated using the SD plans, 4D-CT images, and the deformable image registration technique on end-of-expiration CT. The target coverage (V98%, V100%), homogeneity index (HI), and conformation number (CN) for the iGTVs and organ-at-risk (OAR) doses were calculated for the SD and 4DDD groups and statistically compared between the SD, 4DDD, SFUD, and IMPT treatment plans using paired t-test. RESULTS: In the 3- and 5-phase SFUD, statistically significant differences between the SD and 4DDD groups were observed for V100%, HI, and CN. In addition, statistically significant differences were observed for V98%, V100%, and HI in phases 3 and 5 of IMPT. The mean V98% and V100% in both 3-phase plans were within clinical limits (> 95%) when interplay effects were considered; however, V100% decreased to 89.3% and 94.0% for the 5-phase SFUD and IMPT, respectively. Regarding the significant differences in the deterioration rates of the dose volume histogram (DVH) indices, the 3-phase SFUD plans had lower V98% and CN values and higher V100% values than the IMPT plans. In the 5-phase plans, SFUD had higher deterioration rates for V100% and HI than IMPT. CONCLUSIONS: Interplay effects minimally impacted target coverage and OAR doses in SFUD and robustly optimized IMPT with 3-phase gating and re-scanning for locally advanced NSCLC. However, target coverage significantly declined with an increased gating window. Robustly optimized IMPT showed superior resilience to interplay effects, ensuring better target coverage, prescription dose adherence, and homogeneity than SFUD. TRIAL REGISTRATION: None.

Robust optimization of the energy concept of an industrial process w.r.t. uncertain energy costs and environmental conditions.

In order to limit the global warming to 1.5 °C as decided by the Paris Agreement, the greenhouse gas emissions have to be dramatically reduced within the next couple of years. In order to realize this in industrial sectors with low to medium temperature requirements, such as food or pulp and paper industry, fossil fuels must be replaced by renewable energy sources to generate electricity, steam and process heat. To realize this in a most economical way, a deterministic multi-objective optimization and a robust scalar optimization of the renewable energy concept of an industrial process are carried out, whereby the robust optimization takes uncertainties in the assumptions of the price for purchasing natural gas and the solar radiation into account. To set up the automated optimization processes, suitable mathematical descriptions of generation units (e.g. photovoltaic systems, wind turbines, solar thermal systems), conversion units (e.g. heat pumps, boilers) and storages (e.g. thermal, electrical) are described first. The comparison of both optimization approaches shows that deterministic optimization is able to find very good solutions, but that the spread of the objectives is significantly larger than with robust optimization when there are uncertainties in the assumptions. The robust optimization thus expands the portfolio for selecting suitable energy concepts and enables future scenarios and developments to be considered, which is particularly necessary in dynamic and heavily changing environments. Furthermore, considering the typically long operating times of industrial plants, economically well-founded decisions can be made, which can have a positive effect on the current restraint to make necessary investments..

Multi-Objective Robust Design Optimization for Crashworthiness Enhancement of Hybrid 2D Triaxially Braided Composite Tube Using Evolutionary Algorithms.

An innovative optimal design framework is developed aiming at enhancing the crashworthiness while ensuring the lightweight design of a hybrid two-dimensional triaxial braided composite (2DTBC) tube, drawing insights from the mesostructure of the composite material. To achieve these goals, we first compile the essential mechanical properties of the 2DTBC using a concentric cylinder model (CCM) and an analytical laminate model. Subsequently, a kriging surrogate model to elucidate the intricate relationship between design variables and macroscopic crashworthiness is developed and validated. Finally, employing multi-objective evolutionary optimization, we identify Pareto optimal solutions, highlighting that reducing the total fiber volume and increasing the glass fiber content in the total fiber volume are crucial for optimal crashworthiness and the lightweight design of the hybrid 2DTBC tube. By integrating advanced predictive modeling techniques with multi-objective evolutionary optimization, the proposed approach not only sheds light on the fundamental principles governing the crashworthiness of hybrid 2DTBC but also provides valuable insights for the design of robust and lightweight composite structures.

TORO Indexer: a PyTorch-based indexing algorithm for kilohertz serial crystallography.

