Column Generation-Based Techniques for Intensity-Modulated Radiation Therapy (IMRT) and Volumetric Modulated Arc Therapy (VMAT) Treatment Planning

RÉSUMÉ: Les statistiques ont estimé à environ 14,1 millions le nombre de cas de cancer en 2018 dans le monde, et qui devrait passer à 24 millions d’ici 2035. La radiothérapie est l’une des premières méthodes de traitement du cancer, qu’environ 50% des patients reçoivent au cours de leur maladie. Cette méthode endommage le matériel génétique des cellules cancéreuses, détruisant ainsi leur capacité de reproduction. Cependant, les cellules normales sont également affectées par le rayonnement ; par conséquent, le traitement doit être effectué de manière à maximiser la dose de rayonnement aux tumeurs, tout en minimisant les effets néfastes des radiations sur les tissus sains. Les techniques d’optimisation sont utilisées afin de déterminer la dose et la position du rayonnement à administrer au corps du patient. Ce projet aborde la radiothérapie externe à travers la radiothérapie par modulation d’intensité (IMRT), ainsi qu’une nouvelle forme appelée modulation d’intensité volumétrique par thérapie par arcs (VMAT). En IMRT, un nombre fini de directions sont déterminées pour le rayonnement du faisceau, tandis qu’en VMAT l’accélérateur linéaire tourne autour du corps du patient alors que le faisceau est allumé. Cette technologie permet de modifier dynamiquement la forme du faisceau et le débit de dose pendant le traitement. Le problème de planification du traitement consiste à choisir une séquence de distribution des formes de faisceaux, à optimiser le dé bit de dose du faisceau et à déterminer la vitesse de rotation du portique, si nécessaire. Cette recherche tire profit de la méthode de génération de colonnes, en tant que méthode d’optimisation efficace en particulier pour les problèmes à grande échelle. Cette technique permet d’améliorer le temps de traitement et les objectifs cliniques non linéaires et non convexes, dans la planification de traitement en VMAT. Un nouveau modèle multi-objectif de génération de colonnes pour l’IMRT est également développé. Dans le premier essai, nous développons un nouvel algorithme de génération de colonnes qui optimise le compromis entre le temps et la qualité du traitement délivré pour la planification de traitement en VMAT. Pour ce faire, une génération simultanée de colonnes et de rangées est développée, afin de relier les colonnes, contenant la configuration des ouvertures de faisceaux, aux rangées du modèle, représentant la restriction de temps de traitement. De plus, nous proposons une technique de regroupement par grappe modifiée, afin d’agréger des éléments de volume similaires du corps du patient, et de réduire efficacement le nombre de contraintes dans le modèle. Les résultats de calcul montrent qu’il est possible d’obtenir un traitement de haute qualité sur quatre processeurs en parallèle. Dans le deuxième essai, nous développons une approche de planification automatique intégrant les critères de l’histogramme dose-volume (DVH). Les DVH sont la représentation de dose la plus courante pour l’évaluation de la qualité de traitement en technologie VMAT. Nous profitons de la procédure itérative de génération de colonnes pour ajuster les paramètres du modèle lors de la génération d’ouverture, et répondre aux critères DVH non linéaires, sans tenir compte des contraintes dures dans le modèle. Les résultats sur les cas cliniques montrent que notre méthodologie a été significativement améliorée, pour obtenir des plans cliniquement acceptables sans intervention humaine par rapport à une simple optimisation VMAT. De plus, la comparaison avec un système de planification de traitement commercial existant montre que la qualité des plans obtenus à partir de la méthode proposée, en particulier pour les tissus sains, est largement meilleure alors que le temps de calcul est moindre. Dans le troisième essai, nous abordons la planification de traitement en IMRT, qui est formulée comme un problème d’optimisation convexe à grande échelle, avec un espace de faisabilité simplex. Nous intégrons d’abord une nouvelle approche de solution basée sur la méthode Frank-Wolfe, appelée Blended Conditional Gradients, dans la génération de colonnes, pour améliorer les performances de calcul de la méthode. Nous proposons ensuite une technique de génération de colonnes multi-objectif, pour obtenir directement des ouvertures qui se rapprochent d’un ensemble efficace de plans de traitement non dominés. A cette fin, nous trouvons les limites inférieure et supérieure du front de Pareto, et générons une colonne avec un vecteur de poids des objectifs pré-assigné ou nouveau, réduisant la distance maximale de deux bornes. Nous prouvons que cet algorithme converge vers le front de Pareto. Les résultats de recherche d’un bon compromis de traitement entre la destruction des volumes cibles et la protection des structures saines dans un espace objectif bidimensionnel, montrent l’efficacité de l’algorithme dans l’approche du front de Pareto, avec des plans de traitement livrables en 3 minutes environ, et évitant un grand nombre de colonnes. Cette méthode s’applique également à d’autres classes de problèmes d’optimisation convexe, faisant appel à la fois à une génération de colonnes et à une optimisation multi-objectifs.