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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]

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Combined cooling, heating, and power (CCHP) microgrids are a special form of a microgrid that is attracting increasing attention. This study contributes to the goal of minimising the operation cost of CCHP microgrids by proposing a hierarchical two‐stage robust optimisation dispatch model for multiple CCHP microgrid systems. The uncertainties associated with wind power output, electric power, heating, and cooling loads, and transmission line failures are considered in the proposed model. Moreover, the electricity purchasing and selling prices of each microgrid are independently determined. The proposed model applies the outputs of fuel cells, energy storage devices, and gas turbines, the distribution factor of waste heat, and the power transmission between the microgrids and an external grid as control variables. The optimised dispatch problem is solved using McCormick envelopes relaxation and a novel column and constraint generation algorithm that provides enhanced optimisation performance by implementing co‐evolutionary theory. In this way, the microgrid system is divided into several sections, and each section is represented as an individual min–max–min problem. The rationality and validity of the proposed model and the superiority of the solution performance of the improved algorithm are verified through simulation case studies involving a system composed of four CCHP microgrids. [ABSTRACT FROM AUTHOR]

It is an effective way to regard the electric vehicles as the demand response for reducing the negative impact of large‐scale introduction on the power system. Aiming at the microgrid with demand response, the adaptive uncertainty sets‐based two‐stage robust optimisation method is established in this study. The coordination of micro‐gas turbine, energy storage, and demand response etc. are considered in the economic dispatch model. To effectively consider the uncertain variable contained in the microgrid, the concept of adaptive uncertainty sets is proposed in this study. The uncertainty sets are achieved by the long short‐term memory network and modified fuzzy information granulation. To handle the adaptive uncertainty sets‐based robust optimisation model, the column and constraint generation algorithm and strong duality theory are introduced to decompose the model into a master problem and a subproblem with mixed‐integer linear structure. To verify the performance of the proposed adaptive uncertainty sets‐based two‐stage robust optimisation method, measured data from a plateau city of China are introduced in the simulation test. The simulation results demonstrate the effectiveness of the model and solution strategy. [ABSTRACT FROM AUTHOR]

It is an effective way to regard the electric vehicles as the demand response for reducing the negative impact of large-scale introduction on the power system. Aiming at the microgrid with demand response, the adaptive uncertainty sets-based two-stage robust optimisation method is established in this study. The coordination of micro-gas turbine, energy storage, and demand response etc. are considered in the economic dispatch model. To effectively consider the uncertain variable contained in the microgrid, the concept of adaptive uncertainty sets is proposed in this study. The uncertainty sets are achieved by the long short-term memory network and modified fuzzy information granulation. To handle the adaptive uncertainty sets-based robust optimisation model, the column and constraint generation algorithm and strong duality theory are introduced to decompose the model into a master problem and a subproblem with mixed-integer linear structure. To verify the performance of the proposed adaptive uncertainty sets-based two-stage robust optimisation method, measured data from a plateau city of China are introduced in the simulation test. The simulation results demonstrate the effectiveness of the model and solution strategy. [ABSTRACT FROM AUTHOR]

The inverse max+sum spanning tree problem is considered by modifying the sum-cost vector under weighted l1 norm. On an undirected network G(V, E, c, w), a cost c(e) and a weight w(e) are prescribed for each edge e∈E. The max+sum spanning tree (MSST) problem is to find a spanning tree T∗ which makes the combined weight maxe∈Tw(e)+∑e∈Tc(e) as small as possible. It can be solved in O(mlogn) time, where m=|E| and n=|V|. Whereas, in an inverse MSST problem, T0 is a given spanning tree of G, which is not an optimal MSST. The sum-cost vector c is to be modified to c¯ so that T0 becomes an optimal MSST of the new network G(V,E,c¯,w). The goal is to minimize the modification cost ‖c¯-c‖1 incurred by adjusting the sum-cost vector under weighted l1 norm. The inverse MSST problem under weighted l1 norm can be formulated as a linear programming problem with exponential number of constraints. Then a column generation algorithm is proposed to solve its dual problem. It is extremely interesting that in each iteration the choice of entering variable can be determined by solving an MSST problem with new sum-cost c~. Computational experiments show that the column generation algorithm can find the optimal solutions of the inverse problem although the number of iterations as well as the running time grow fast with the increase in the size of the instance. [ABSTRACT FROM AUTHOR]