Serial crystallography (SX) involves combining observations from a very large number of diffraction patterns coming from crystals in random orientations. To compile a complete data set, these patterns must be indexed (i.e. their orientation determined), integrated and merged. Introduced here is TORO (Torch-powered robust optimization) Indexer, a robust and adaptable indexing algorithm developed using the PyTorch framework. TORO is capable of operating on graphics processing units (GPUs), central processing units (CPUs) and other hardware accelerators supported by PyTorch, ensuring compatibility with a wide variety of computational setups. In tests, TORO outpaces existing solutions, indexing thousands of frames per second when running on GPUs, which positions it as an attractive candidate to produce real-time indexing and user feedback. The algorithm streamlines some of the ideas introduced by previous indexers like DIALS real-space grid search [Gildea, Waterman, Parkhurst, Axford, Sutton, Stuart, Sauter, Evans & Winter (2014). Acta Cryst. D70, 2652-2666] and XGandalf [Gevorkov, Yefanov, Barty, White, Mariani, Brehm, Tolstikova, Grigat & Chapman (2019). Acta Cryst. A75, 694-704] and refines them using faster and principled robust optimization techniques which result in a concise code base consisting of less than 500 lines. On the basis of evaluations across four proteins, TORO consistently matches, and in certain instances outperforms, established algorithms such as XGandalf and MOSFLM [Powell (1999). Acta Cryst. D55, 1690-1695], occasionally amplifying the quality of the consolidated data while achieving superior indexing speed. The inherent modularity of TORO and the versatility of PyTorch code bases facilitate its deployment into a wide array of architectures, software platforms and bespoke applications, highlighting its prospective significance in SX.

Reconciling the EU forest, biodiversity, and climate strategies.

Forests provide important ecosystem services (ESs), including climate change mitigation, local climate regulation, habitat for biodiversity, wood and non-wood products, energy, and recreation. Simultaneously, forests are increasingly affected by climate change and need to be adapted to future environmental conditions. Current legislation, including the European Union (EU) Biodiversity Strategy, EU Forest Strategy, and national laws, aims to protect forest landscapes, enhance ESs, adapt forests to climate change, and leverage forest products for climate change mitigation and the bioeconomy. However, reconciling all these competing demands poses a tremendous task for policymakers, forest managers, conservation agencies, and other stakeholders, especially given the uncertainty associated with future climate impacts. Here, we used process-based ecosystem modeling and robust multi-criteria optimization to develop forest management portfolios that provide multiple ESs across a wide range of climate scenarios. We included constraints to strictly protect 10% of Europe's land area and to provide stable harvest levels under every climate scenario. The optimization showed only limited options to improve ES provision within these constraints. Consequently, management portfolios suffered from low diversity, which contradicts the goal of multi-functionality and exposes regions to significant risk due to a lack of risk diversification. Additionally, certain regions, especially those in the north, would need to prioritize timber provision to compensate for reduced harvests elsewhere. This conflicts with EU LULUCF targets for increased forest carbon sinks in all member states and prevents an equal distribution of strictly protected areas, introducing a bias as to which forest ecosystems are more protected than others. Thus, coordinated strategies at the European level are imperative to address these challenges effectively. We suggest that the implementation of the EU Biodiversity Strategy, EU Forest Strategy, and targets for forest carbon sinks require complementary measures to alleviate the conflicting demands on forests.

DiffuseRT: predicting likely anatomical deformations of patients undergoing radiotherapy.

Objective. Predicting potential deformations of patients can improve radiotherapy treatment planning. Here, we introduce new deep-learning models that predict likely anatomical changes during radiotherapy for head and neck cancer patients.Approach. Denoising diffusion probabilistic models (DDPMs) were developed to generate fraction-specific anatomical changes based on a reference cone-beam CT (CBCT), the fraction number and the dose distribution delivered. Three distinct DDPMs were developed: (1) theimage modelwas trained to directly generate likely future CBCTs, (2) the deformable vector field (DVF) model was trained to generate DVFs that deform a reference CBCT and (3) thehybrid modelwas trained similarly to the DVF model, but without relying on an external deformable registration algorithm. The models were trained on 9 patients with longitudinal CBCT images (224 CBCTs) and evaluated on 5 patients (152 CBCTs).Results. The generated images mainly exhibited random positioning shifts and small anatomical changes for early fractions. For later fractions, all models predicted weight losses in accordance with the training data. The distributions of volume and position changes of the body, esophagus, and parotids generated with the image and hybrid models were more similar to the ground truth distribution than the DVF model, evident from the lower Wasserstein distance achieved with the image (0.33) and hybrid model (0.30) compared to the DVF model (0.36). Generating several images for the same fraction did not yield the expected variability since the ground truth anatomical changes were only in 76% of the fractions within the 95% bounds predicted with the best model. Using the generated images for robust optimization of simplified proton therapy plans improved the worst-case clinical target volume V95 with 7% compared to optimizing with 3 mm set-up robustness while maintaining a similar integral dose.Significance. The newly developed DDPMs generate distributions similar to the real anatomical changes and have the potential to be used for robust anatomical optimization.

