Humberto Rocha

PATTERN SEARCH METHODS FOR USER-PROVIDED POINTS: APPLICATION TO MOLECULAR GEOMETRY PROBLEMS ∗

This paper deals with the application of pattern search methods to the numerical solution of a class of molecular geometry problems with important applications in molecular physics and chemistry. The goal is to find a configuration of a cluster or a molecule with minimum total energy. The minimization problems in this class of molecular geometry problems have no constraints, and the objective function is smooth. The difficulties arise from the existence of several local minima and, especially, from the expensive function evaluation (total energy) and the possible nonavailability of first-order derivatives. We introduce a pattern search approach that attempts to exploit the physical nature of the problem by using energy lowering geometrical transformations and to take advantage of parallelism without the use of derivatives. Numerical results for a particular instance of this new class of pattern search methods are presented, showing the promise of our approach. The new pattern search methods can be used in any other context where there is a user-provided scheme to generate points leading to a potential objective function decrease.

Beam angle optimization for intensity-modulated radiation therapy using a guided pattern search method

Generally, the inverse planning of radiation therapy consists mainly of the fluence optimization. The beam angle optimization (BAO) in intensity-modulated radiation therapy (IMRT) consists of selecting appropriate radiation incidence directions and may influence the quality of the IMRT plans, both to enhance better organ sparing and to improve tumor coverage. However, in clinical practice, most of the time, beam directions continue to be manually selected by the treatment planner without objective and rigorous criteria. The goal of this paper is to introduce a novel approach that uses beams-eye-view dose ray tracing metrics within a pattern search method framework in the optimization of the highly non-convex BAO problem. Pattern search methods are derivative-free optimization methods that require a few function evaluations to progress and converge and have the ability to better avoid local entrapment. The pattern search method framework is composed of a search step and a poll step at each iteration. The poll step performs a local search in a mesh neighborhood and ensures the convergence to a local minimizer or stationary point. The search step provides the flexibility for a global search since it allows searches away from the neighborhood of the current iterate. Beams-eye-view dose metrics assign a score to each radiation beam direction and can be used within the pattern search framework furnishing a priori knowledge of the problem so that directions with larger dosimetric scores are tested first. A set of clinical cases of head-and-neck tumors treated at the Portuguese Institute of Oncology of Coimbra is used to discuss the potential of this approach in the optimization of the BAO problem.

Simulated annealing applied to IMRT beam angle optimization: A computational study

Electing irradiation directions to use in IMRT treatments is one of the first decisions to make in treatment planning. Beam angle optimization (BAO) is a difficult problem to tackle from the mathematical optimization point of view. It is highly non-convex, and optimization approaches based on gradient descent methods will probably get trapped in one of the many local minima. Simulated Annealing (SA) is a local search probabilistic procedure that is known to be able to deal with multimodal problems. SA for BAO was retrospectively applied to ten clinical examples of treated cases of head-and neck tumors signalized as complex cases where proper target coverage and organ sparing proved difficult to achieve. The number of directions to use was considered fixed and equal to 5 or 7. It is shown that SA can lead to solutions that significantly improve organ sparing, even considering a reduced number of angles, without jeopardizing tumor coverage.

Automated fluence map optimization based on fuzzy inference systems.

