OPTIMIZATION OF PARAMETERS OF POINT SOURCES OF ENERGY AT SPECIFIC PARAMETERS OF INDIVIDUAL POINTS OF THE ENERGY FIELD

Abstract

In most cases, when modeling energy fields, it is impossible to explicitly write the objective function of the energy field, and this greatly complicates the solution of a problem called nonlinear programming [1]. 
 One possible way to solve nonlinear programming problems is to transform a mathematical model into a function from a single variable or to organize an iterative process by repeatedly searching for the minimum of a function of a single variable. In this case, you can use the known iterative methods for solving the problem [1]: the method of dichotomy (the method of division in half); the method of "golden section", the Fibonacci method; polynomial approximation method; Newton's method, etc.
 Geometric problems of energy field optimization derive from the practical problems of energy conservation in the placement of equipment for heating or cooling of architectural structures, reducing the negative acoustic effects of sound energy in the entertainment halls of public buildings, lighting in interiors and exteriors. Most of these tasks are aimed at minimizing the total power of point energy sources while providing the specified parameters of the energy field.
 The target optimization function contains both steel and variable parameters (optimization parameters). The set parameters of the energy field are constant, namely: coordinates of individual points of the field and potentials at these points; the variable parameters are the coordinates of point energy sources and their power. Restrictions are the dimensions of the room or exterior.
 Solving this optimization problem involves several steps:
 - formation of a mathematical model of the energy field;
 - formation of the target optimization function based on a mathematical model;
 - choosing a method of mathematical programming to solve the problem.
 The mathematical model of the energy field in solving such an optimization problem is written in the form of a system of equations.