A novel fast robust optimization algorithm for intensity-modulated proton therapy with minimum monitor unit constraint.

BACKGROUND: Intensity-modulated proton therapy (IMPT) optimizes spot intensities and position, providing better conformability. However, the successful application of IMPT is dependent upon addressing the challenges posed by range and setup uncertainties. In order to address the uncertainties in IMPT, robust optimization is essential. PURPOSE: This study aims to develop a novel fast algorithm for robust optimization of IMPT with minimum monitor unit (MU) constraint. METHODS AND MATERIALS: The study formulates a robust optimization problem and proposes a novel, fast algorithm based on the alternating direction method of multipliers (ADMM) framework. This algorithm enables distributed computation and parallel processing. Ten clinical cases were used as test scenarios to evaluate the performance of the proposed approach. The robust optimization method (RBO-NEW) was compared with plans that only consider nominal optimization using CTV (NMO-CTV) without handling uncertainties and PTV (NMO-PTV) to handle the uncertainties, as well as with conventional robust-optimized plans (RBO-CONV). Dosimetric metrics, including D95, homogeneity index, and Dmean, were used to evaluate the dose distribution quality. The area under the root-mean-square dose (RMSD)-volume histogram curves (AUC) and dose-volume histogram (DVH) bands were used to evaluate the robustness of the treatment plan. Optimization time cost was also assessed to measure computational efficiency. RESULTS: The results demonstrated that the RBO plans exhibited better plan quality and robustness than the NMO plans, with RBO-NEW showing superior computational efficiency and plan quality compared to RBO-CONV. Specifically, statistical analysis results indicated that RBO-NEW was able to reduce the computational time from 389.70 ± 207.40 $389.70\pm 207.40$ to 228.60 ± 123.67 $228.60\pm 123.67$ s ( p < 0.01 $p<0.01$ ) and reduce the mean organ-at-risk (OAR) dose from 9.38 ± 12.80 $9.38\pm 12.80$ % of the prescription dose to 9.07 ± 12.39 $9.07\pm 12.39$ % of the prescription dose ( p < 0.05 $p<0.05$ ) compared to RBO-CONV. CONCLUSION: This study introduces a novel fast robust optimization algorithm for IMPT treatment planning with minimum MU constraint. Such an algorithm is not only able to enhance the plan's robustness and computational efficiency without compromising OAR sparing but also able to improve treatment plan quality and reliability.

Robust optimization strategies for contour uncertainties in online adaptive radiation therapy.

Objective.Online adaptive radiation therapy requires fast and automated contouring of daily scans for treatment plan re-optimization. However, automated contouring is imperfect and introduces contour uncertainties. This work aims at developing and comparing robust optimization strategies accounting for such uncertainties.Approach.A deep-learning method was used to predict the uncertainty of deformable image registration, and to generate a finite set of daily contour samples. Ten optimization strategies were compared: two baseline methods, five methods that convert contour samples into voxel-wise probabilities, and three methods accounting explicitly for contour samples as scenarios in robust optimization. Target coverage and organ-at-risk (OAR) sparing were evaluated robustly for simplified proton therapy plans for five head-and-neck cancer patients.Results.We found that explicitly including target contour uncertainty in robust optimization provides robust target coverage with better OAR sparing than the baseline methods, without increasing the optimization time. Although OAR doses first increased when increasing target robustness, this effect could be prevented by additionally including robustness to OAR contour uncertainty. Compared to the probability-based methods, the scenario-based methods spared the OARs more, but increased integral dose and required more computation time.Significance.This work proposed efficient and beneficial strategies to mitigate contour uncertainty in treatment plan optimization. This facilitates the adoption of automatic contouring in online adaptive radiation therapy and, more generally, enables mitigation also of other sources of contour uncertainty in treatment planning.