PURPOSE The planning of an intensity modulated radiation therapy treatment requires the optimization of the fluence intensities. The fluence map optimization (FMO) is many times based on a nonlinear continuous programming problem, being necessary for the planner to define a priori weights and/or lower bounds that are iteratively changed within a trial-and-error procedure until an acceptable plan is reached. In this work, the authors describe an alternative approach for FMO that releases the human planner from trial-and-error procedures, contributing for the automation of the planning process. METHODS The FMO is represented by a voxel-based convex penalty continuous nonlinear model. This model makes use of both weights and lower/upper bounds to guide the optimization process toward interesting solutions that are able to satisfy all the constraints defined for the treatment. All the models parameters are iteratively changed by resorting to a fuzzy inference system. This system analyzes how far the current solution is from a desirable solution, changing in a completely automated way both weights and lower/upper bounds. The fuzzy inference system is based on fuzzy reasoning that enables the use of common-sense rules within an iterative optimization process. The method is built in two stages: in a first stage, an admissible solution is calculated, trying to guarantee that all the treatment planning constraints are being satisfied. In this first stage, the algorithm tries to improve as much as possible the irradiation of the planning target volumes. In a second stage, the algorithm tries to improve organ sparing, without jeopardizing tumor coverage. RESULTS The proposed methodology was applied to ten head-and-neck cancer cases already treated in the Portuguese Oncology Institute of Coimbra (IPOCFG) and signalized as complex cases. IMRT treatment was considered, with 7, 9, and 11 equidistant beam angles. It was possible to obtain admissible solutions for all the patients considered and with no human planner intervention. The results obtained were compared with the optimized solution using a similar optimization model but with human planner intervention. For the vast majority of cases, it was possible to improve organ sparing and at the same time to assure better tumor coverage. CONCLUSIONS Embedding a fuzzy inference system into FMO allows human planner reasoning to be used in the guidance of the optimization process toward interesting regions in a truly automated way. The proposed methodology is capable of calculating high quality plans within reasonable computational times and can be an important contribution toward fully automated radiation therapy treatment planning.

A derivative-free multistart framework for an automated noncoplanar beam angle optimization in IMRT.

PURPOSE The inverse planning of an intensity-modulated radiation therapy (IMRT) treatment requires decisions regarding the angles used for radiation incidence, even when arcs are used. The possibility of improving the quality of treatment plans by an optimized selection of the beam angle incidences-beam angle optimization (BAO)-is seldom done in clinical practice. The inclusion of noncoplanar beam incidences in an automated optimization routine is even more unusual. However, for some tumor sites, the advantage of considering noncoplanar beam incidences is well known. This paper presents the benefits of using a derivative-free multistart framework for the optimization of the noncoplanar BAO problem. METHODS Multistart methods combine a global strategy for sampling the search space with a local strategy for improving the sampled solutions. The proposed global strategy allows a thorough exploration of the continuous search space of the highly nonconvex BAO problem. To avoid local entrapment, a derivative-free method is used as local procedure. Additional advantages of the derivative-free method include the reduced number of function evaluations required to converge and the ability to use multithreaded computing. Twenty nasopharyngeal clinical cases were selected to test the proposed multistart framework. The planning target volumes included the primary tumor, the high and low risk lymph nodes. Organs-at-risk included the spinal cord, brainstem, optical nerves, chiasm, parotids, oral cavity, brain, thyroid, among others. For each case, a setup with seven equispaced beams was chosen and the resulting treatment plan, using a multicriteria optimization framework, was then compared against the coplanar and noncoplanar plans using the optimal beam setups obtained by the derivative-free multistart framework. RESULTS The optimal noncoplanar beam setup obtained by the derivative-free multistart framework leads to high quality treatment plans with better target coverage and with improved organ sparing compared to treatment plans using equispaced or optimal coplanar beam angle setups. The noncoplanar treatment plans achieved, e.g., an average reduction in the mean dose of the oral cavity of 6.1 Gy and an average reduction in the maximum-dose of the brainstem of 7 Gy when compared to the equispaced treatment plans. CONCLUSIONS The noncoplanar BAO problem is an extremely challenging multimodal optimization problem that can be successfully addressed through a thoughtful exploration of the continuous highly nonconvex BAO search space. The proposed framework is capable of calculating high quality treatment plans and thus can be an interesting alternative toward automated noncoplanar beam selection in IMRT treatment planning which is nowadays the natural trend in treatment planning.

IMRT Beam Angle Optimization Using Dynamically Dimensioned Search

In Intensity Modulated Radiation Therapy (IMRT), the selection of appropriate radiation incidence directions is one of the determinants of proper tumor coverage and sparing of healthy tissues. Nevertheless, most of the times, the incidence directions used in clinical practice are equidistant or determined by a trial and error procedure that is very time consuming and does not guarantee the best possible treatment plan. This paper presents some preliminary results considering the application of DDS (Dynamically Dimensioned Search) algorithm to the problem of Beam Angle Optimization (BAO) for IMRT treatment planning. BAO is a problem known by having many local minima. DDS is a derivative-free optimization algorithm, and presents the capability of not getting trapped in these local minima as happens with, for instance, gradient descent based algorithms. In this paper we will briefly describe the problem, the algorithm, and present computational results for clinical cases of head and neck tumors.