----------ABSTRACT: The statistics have estimated about 18.1 million cancer cases in 2018 around the world, which is expected to increase to 24 million by 2035. Radiation therapy is one of the most important cancer treatment methods, which about 50% of patients receive during their illness. This method works by damaging the genetic material within cancerous cells and destroying their ability to reproduce. However, normal cells are also affected by radiation; therefore, the treatment should be performed in such a way that it maximizes the dose of radiation to tumors, while simultaneously minimizing the adverse effects of radiations to healthy tissues. The optimization techniques are useful to determine where and how much radiation should be delivered to patient’s body. In this project, we address the intensity-modulated radiation therapy (IMRT) as a widelyused external radiotherapy method and also a novel form called volumetric modulated arc therapy (VMAT). In IMRT, a finite number of directions are determined for the beam radiation, while in VMAT, the linear accelerator rotates around the patient’s body while the beam is on. These technologies give us the ability of changing the beam shape and the dose rate dynamically during the treatment. The treatment planning problem consists of selecting a delivery sequence of beam shapes, optimizing the dose rate of the beam, and determining the rotation speed of the gantry, if required. In this research, we take advantages of the column generation technique, as a leading optimization method specifically for large-scale problems, to improve the treatment time and non-linear non-convex clinical objectives in VMAT treatment planning, and also develop a new multi-objective column generation framework for IMRT. In the first essay, we develop a novel column generation algorithm optimizing the trade-off between delivery time and treatment quality for VMAT treatment planning. To this end, simultaneous column-and-row generation is developed to relate the configuration of beam apertures in columns to the treatment time restriction in the rows of the model. Moreover, we propose a modified clustering technique to aggregate similar volume elements of the patient’s body and efficiently reduce the number of constraints in the model. The computational results show that a high-quality treatment is achievable using a four-thread CPU. In the second essay, we develop an automatic planning approach integrating dose-volume histogram (DVH) criteria, the most common method of treatment evaluation in practice, for VMAT treatment planning. We take advantage of the iterative procedure of column generation to adjust the model parameters during aperture generation and meet nonlinear DVH criteria without considering hard constraints in the model. The results on clinical cases show that our methodology had significant improvement to obtain clinically acceptable plans without human intervention in comparison to simple VMAT optimization. In addition, the comparison to an existing commercial treatment planning system shows the quality of the obtained plans from the proposed method, especially for the healthy tissues, is significantly better while the computational time is less. In the third essay, we address the IMRT treatment planning, which is formulated as a large scale convex optimization problem with simplex feasibility space. We first integrate a novel Frank-Wolfe-based solution approach, so-called Blended Conditional Gradients, into the column generation to improve the computational performance for the method. We then propose a multi-objective column generation technique to directly obtain apertures that approximate an efficient non-dominated set of treatment plans. To this end, we find lower and upper bounds for the Pareto front and generate a column with a pre-assigned or new weight-vector of the objectives, reducing the maximum distance of two bounds. We prove this algorithm converges to the Pareto front. The results in a two-dimensional objective space to find the trade-off plans between the treat of target volumes and sparing the healthy structures show the efficiency of the algorithm to approximate the Pareto front with deliverable treatment plans in about 3 minutes, avoiding a large number of columns. This method is also applicable for other classes of convex optimization problems requiring both column generation and multi-objective optimization