Robust optimization and assessment of dynamic trajectory and mixed-beam arc radiotherapy: a preliminary study.

Objective.Dynamic trajectory radiotherapy (DTRT) and dynamic mixed-beam arc therapy (DYMBARC) exploit non-coplanarity and, for DYMBARC, simultaneously optimized photon and electron beams. Margin concepts to account for set-up uncertainties during delivery are ill-defined for electron fields. We develop robust optimization for DTRT&DYMBARC and compare dosimetric plan quality and robustness for both techniques and both optimization strategies for four cases.Approach.Cases for different treatment sites and clinical target volume (CTV) to planning target volume (PTV) margins,m, were investigated. Dynamic gantry-table-collimator photon paths were optimized to minimize PTV/organ-at-risk (OAR) overlap in beam's-eye-view and minimize potential photon multileaf collimator (MLC) travel. For DYMBARC plans, non-isocentric partial electron arcs or static fields with shortened source-to-surface distance (80 cm) were added. Direct aperture optimization (DAO) was used to simultaneously optimize MLC-based intensity modulation for both photon and electron beams yielding deliverable PTV-based DTRT&DYMBARC plans. Robust-optimized plans used the same paths/arcs/fields. DAO with stochastic programming was used for set-up uncertainties with equal weights in all translational directions and magnitudeδsuch thatm= 0.7δ. Robust analysis considered random errors in all directions with or without an additional systematic error in the worst 3D direction for the adjacent OARs.Main results.Electron contribution was 7%-41% of target dose depending on the case and optimization strategy for DYMBARC. All techniques achieved similar CTV coverage in the nominal (no error) scenario. OAR sparing was overall better in the DYMBARC plans than in the DTRT plans and DYMBARC plans were generally more robust to the considered uncertainties. OAR sparing was better in the PTV-based than in robust-optimized plans for OARs abutting or overlapping with the target volume, but more affected by uncertainties.Significance.Better plan robustness can be achieved with robust optimization than with margins. Combining electron arcs/fields with non-coplanar photon trajectories further improves robustness and OAR sparing.

Robust optimization of a novel ultraviolet (UV) photoreactor for water disinfection: A neural network approach.

To optimize the ultraviolet (UV) water disinfection process, it is crucial to determine the ideal geometric dimensions of a corresponding model that enhance performance while minimizing the impact of uncertain photoreactor inputs. As water treatment directly affects people's lives, it is crucial to eliminate the risks associated with the non-ideal performance of disinfection photoreactors. Input uncertainties greatly affect photoreactor performance, making it essential to develop a robust optimization algorithm in advance to mitigate these effects and minimize the physical and financial resources required for constructing the photoreactors. In the suggested algorithm, a two-objective genetic algorithm is integrated with a non-intrusive polynomial chaos expansion (PCE) technique. Additionally, the Sobol sampling method is employed to select the necessary samples for understanding the system's behavior. An artificial neural network surrogate model is trained using sufficient data points derived from computational fluid dynamics (CFD) simulations. A novel type of UV photoreactors working based on exterior reflectors is chosen to optimize the process with three uncertain input parameters, including UV lamp power, UV transmittance of water, and diffusive fraction of the reflective surface. In addition, four geometrical design variables are considered to find the optimal configuration of the photoreactor. The standard deviation (SD) and the reciprocal of log reduction value (LRV) are set as the objective functions, calculated using PCE. The optimal design provides a LRV of 3.95 with SD of 0.2. The coefficient of variation (CoV) of the model significantly declines up to 7%, indicating the decreased sensitivity of the photoreactor to the input uncertainties. Additionally, it is discovered that the robust model exhibits minimal sensitivity to changes in reflectivity in various flow rates, and its output variability aligns with the SD obtained through robust optimization.

Dosimetric and NTCP advantages of robust proton therapy over robust VMAT for Stage III NSCLC in the immunotherapy era.

