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    TH‐A‐213AB‐04: Improving VMAT Delivery Accuracy by Using an Aperture Complexity Penalty during Optimization
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    Abstract:
    Purpose: Apertures optimized during VMAT planning can be small and irregular, resulting in dosimetric inaccuracies during delivery. Our purpose is to develop and integrate an aperture‐regularization objective function into the optimization process for VMAT, and to quantify the impact of using this objective function on dose delivery accuracy and optimized dose distributions. Methods: An aperture‐based metric (‘edge penalty’) was developed that penalizes complex aperture shapes based on the ratio of MLC side edge length and aperture area. To assess the utility of the metric, VMAT plans were created for an example paraspinal SBRT case with and without incorporating the edge penalty in the cost function. To investigate the dose accuracy, Gafchromic EBT2 film was used to measure 15 sample individual apertures and composite plans with and without the edge penalty applied. Films were analyzed using a triple‐channel uniformity correction and measurements were compared directly to calculations. Results: Apertures generated with the edge penalty were larger, more regularly shaped and required 22% fewer monitor units than those created without the edge penalty. DVH analysis showed that the changes in doses to organs at risk and normal tissues were minimal. Edge penalty apertures showed a significant decrease in the number of pixels disagreeing with calculation by more than 10%. The number of pixels passing in the composite dose distributions for the edge penalty and non‐edge penalty plans were 52% and 96%, respectively. Employing gamma criteria of 3%/1mm resulted in a 79.5% (without penalty) / 95.4% (with penalty) pass rate for the two plans. Conclusions: The use of the edge penalty during optimization has the potential to significantly improve dose delivery accuracy for VMAT plans while minimally affecting optimized dose distributions.
    Keywords:
    Penalty Method
    Aperture (computer memory)
    Abstract In this paper we use the penalty approach in order to study constrained minimization problems. A penalty function is said to have the exact penalty property if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem. We discuss very simple sufficient conditions for the exact penalty property. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
    Penalty Method
    Minification
    Constrained optimization
    Constrained optimization problem
    Citations (0)
    In this paper, a method of region expanding evenly along edge is presented, meanwhile holes can be detected as byproducts. The complexity of the algorithm is O(n), where n is the quantity of pixels in the region. The source region is selected by 5 contiguous pixels with shape "+", of which the surrounding 4 pixels constitute the original edge. For every edge segment, a pixel out of the edge is checked whether it is similar to region pixels. The region is expanded by one pixel when a positive answer is given. During expanding period, if the pixel to be checked is already an edge pixel, the edge circle is divided into two parts - the one with more pixels remains as the surrounding edge, the other is the inner edge of a hole. Expanding process will stop if no change takes place in a repetition period.
    Morphological gradient
    Citations (0)
    Abstract Numerous techniques have been proposed for handling almost all kinds of constraints in searching for solutions to constrained optimization problems. Among these methods, penalty function has been the most commonly used approach. However, a drawback of the penalty function method lies in the difficulty of setting adequate penalty factors. Thus, due to the unavailability of appropriate penalty factors, the factor-free penalty function is created to decide penalties directly by the severities of constraint violations, and is expected to capture the distance to feasibility without any user-defined factors. However, although various factor-free penalty functions have been developed, a formal comparison of these functions is short. Therefore, in order to have a clearer picture of the factor-free penalty functions and their performances, this article surveys and compares the factor-free penalty functions proposed in prior literature, and performs a numerical comparison of these (nine) functions by applying the genetic algorithm on a collection of 37 popular test problems. 對於有限最佳化的問題, 已經有許多研究提出方法來對應各式各樣的限制式以求解。 在這些方法中, 懲罰函數是最常被使用的一類。 然而懲罰函數的使用通常需搭配適當的參數, 因而成為此方法應用上的一項缺憾。 正由於適當的參數難以取得, 無參數懲罰函數於是應運而生, 藉由違反限制式的程度, 來決定一組解離合理解區域的距離。 只是, 雖然也有許多研究提出許多無參數懲罰函數, 有關這些函數的全面性績效比較卻較缺乏。 也因此, 為了對這些無參數懲罰函數的績效能有較完整的了解, 本研究探討比較既有的各種函數, 並以其中代表性的九種方法, 針對37個試驗性問題以基因演算法求解, 以比較其求解成效。 (*聯絡人: ricky_lrh@hotmail.com) Keywords: factor-free penalty functionconstraint-handling techniquenumerical comparisonconstrained optimization problemgenetic algorithmKeywords: 關鍵詞: 無參數懲罰函數; 限制式處理方法; 成效比較; 有限最佳化問題 ; 基因演算法 Notes (*聯絡人: ricky_lrh@hotmail.com)
    Penalty Method
    Factor (programming language)
    In this paper, we use the penalty approach in order to study constrained minimization problems in infinite dimensional spaces. A penalty function is said to have the exact penalty property if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem. In this paper, we establish the exact penalty property for a large class of inequality-constrained minimization problems.
    Penalty Method
    Constrained optimization
    Citations (6)
    Abstract In this paper, we present methods of penalty functions for solving constrained optimization problems. The methods that we characterize presently, attempt to approximate a constrained optimization problem with an unconstrained, one and then apply standard search techniques such as the exterior penalty function method and the interior penalty method to get solutions. The paper that follows assure exterior penalty methods recognizing that interior penalty function methods incarnate the same principles.
    Penalty Method
    Bridge (graph theory)
    Constrained optimization problem
    Constrained optimization
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    Citations (11)