Combinatorial optimization for an improved transition from fluence optimization to fluence delivery in IMRT treatment planning

The intensity modulated radiation therapy (IMRT) treatment planning problem is usually divided into three smaller problems that are solved sequentially: geometry problem, intensity problem and realization problem. There are many models and algorithms that address each one of the problems in a satisfactory way. However, these problems cannot be seen separately, because strong links exist between them. While the linkage between the geometry problem and the intensity problem is straightforward, the linkage between the intensity problem and the realization problem is all but simple and will determine the quality of the treatment planning. In practice, the linkage between these problems is, most of the times, done in a rather simple way, usually by rounding. This can lead to a significant deterioration of the treatment plan quality. We propose a combinatorial optimization approach to enable an improved transition from optimized to delivery fluence maps in IMRT treatment planning. Two clinical examples of head and neck cancer cases are used, both to present numerical evidences of the resulting deterioration of plan quality if a simplistic approach is used, and also to highlight a combinatorial optimization approach as a valuable alternative when linking the intensity problem and the realization problem.

A Nonlinear Multicriteria Model for Team Effectiveness

The study of team effectiveness has received significant attention in recent years. Team effectiveness is an important subject since teams play an increasingly decisive role on modern organizations. This study is inherently a multicriteria problem as different criteria are typically required to assess team effectiveness. Among the different aspects of interest on the study of team effectiveness one of the utmost importance is to acknowledge, as accurately as possible, the relationships that team resources and team processes establish with team effectiveness. Typically, these relationships are studied using linear models which fail to explain the complexity inherent to group phenomena. In this study we propose a novel approach using radial basis functions to construct a multicriteria nonlinear model to more accurately capture the relationships between the team resources/processes and team effectiveness. By combining principal component analysis, radial basis functions interpolation, and cross-validation for model parameter tuning, we obtained a data fitting method that generated an approximate response with reliable trend predictions between the given data points.

Noncoplanar beam angle optimization in IMRT treatment planning using pattern search methods

Radiation therapy is used to treat localized cancers, aiming to deliver a dose of radiation to the tumor volume to sterilize all cancer cells while minimizing the collateral effects on the surrounding healthy organs and tissues. The planning of radiation therapy treatments requires decisions regarding the angles used for radiation incidence, the fluence intensities and, if multileaf collimators are used, the definition of the leaf sequencing. The beam angle optimization problem consists in finding the optimal number and incidence directions of the irradiation beams. The selection of appropriate radiation incidence directions is important for the quality of the treatment. However, the possibility of improving the quality of treatment plans by an optimized selection of the beam incidences is seldom done in the clinical practice. Adding the possibility for noncoplanar incidences is even more rarely used. Nevertheless, the advantage of noncoplanar beams is well known. The optimization of noncoplanar beam incidences may further allow the reduction of the number of beams needed to reach a clinically acceptable plan. In this paper we present the benefits of using pattern search methods for the optimization of the highly non-convex noncoplanar beam angle optimization problem.

IMRT Beam Angle Optimization Using DDS with a Cross-Validation Approach for Configuration Selection

Radiation incidences (angles) that are used in Intensity Modulated Radiation Therapy (IMRT) treatments have a significant influence in the treatment clinical outcome. In clinical practice, the angles are usually chosen after a lengthy trial and error procedure that is significantly dependent on the planner’s experience and time availability. The use of optimization models and algorithms can be an important contribution to the treatment planning, improving the quality of the solution reached and decreasing the time spent on the process. This paper describes a Dynamically Dimensioned Search (DDS) approach for IMRT beam angle optimization. Several different sets of parameters and search options were analyzed. Computational tests show that the final outcome is strongly influenced by these choices. This motivated the use of a cross-validation based procedure for choosing the algorithm’s configuration, considering a set of ten retrospective treated cases of head-and-neck tumors at the Portuguese Institute of Oncology of Coimbra.