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Volumetric-modulated arc therapy (VMAT) treatment planning is an efficient treatment technique with a high degree of flexibility in terms of dose rate, gantry speed, and aperture shapes during rotation around the patient. However, the dynamic nature of VMAT results in a large-scale nonconvex optimization problem. Determining the priority of the tissues and voxels to obtain clinically acceptable treatment plans poses additional challenges for VMAT optimization. The main purpose of this paper is to develop an automatic planning approach integrating dose-volume histogram (DVH) criteria in direct aperture optimization for VMAT, by adjusting the model parameters during the algorithm. The proposed algorithm is based on column generation, an optimization technique that sequentially generates the apertures and optimizes the corresponding intensities. We take the advantage of iterative procedure in this method to modify the weight vector of the penalty function based on the DVH criteria and decrease the use of trial-and-error in the search for clinically acceptable plans. We evaluate the efficiency of the algorithm and treatment quality using a clinical prostate case and a challenging head-and-neck case. In both cases, we generate 15 random initial weight vectors to assess the robustness of the algorithm. In the prostate case, our methodology obtained clinically acceptable plans in all instances with only a 10% increase in the computational time, while simple VMAT optimization found just three acceptable plans. To have an idea with respect to the existing software, we compared the obtained DVH to a commercial software. The quality of the diagrams of the proposed method, especially for the healthy tissues, is significantly better while the computational time is less. In the head-and-neck case, 93.3% of the clinically acceptable plans are obtained while no plan was acceptable in simple VMAT. In sum, the results demonstrate the ability of the proposed optimization algorithm to obtain clinically acceptable plans without human intervention and also its robustness to weight parameters. Moreover, our proposed weight adjustment procedure proves to reduce the symmetry in the solution space and the time required for the post-optimization phase.

This paper presents a heuristic algorithm to schedule a hot rolling mill in the aluminum industry. One problematic issue is the tight coupling between the homogenizing furnaces and the mill, which needs to be integrated into the heuristic design. The latter also takes into account standard technological constraints like alloy hardness transitions, roll wear, homogenization code compatibilities and width transitions. The objective is to minimize the idle time on the mill and penalties for soft constraint violations related to production quality. The heuristic is divided into two phases. First, batches of ingots are constructed for the furnaces. These batches, called blocks, are then sequenced on the mill. Numerical results are reported on test instances derived from real-world data. [ABSTRACT FROM AUTHOR]

Presents a study that summarized and compared several classical and modern heuristics for the vehicle routing problem (VRP) using several criteria. Attributes of VRP heuristics; Information on the Clarke and Wright savings heuristic; Description of the Fisher and Jaikumar algorithm.