Risk based multi-objective security control and congestion management

Deterministic security criterion has served power system operation, congestion management quite well in last decades. It is simple to be implemented in a security control model, for example, security constrained optimal power flow (SCOPF). However, since event likelihood and violation information are not addressed, it does not provide quantitative security understanding, and so results in system inadequate awareness. Therefore, even if computation capability and information techniques have been greatly improved and widely applied in the operation support tool, operators are still not able to get rid of the security threat, especially in the market competitive environment.;Probability approach has shown its strong ability for planning purpose, and recently gets attention in operation area. Since power system security assessment needs to analyze consequence of all credible events, risk defined as multiplication of event probability and severity is well suited to give an indication to quantify the system security level, and congestion level as well. Since risk addresses extra information, its application for making BETTER online operation decision becomes an attractive research topic.;This dissertation focus on system online risk calculation, risk based multi-objective optimization model development, risk based security control design, and risk based congestion management. A regression model is proposed to predict contingency probability using weather and geography information for online risk calculation. Risk based multi-objective optimization (RBMO) model is presented, considering conflict objectives: risks and cost. Two types of method, classical methods and evolutionary algorithms, are implemented to solve RBMO problem, respectively. A risk based decision making architecture for security control is designed based on the Pareto-optimal solution understanding, visualization tool and high level information analysis. Risk based congestion management provides a market lever to uniformly expand a security VOLUME , where greater volume means more risk. Meanwhile, risk based LMP signal contracts ALL dimensions of this VOLUME in proper weights (state probabilities) at a time.;Two test systems, 6-bus and IEEE RTS 96, are used to test developed algorithms. The simulation results show that incorporating risk into security control and congestion management will evolve our understanding of security level, improve control and market efficiency, and support operator to maneuver system in an effective fashion

Pump Scheduling for Optimised Energy Cost and Water Quality in Water Distribution Networks

Delivering water to customers in sufficient quantity and quality and at low cost is the main driver for many water utilities around the world. One way of working toward this goal is to optimize the operation of a water distribution system. This means scheduling the operation of pumps in a way that results in minimal cost of energy used. It is not an easy process due to nonlinearity of hydraulic system response to different schedules and complexity of water networks in general. This thesis reviewed over 250 papers about pump scheduling published in the last 5 decades. The review revealed that, despite a lot of good work done in the past, the existing pump scheduling methods have several drawbacks revolving mainly around the ability to find globally optimal pump schedules and in a computationally efficient manner whilst dealing with water quality and other complexities of large pipe networks. A new pump scheduling method, entitled iterative Extended Lexicographic Goal Programming (iELGP) method, is developed and presented in this thesis with aim to overcome above drawbacks. The pump scheduling problem is formulated and solved as an optimisation problem with objectives being the electricity cost and the water age (used as a surrogate for water quality). The developed pump scheduling method is general and can be applied to any water distribution network configuration. Moreover, the new method can optimize the operation of fixed and variable speed pumps. The new method was tested on three different case studies. Each case study has different topography, demand patterns, number of pumps and number of tanks. The objective in the first and second case studies is to minimise energy cost only, whereas in the third case study, energy cost and water age are minimized simultaneously. The results obtained by using the new method are compared with results obtained from other pump scheduling methods that were applied to the same case studies. The results obtained demonstrate that the iELGP method is capable of determining optimal, low cost pump schedules whilst trading-off energy costs and water quality. The optimal schedules can be generated in a computationally very efficient manner. Given this, the iELGP method has potential to be applied in real-time scheduling of pumps in larger water distribution networks and without the need to simplify the respective hydraulic models or replace these with surrogate models

On finding paths and flows in multicriteria, stochastic and time-varying networks