AIMS: To assess the robustness and to define the dosimetric and NTCP advantages of pencil-beam-scanning proton therapy (PBSPT) compared with VMAT for unresectable Stage III non-small lung cancer (NSCLC) in the immunotherapy era. MATERIAL AND METHODS: 10 patients were re-planned with VMAT and PBSPT using: 1) ITV-based robust optimization with 0.5 cm setup uncertainties and (for PBSPT) 3.5 % range uncertainties on free-breathing CT 2) CTV-based RO including all 4DCTs anatomies. Target coverage (TC), organs at risk dose and TC robustness (TCR), set at V95%, were compared. The NTCP risk for radiation pneumonitis (RP), 24-month mortality (24MM), G2 + acute esophageal toxicity (ET), the dose to the immune system (EDIC) and the left anterior descending (LAD) coronary artery V15 < 10 % were registered. Wilcoxon test was used. RESULTS: Both PBSPT methods improved TC and TCR (p < 0.01). The mean lung dose and lung V20 were lower with PBSPT (p < 0.01). Median mean heart dose reduction with PBSPT was 8 Gy (p < 0.001). PT lowered median LAD V15 (p = 0.004). ΔNTCP > 5 % with PBSPT was observed for two patients for RP and for five patients for 24 MM. ΔNTCP for ≥ G2 ET was not in favor of PBSPT for all patients. PBSPT halved median EDIC (4.9/5.1 Gy for ITV/CTV-based VMAT vs 2.3 Gy for both ITV/CTV-based PBSPT, p < 0.01). CONCLUSIONS: PBSPT is a robust approach with significant dosimetric and NTCP advantages over VMAT; the EDIC reduction could allow for a better integration with immunotherapy. A clinical benefit for a subset of NSCLC patients is expected.

Solving the waste bin location problem with uncertain waste generation rate: A bi-objective robust optimization approach.

An efficient municipal solid waste (MSW) system is critical to modern cities in order to enhance sustainability and liveability of urban life. With this aim, the planning phase of the MSW system should be carefully addressed by decision makers. However, planning success is dependent on many sources of uncertainty that can affect key parameters of the system, for example, the waste generation rate in an urban area. With this in mind, this article contributes with a robust optimization model to design the network of collection points (i.e. location and storage capacity), which are the first points of contact with the MSW system. A central feature of the model is a bi-objective function that aims at simultaneously minimizing the network costs of collection points and the required collection frequency to gather the accumulated waste (as a proxy of the collection cost). The value of the model is demonstrated by comparing its solutions with those obtained from its deterministic counterpart over a set of realistic instances considering different scenarios defined by different waste generation rates. The results show that the robust model finds competitive solutions in almost all cases investigated. An additional benefit of the model is that it allows the user to explore trade-offs between the two objectives.

Optimal demand response aggregation in wholesale electricity markets: Comparative analysis of polyhedral; ellipsoidal and box methods for modeling uncertainties.

This paper presents an optimal framework for demand response aggregators in wholesale electricity markets. Demand response aggregators provide customers with flexible contracts in the proposed model. These contracts allow for hourly load reductions through load curtailment, load shifting, onsite generation utilization, and energy storage systems. The study suggests the price-based self-scheduling model for demand response aggregators, which seeks to maximize the aggregator's payoff for participation in day-ahead energy markets. The proposed model is implemented on a sample demand response aggregator with uncertainty and without uncertainty. Three methods, box, polyhedral, and ellipsoidal, based on robust optimization, are proposed for uncertainty modeling in this work, and their effectiveness is compared with each other. The results show that if the uncertainty is modeled using the polyhedral method, the value of the objective function will deviate by only 22.72 % compared to the case without uncertainty. However, this deviation in box and ellipsoidal methods is 118.48 % and 49.20 %, respectively, which shows the superiority of the polyhedral method compared to the oval and box methods.

A novel robust evaluation approach to improve systematic behavior of failure safety in water supply system under various ellipsoid uncertainties.

This study proposes a novel robust optimization approach for an integrated water supply system, wherein the decision-makers attempt to improve failure safety of system under various uncertainty strategies. To cope with uncertainty, the ellipsoid uncertainty set is assumed to evaluate the best feasible solution in the direction of water supply under various strategies. We assessed the case of Hamoun watershed, a water-stressed watershed in southeastern of Iran, to evaluate the developed robust optimization model. In the following, the comparative feasibility under uncertainty levels is conducted to analyze the impacts of simulation strategies on the status of robust model. Based on the final results, the reliability of the model's objective functions experienced an increasing trend ( 58.3 % ), and the objective function values under the uncertainty strategies is greatly improved. The findings of the analysis show that the robust strategies in response to the failure safety achieve outstanding optimal objectives under uncertainty.