Construction of the fractional-nonlinear optimization method
Journal Title: Восточно-Европейский журнал передовых технологий - Year 2019, Vol 4, Issue 4
Abstract
<p>A method for solving the fractional nonlinear optimization problem has been proposed. It is shown that numerous inventory management tasks, on the rational allocation of limited resources, on finding the optimal paths in a graph, on the rational organization of transportation, on control over dynamical systems, as well as other tasks, are reduced exactly to such a problem in cases when the source data of a problem are described in terms of a probability theory or fuzzy math. We have analyzed known methods for solving the fractional nonlinear optimization problems. The most efficient among them is based on the iterative procedure that sequentially improves the original solution to a problem. In this case, every step involves solving the problem of mathematical programming. The method converges if the region of permissible solutions is compact. The obvious disadvantage of the method is the uncontrolled rate of convergence. The current paper has proposed a method to solve the problem, whose concept echoes the known method of fractional-linear optimization. The proposed technique transforms an original problem with a fractional-rational criterion to the typical problem of mathematical programming. The main advantage of the method, as well its difference from known ones, is the fact that the method is implemented using a single-step procedure for obtaining a solution. In this case, the dimensionality of a problem is not a limiting factor. The requirements to a mathematical model of the problem, which narrow the region of possible applications of the devised procedure, imply:</p><p>1) the components of the objective function must be separable functions;</p><p>2) the indicators for the power of all nonlinear terms of component functions should be the same.</p><p>Another important advantage of the method is the possibility of using it to solve the problem on unconditional and conditional optimization. The examples have been considered.</p>
Authors and Affiliations
Lev Raskin, Oksana Sira
Keywords
Related Articles
- EP ID EP666834
- DOI 10.15587/1729-4061.2019.174079
- Views 60
- Downloads 0
Principles of construction and identification of a multilevel system for monitoring parameters of technological cycle of casting
<p>For the creation of a multi-level system of integrated control and operational management of physical-chemical and technological casting processes, deterministic causality of technological objects was determined. Thes...
Estimation model of the diesel engine fuel system with an electromechanical device to intensify fuel supply
<p>The key directions of the development and improvement of the fuel supply system for internal combustion engines with ignition from compression of the fuel/air mixture were pointed out. The need for the comprehensive i...
Specific features of defect formation in the nSi <P> single crystals at electron irradiation
Based on measurements of infrared Fourier spectroscopy, Hall effect, and the tensor Hall-effect, we have established the nature, and determined the concentration, of the main types of radiation defects in the single crys...
Development of a technology for utilizing the electroplating wastes by applying a ferritization method to the alkalineactivated materials
The study reported in this paper reveals the effective way of recycling water treatment products by using them as a component of alkaline cements and concretes based on them. Large-scale utilization of products from wast...
Development of a formal algorithm for the formulation of a dual linear optimization problem
<p>The rigorous formal algorithm for formulating a dual problem for different forms (general, basic, standard, and canonical) of a primal linear programming problem is proposed. First, definitions of a pair of dual probl...