This dissertation addresses two classes of network flow problems in networks with multiple, stochastic and time-varying attributes. The first problem class is concerned with providing routing instructions with the ability to make updated decisions as information about travel conditions is revealed for individual travelers in a transportation network. Three exact algorithms are presented for identifying all or a subset of the adaptive Pareto-optimal solutions with respect to the expected value of each criterion from each node to a desired destination for each departure time in the period of interest. The second problem class is concerned with problems of determining the optimal set of a priori path flows for evacuation in capacitated networks are addressed, where the time-dependent and stochastic nature of arc attributes and capacities inherent in these problems is explicitly considered. The concept of Safest Escape is formulated for developing egress instructions. An exact algorithm is proposed to determine the pattern of flow that maximizes the minimum path probability of successful arrival of supply at the sink. While the Safest Escape problem considers stochastic, time-varying capacities, arc travel times, while time-varying, are deterministic quantities. Explicit consideration of stochastic and time-varying travel times makes the SEscape problem and other related problems significantly more difficult. A meta-heuristic based on the principles of genetic algorithms is developed for determining optimal path flows with respect to several problems in dynamic networks, where arc traversal times and capacities are random variables with probability mass functions that vary with time. The proposed genetic algorithm is extended for use in more difficult, stochastic, time-varying and multicriteria, capacitated networks, for which no exact, efficient algorithms exist. Several objectives may be simultaneously considered in determining the optimal flow pattern: minimize total time, maximize expected flow and maximize the minimum path probability of successful arrival at the sink (the objective of the SEscape problem). Numerical experiments are conducted to assess the performance of all proposed approaches

Assembly Line

An assembly line is a manufacturing process in which parts are added to a product in a sequential manner using optimally planned logistics to create a finished product in the fastest possible way. It is a flow-oriented production system where the productive units performing the operations, referred to as stations, are aligned in a serial manner. The present edited book is a collection of 12 chapters written by experts and well-known professionals of the field. The volume is organized in three parts according to the last research works in assembly line subject. The first part of the book is devoted to the assembly line balancing problem. It includes chapters dealing with different problems of ALBP. In the second part of the book some optimization problems in assembly line structure are considered. In many situations there are several contradictory goals that have to be satisfied simultaneously. The third part of the book deals with testing problems in assembly line. This section gives an overview on new trends, techniques and methodologies for testing the quality of a product at the end of the assembling line

Optimal energy management and control of microgrids in modern electrical power systems

Microgrids (MGs) are becoming more popular in modern electric power systems owing to their reliability, efficiency, and simplicity. The proportional-integral (PI) based droop control mechanism has been widely used in the MG control domain as the setpoint generator for the primary controller which has several drawbacks. In order to mitigate these issues, and to enhance the transient and steady-state operations in islanded MGs, advanced control and intelligent optimization methodologies are presented in this dissertation. First, to improve the existing PI-based droop relationship in DCMGs, a multi-objective optimization (MOO) based optimal droop coefficient computation method is proposed. Considering the system voltage regulation, system total loss minimization, and enhanced current sharing among the distributed generators (DGs), the Pareto optimal front is obtained using the Elitist non dominated sorting genetic algorithm (NSGA II). Then, a fuzzy membership function approach is introduced to extract the best compromise solution from the Pareto optimal front. The drawbacks of PI-based droop control cannot be entirely mitigated by tuning the droop gains. Hence, a droop free, approximate optimal feedback control strategy is proposed to optimally control DGs in islanded DCMGs. Further, to gain the fully optimal behavior, and to mitigate constant power load (CPL) instabilities, a decentralized optimal feedback control strategy is also introduced for the active loads (ALs) in the MG. In both algorithms, the approximate dynamic programming (ADP) method is employed to solve the constrained input infinite horizon optimal control problem by successive approximation of the value function via a linear in the parameter (LIP) neural network (NN). The NN weights are updated online by a concurrent reinforcement learning (RL) based tuning algorithm, and the convergence of the unknown weights to a neighborhood of the optimal weights is guaranteed without the persistence of excitation (PE). Finally, a local optimal control strategy is presented to path optimization of islanded ACMGs to enhance the transient operations while mitigating the voltage and frequency deviations caused by the traditional droop control. Optimal state and control transient trajectories in the d-q reference frame are obtained by Pontryagin's minimum principle which drives each DG from a given initial condition to their steady-state manifold. Both simulation and experimental results are presented to validate the concepts