The exact solution and heuristic solution have their own strengths and weaknesses on solving the Vehicle Routing Problems with Time Windows (VRPTW). This paper proposes a hybrid Column Generation Algorithm with Metaheuristic Optimization (CGAMO) to overcome their weaknesses. Firstly, a Modified Labelling Algorithm (MLA) in the sub-problem of path searching is analysed. And a search strategy in CGAMO based on the demand of sub-problem is proposed to improve the searching efficiency. While putting the paths found in the sub-problem into the main problems of CGAMO, the iterations may fall into endless loops. To avoid this problem and keep the main problems in a reasonable size, two conditions on saving the old paths in the main problem are used. These conditions enlarge the number of constraints considered in the iterations to strengthen the limits of dual variables. Through analysing the sub-problem, we can find many useless paths that have no effect on the objective function. Secondly, in order to reduce the number of useless paths and improve the efficiency, this paper proposes a heuristic optimization strategy of CGAMO for dual variables. It is supposed to accelerate the solving speed from the view of on the dual problem. Finally, extensive experiments show that CGAMO achieves a better performance than other state-of-the-art methods on solving VRPTW. The comparative experiments also present the parameters sensitivity analysis, including the different effects of MLA in the different path selection strategies, the characteristics and the applicable scopes of the two path-keeping conditions in the main problem. [ABSTRACT FROM PUBLISHER]

Airlines' expensive resources, especially aircraft, are to be optimally scheduled to cover flights of timetables. However, the irregular flight, due to bad weather, mechanical fault and so on, is inevitable. Moreover, flight delays become more severe with the rapid development of the air transport industry in China and have huge irregular flight cost. In order to alleviate flight delays impact on the flight plan, we present a double objective multi-commodity network flow model of flight delay propagation-based aircraft scheduling and minimize the total delay propagation and airline operation cost as the optimization objective. Branch-and-price solution and column generation algorithm are used to solve the problem. Computational results obtained by using data from a major domestic airline show that our approach can reduce delay propagation significantly, thus improving on-time performance and robustness of aircraft scheduling, and decreasing the total cost simultaneously. [ABSTRACT FROM AUTHOR]

The paper presents a copula-based extension of Conditional Value-at-Risk and its application to portfolio optimization. Copula-based conditional value-at-risk (CCVaR) is a scalar risk measure for multivariate risks modeled by multivariate random variables. It is assumed that the univariate risk components are perfect substitutes, i.e., they are expressed in the same units. CCVaR is a quantile risk measure that allows one to emphasize the consequences of more pessimistic scenarios. By changing the level of a quantile, the measure permits to parameterize prudent attitudes toward risk ranging from the extreme risk aversion to the risk neutrality. In terms of definition, CCVaR is slightly different from popular and well-researched CVaR. Nevertheless, this small difference allows one to efficiently solve CCVaR portfolio optimization problems based on the full information carried by a multivariate random variable by employing column generation algorithm. [ABSTRACT FROM AUTHOR]

We propose a new dimensionality reduction method called maximum margin projection (MMP), which aims to project data samples into the most discriminative subspace, where clusters are most well-separated. Specifically, MMP projects input patterns onto the normal of the maximum margin separating hyperplanes. As a result, MMP only depends on the geometry of the optimal decision boundary and not on the distribution of those data points lying further away from this boundary. Technically, MMP is formulated as an integer programming problem and we propose a column generation algorithm to solve it. Moreover, through a combination of theoretical results and empirical observations we show that the computation time needed for MMP can be treated as linear in the dataset size. Experimental results on both toy and real-world datasets demonstrate the effectiveness of MMP. [ABSTRACT FROM AUTHOR]

The sustained and steady development of China’s economy has led to the rapid improvement of the logistics. At the same time, the rise of the e-commerce mode has given rise to a huge demand for express delivery and the express industry has entered a period of boom. Fortunately, China’s high-speed rail network has been networked, and the development of a high-speed rail express train has entered the test stage. After the high-speed rail express train is put into use, it could effectively relieve the pressure of highway transportation and significantly reduce transport pollution. To make better use of high-speed rail transport resources and give full play to its green and efficient advantages, this study established a two-stage model of a high-speed rail express train operation plan. In the first stage, a train candidate set generation model aiming for the minimum total cost of train operation was established that considered the high-speed line carrying capacity, section flow capacity, and OD requirement satisfaction constraints, which reduces the scale of train spare parts and improves the efficiency of solution. In addition, a column generation algorithm was designed to solve the model. In the second stage, an accurate flow distribution model aiming for the optimal economic efficiency was established, and then the high-speed express train operation plan was designed completely. The computational results are encouraging and demonstrate the effectiveness of the model and solution method. [ABSTRACT FROM AUTHOR]