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Athlete training optimization is an important part of sports management, and the scientific management program is of practical significance for athletes to improve their sports level. This paper collects sports training data for cluster analysis, establishes the optimization function of the distance from the data point to the center of the class, solves it, and determines the consistency matrix to judge the data category. Establish the column generation optimization model, get the linear programming model based on the matrix change column generation, in the process of transforming the model to solve the recursive matrix recursive relationship formula and solve the objective function. According to the solution of the optimization function to adjust the athletes’ sports training program. After the test, it was found that the pre-and post-test scores of the three tests of the experimental class were improved by 1.03 seconds, 1.05 meters, and 1.33 meters, respectively, and were significantly ahead of the scores of the control group. According to the satisfaction analysis, 76.67% of students were satisfied with the training effect. It indicates that the new training mode improved by the algorithm has good application effects.

In this paper, in the process of solving the mathematical model of sports facility optimization, the integer linear programming issue of choosing a sports facility is solved using a branch delimitation approach paired with a recursive matrix-based column-generating method. As part of the process of creating a scientific evaluation system for physical education, a hierarchical gray correlation-based evaluation model for the quality of physical education in colleges and universities is built by combining the hierarchical analysis weight-solving method and the solution method of the gray correlation degree. After the analysis, 81.1% of the teachers and students were satisfied after physical education facilities were optimized with the physical education teaching facilities. The gray correlation coefficient of physical education hardware facilities and software is 0.7, and the gray correlation coefficient of physical education effect is 0.18.

Purpose: To incorporate four‐dimensional computed tomography (4DCT)‐based ventilation imaging into intensity‐modulated radiation therapy (IMRT) treatment planning for pulmonary functional avoidance. Methods and Materials: Nineteen locally advanced lung cancer patients are retrospectively studied. 4DCT images are employed to create ventilation maps for each patient via a density‐change‐based algorithm with mass correction. The regional ventilation is directly incorporated into the mathematical formulation of a direct aperture optimization model in IMRT treatment planning to achieve functional avoidance and a voxel‐based treatment plan. The proposed functional avoidance planning and voxel‐based planning are compared to the conventional treatment planning approach purely based on the anatomy of patients. Paired sample t‐tests are conducted to see whether dosimetric differences among the three approaches are significant. Results: Similar planning target volume (PTV) coverage is achieved by anatomical, functional avoidance, and voxel‐based approaches. The voxel‐based treatment planning performs better than both functional avoidance and anatomical planning to the lung. For a total lung, the average volume reductions in a functional avoidance plan from an anatomical plan, a voxel‐based plan from an anatomical plan, and a voxel‐based plan from a functional avoidance plan are 7.0%, 16.8%, and 10.6%, respectively for V40; and 0.4%, 6.4%, and 6.0%, respectively for mean Lung Dose (MLD). For a functional lung, the reductions are 8.8%, 17.2%, and 9.2%, respectively, for fV40; and 1.1%, 6.2%, and 5.2%, respectively, for functional mean lung dose (fMLD). These reductions are obtained without significantly increasing doses to other organs‐at‐risk. All the pairwise treatment planning comparisons for both total lung and functional lung are statistically significant (p‐value <α=0.05$< \alpha =0.05$) except for the functional avoidance plan with the anatomical plan pair in which the p‐value >α=0.05$> \alpha =0.05$. From these results, we can conclude that voxel‐based treatment planning outperforms both anatomical and functional‐avoidance planning. Conclusions: We propose a treatment planning framework that directly utilizes functional images and compares voxel‐based treatment planning with functional avoidance and anatomical treatment planning. [ABSTRACT FROM AUTHOR]

• A public transit accessibility under heat exposure model is studied with time-dependent consideration. • A column generation method to urban rail-bus-walk service network integration is devised. • Experiments in Beijing show the impact of heat exposure on public transit accessibility. The evolution of urban transportation systems is increasingly driven by the integration of rail, bus, and walking pathways, forming a cohesive service network. This urban rail-bus-walk service network integration is pivotal in addressing urban challenges and ensuring seamless mobility. Nevertheless, the effectiveness of such integrated systems depends on their accessibility and the willingness of individuals to take them as their primary transportation mode. In the context of climate change, extreme heat events pose an increasing threat to passenger comfort and health, which in turn, affects individuals' decisions to use public transit. Additionally, walking to transit stops or waiting for transportation becomes more challenging during such extreme heat conditions. This paper tackles the challenge of comprehensively addressing the evolving issues related to public transit accessibility in response to rising temperatures, an area of research that has received limited attention until now. This paper introduced an approach aimed at optimizing the urban rail-bus-walk service network with a focus on both accessibility and heat exposure considerations. By calculating the transportation accessibility level under varying temperature conditions and identifying its vulnerability to high temperatures, this paper presents a methodology to enhance the transit service. Such improvement involves not only adjustments to the integration network but also considering of cooling facilities, such as shaded routes and shelters. Column generation is applied to solve this problem and the optimization result demonstrates improvement of accessibility under the extreme heat condition. [ABSTRACT FROM AUTHOR]

With the growing traffic of containerized shipping worldwide, container liners have seen increasing cooperation. Slot co-chartering has drawn wide attention as a way of cooperation within liner alliances. However, liners face the issue of finding proper measures to optimize alliance operations. In response to this, this paper comprehensively considers shipping capacity dispatch for containerized shipping companies within liner alliances. First, we explained the general rules of liner shipping dispatch and analyzed the interfering factors. Second, we created a liner shipping capacity dispatch model without consideration of slot co-chartering costs and a liner shipping capacity dispatch model with consideration of slot co-chartering costs and proposed a new column generation algorithm to solve both problems. Third, we tested our algorithm in a real case of a large Chinese containerized shipping company, which belongs to Ocean Alliance, and an optimal ship dispatch strategy on relevant routes and a decision on optimal slot chartering can be reached. Computational results indicate that the proposed column generation algorithm exhibits effective and efficient performance for large-scale slot co-chartering in liner shipping. [ABSTRACT FROM AUTHOR]