Vector Optimization w.r.t. Relatively Solid Convex Cones in Real Linear Spaces

In vector optimization, it is of increasing interest to study problems where the image space (a real linear space) is preordered by a not necessarily solid (and not necessarily pointed) convex cone. It is well-known that there are many examples where the ordering cone of the image space has an empty (topological/algebraic) interior, for instance in optimal control, approximation theory, duality theory. Our aim is to consider Pareto-type solution concepts for such vector optimization problems based on the intrinsic core notion (a well-known generalized interiority notion). We propose a new Henig-type proper efficiency concept based on generalized dilating cones which are relatively solid (i.e., their intrinsic cores are nonempty). Using linear functionals from the dual cone of the ordering cone, we are able to characterize the sets of (weakly, properly) efficient solutions under certain generalized convexity assumptions. Toward this end, we employ separation theorems that are working in the considered setting.

DEVELOPMENT OF A METHODOLOGYFOR DETERMINING THE BEST OPTION FOR THE ROUTE OF THE HEAT NETWORK AT THE INITIAL DESIGN STAGE

Statement of the problem. Choosing the best option for the route of the thermal network at the initial stage of design is a complex multifactorial task, in addition, due to the lack of a number of necessary design calculations, its solution is accompanied by a limited set of initial data. Thus, it becomes relevant to develop a new methodology for designing the optimal route of the heat supply system considering the qualitative and quantitative characteristics of the discussed object.Results. A mathematical model of a generalized additive vector optimality criterion has been developed, taking into account the material consumption of the heat network, its reliability, construction time, annual thermal losses, heat turnover and temperature dispersion at the consumer. A method is proposed for determining the best option for the route of a thermal network at the initial design stage by jointly solving the optimization problem using vector optimization and matrix generalization methods. The expediency of the joint application of the methods of pairwise comparison and vector optimization in solving the problem under consideration is noted.Conclusions. An important characteristic of the developed mathematical model of the generalized criterion is the possibility of obtaining a more accurate solution to the optimization problem under consideration with an uneven distribution of the heat load by means of a biased estimate of the temperature variance among consumers. A combination of the methods of matrix generalization, pairwise comparison and vector optimization can improve the accuracy of the calculation while solving the optimization problem of choosing the best route of the thermal network.

Design and Optimization of Parallel Algorithm for Kalman Filter on SW26010 Many-Core Processors

Kalman filter algorithm, an effective data processing algorithm, has been widely used in space monitoring, wireless communications, tracking systems, financial industry, big data and so on. On Sunway TaihuLight platform, we present an optimized Kalman filter parallel algorithm which is according to new architecture of the SW26010 many-core processors (260 cores) and new programming mode (master and slave heterogeneous collaboration mode). Furthermore, we propose a pipelined parallel mode for Kalman filter algorithm based on seven-level pipeline of SW26010 processor. The vector optimization strategy and double buffering mechanisms are provided to improve parallel efficiency of Kalman filter parallel algorithm on SW26010 processors. The vector optimization strategy can improve data concurrency in parallel computing. In addition, the communication time can be hidden by double buffering mechanisms of SW26010 processors. The experimental results show that the performance and scalability of the parallel Kalman filter algorithm based on SW26010 are greatly improved compared with the CPU algorithm for five data sets, and is also improved compared to the algorithm on GPU.

Development of a Methodology for Determining the Best Option for the Route of the Heat Network at the Initial Design Stage

Постановка задачи. Выбор наилучшего варианта трассы тепловой сети на начальном этапе проектирования является сложной многофакторной задачей, кроме того, ввиду отсутствия ряда необходимых конструктивных расчетов ее решение сопровождается ограниченностью набора исходных данных. Таким образом, становится актуальной разработка новой методики проектирования оптимальной трассы системы теплоснабжения, учитывающей качественные и количественные характеристики рассматриваемого объекта. Результаты. Разработана математическая модель обобщенного аддитивного векторного критерия оптимальности, учитывающая материалоемкость тепловой сети, ее надежность, время строительства, годовые тепловые потери, оборот теплоты и дисперсию температуры у потребителя. Предложен способ определения наилучшего варианта трассы тепловой сети на начальном этапе проектирования путем совместного решения задачи оптимизации методами векторной оптимизации и матричного обобщения. Отмечена целесообразность совместного применения методов попарного сравнения и векторной оптимизации при решении рассматриваемой задачи. Выводы. Важной характеристикой разработанной математической модели обобщенного критерия является возможность получения более точного решения рассматриваемой оптимизационной задачи при неравномерным распределении тепловой нагрузки посредством смещенной оценки дисперсии температуры у потребителей. Совместное применение методов матричного обобщения, попарного сравнения и векторной оптимизации позволяет повысить точность расчета при решении оптимизационной задачи выбора наилучшей трассы тепловой сети. Statement of the problem. Choosing the best option for the route of the thermal network at the initial stage of design is a complex multifactorial task, in addition, due to the lack of a number of necessary design calculations, its solution is accompanied by a limited set of initial data. Thus, it becomes relevant to develop a new methodology for designing the optimal route of the heat supply system, taking into account the qualitative and quantitative characteristics of the object under consideration. Results. A mathematical model of a generalized additive vector optimality criterion has been developed, taking into account the material consumption of the heat network, its reliability, construction time, annual thermal losses, heat turnover and temperature dispersion at the consumer. A method is proposed for determining the best option for the route of a thermal network at the initial design stage by jointly solving the optimization problem using vector optimization and matrix generalization methods. The expediency of the joint application of the methods of pairwise comparison and vector optimization in solving the problem under consideration is noted. Conclusions. An important characteristic of the developed mathematical model of the generalized criterion is the possibility of obtaining a more accurate solution to the optimization problem under consideration with an uneven distribution of the heat load by means of a biased estimate of the temperature variance among consumers. The combined application of the methods of matrix generalization, pairwise comparison and vector optimization can improve the accuracy of the calculation when solving the optimization problem of choosing the best route of the thermal network.