Abstract
The article discusses the problems of energy-saving, which can be solved by using mathematical optimization methods, and the mathematical optimization algorithms related to these problems. There has been given the review of Russian and foreign works on energy saving and energy optimization. The need for solving the problems of optimizing the thermohydraulic regimes of buildings is explained. There is given the mathematical formulation of the problem of optimizing the temperature regime of indoor areas using adjustable devices and two methods for solving the problem: the directed search method and the genetic algorithm. The above algorithms including the mathematical apparatus are described. The objective function is described as the standard deviation of the temperature of the heated rooms. Various options for using the genetic algorithm have been investigated. A modification of the genetic algorithm is proposed, which allows obtaining the best results in relation to the problem under consideration. The results of a computation experiment for the considered optimization methods are presented. The calculations were carried out for a typical building in Izhevsk under average design conditions, taking into account the actual condition of the enclosing structures, the heating system of the building, and heating devices of indoor areas. 
 A comparative analysis of the convergence of the iterative process for various options for the application of the genetic algorithm and directional search has been carried out. It is concluded that the new modification allows us to improve the quality of the genetic algorithm. The dependence of the convergence of the genetic algorithm on its parameters was investigated and a modification of this algorithm was proposed in relation to the problem of optimizing the thermo-hydraulic modes of heated rooms. The study is of practical value in terms of using the proposed methodology of saving heat energy in the system of housing and communal services.Practical value is the ability to use in the housing and communal services to save thermal energy.
Highlights
The article discusses the problems of energy-saving, which can be solved by using mathematical optimization methods, and the mathematical optimization algorithms related to these problems
There is given the mathematical formulation of the problem of optimizing the temperature regime of indoor areas using adjustable devices and two methods for solving the problem: the directed search method and the genetic algorithm
The objective function is described as the standard deviation of the temperature of the heated rooms
Summary
Приводится математическая постановка задачи оптимизации температурного режима помещений с помощью регулируемых устройств, а также два метода решения поставленной задачи: метод направленного поиска и генетический алгоритм. Исследована зависимость сходимости генетического алгоритма от его параметров и предложена модификация данного алгоритма применительно к задаче оптимизации термогидравлических режимов отапливаемых помещений. В. Исследование характеристик генетического алгоритма, применяемого для оптимизации температурного режима отапливаемых помещений // Вестник Астраханского государственного технического университета. Несмотря на многообразие решений в области энергосбережения, проблема устранения температурного дисбаланса рассмотрена недостаточно и в настоящий момент является актуальной, в связи с чем исследование алгоритмов оптимизации температурных режимов отапливаемых помещений является актуальной задачей. Сопротивление клапанов влияет на расход теплоносителя xпр в данном тепловом приборе, а следовательно, на поток тепловой энергии от радиатора Qпр , который пропорционален его нагревательной площади Fпр , и зависит от температуры воздуха в помещении tв. Температура в помещении tвi определяется путем решения системы нелинейных уравнений теплового баланса, отдельно для каждого i-го помещения [3]:
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