conditional optimization
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Borys Liubarskyi ◽  
Dmytro Iakunin ◽  
Oleh Nikonov ◽  
Dmytro Liubarskyi ◽  
Vladyslav Vasenko ◽  

This paper reports the construction of a mathematical model for determining the electromagnetic momentum of a synchronous reluctance motor with non-partitioned permanent magnets. Underlying it is the calculation of the engine magnetic field using the finite-element method in the flat-parallel problem statement. The model has been implemented in the FEMM finite-element analysis environment. The model makes it possible to determine the engine's electromagnetic momentum for various rotor geometries. The problem of conditional optimization of the synchronous reluctance motor rotor was stated on the basis of the rotor geometric criteria. As an analysis problem, it is proposed to use a mathematical model of the engine's magnetic field. Constraints for geometric and strength indicators have been defined. The Nelder-Mead method was chosen as the optimization technique. The synthesis of geometrical parameters of the synchronous reluctance motor rotor with non-partitioned permanent magnets has been proposed on the basis of solving the problem of conditional optimization. The restrictions that are imposed on optimization parameters have been defined. Based on the study results, the dependence of limiting the angle of rotation of the magnet was established on the basis of strength calculations. According to the calculation results based on the proposed procedure, it is determined that the optimal distance from the interpole axis and the angle of rotation of magnets is at a limit established by the strength of the rotor structure. Based on the calculations, the value of the objective function decreased by 24.4 % (from −847 Nm to −1054 Nm), which makes it possible to significantly increase the electromagnetic momentum only with the help of the optimal arrangement of magnets on the engine rotor. The results of solving the problem of synthesizing the rotor parameters for a trolleybus traction motor helped determine the optimal geometrical parameters for arranging permanent magnets.

2021 ◽  
Vol 82 (10) ◽  
pp. 1651-1667
M. S. Germanchuk ◽  
M. G. Kozlova ◽  
V. A. Lukianenko

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2334
Ángel Luis Muñoz Castañeda ◽  
Noemí DeCastro-García ◽  
David Escudero García

This work proposes a new algorithm for optimizing hyper-parameters of a machine learning algorithm, RHOASo, based on conditional optimization of concave asymptotic functions. A comparative analysis of the algorithm is presented, giving particular emphasis to two important properties: the capability of the algorithm to work efficiently with a small part of a dataset and to finish the tuning process automatically, that is, without making explicit, by the user, the number of iterations that the algorithm must perform. Statistical analyses over 16 public benchmark datasets comparing the performance of seven hyper-parameter optimization algorithms with RHOASo were carried out. The efficiency of RHOASo presents the positive statistically significant differences concerning the other hyper-parameter optimization algorithms considered in the experiments. Furthermore, it is shown that, on average, the algorithm needs around 70% of the iterations needed by other algorithms to achieve competitive performance. The results show that the algorithm presents significant stability regarding the size of the used dataset partition.

2021 ◽  
Vol 3 (134) ◽  
pp. 31-39
Anatolii Kosolap

Currently, test problems are used to test the effectiveness of new global optimization methods. In this article, we analyze test global optimization problems to test the numerical efficiency of methods for their solution. At present, about 200 test problems of unconditional optimization and more than 1000 problems of conditional optimization have been developed. We can find these test problems on the Internet. However, most of these test problems are not informative for testing the effectiveness of global optimization methods. The solution of test problems of conditional optimization, as a rule, has trivial solutions. This allows the parameters of the algorithms to be tuned before these solutions are obtained. In test problems of conditional optimization, the accuracy of the fulfillment of constraints is important. Often, small errors in the constraints lead to a significant change in the value of an objective function. Construction of a new package of test problems to test the numerical efficiency of global optimization methods and compare the exact quadratic regularization method with existing methods.The author suggests limiting oneself to test problems of unconstrained optimization with unknown solutions. A package of test problems of unconstrained optimization is pro-posed, which includes known test problems with unknown solutions and modifications of some test problems proposed by the author. We also propose to include in this package J. Nie polynomial functions with unknown solutions. This package of test problems will simplify the verification of the numerical effectiveness of methods. The more effective methods will be those that provide the best solutions. The paper compares existing global optimization methods with the exact quadratic regularization method proposed by the author. This method has shown the best results in solving most of the test problems. This paper presents some of the results of the author's numerical experiments. In particular, the best solutions were obtained for test problems with unknown solutions. This method allows solving multimodal problems of large dimensions and only a local search program is required for its implementation.

2021 ◽  
Vol 20 (3) ◽  
pp. 577-588
Aleksei Yu. CHUDNOVETS ◽  
Sodnom B. BAINOV

Subject. In the article, we calculate the period of a borrowing, in which the interest burden and monthly payments are minimal. Objectives. The aim is to create an algorithm to optimize the term of the mortgage loan, taking into account the amount of debt and interest rate of the loan. Methods. The study employs methods to analyze the formula of annuity payments of a mortgage loan, and to model the final optimization algorithm. Results. We developed an algorithm, to determine the optimal term of the loan, using the certain loan amount and interest rate. The study considers the case for banks, operating in Krasnoyarsk. Conclusions. The paper considers two parameters of a mortgage loan, i.e. the interest burden and the monthly payment, which is calculated, according to the annuity formula. Both parameters depend on the loan amount, the interest rate, and the period of the loan. However, the interest rate is set by the bank, so the only parameter that the borrower can change is the period of payment. By changing the term to maturity, it is possible to have a loan with minimum payments and interest burden. For the purpose of optimization, we consider both parameters simultaneously. Taking into account their versatile nature, we consider the optimal time, when payments and interest burden are minimized. The paper also reviews the case of optimization of credit parameters for construction enterprises of the Krasnoyarsk Krai, in various banks.

M. S. Germanchuk

Formalizing routing problems of many traveling salesman (mTSP) in complex networks leads to NP-complete pseudobulous conditional optimization problems. The subclasses of polynomially solvable problems are distinguished, for which the elements of the distance matrix satisfy the triangle inequality and other special representations of the original data. The polynomially solvable assignment problem can be used to determine the required number of salesmen and to construct their routes. Uses a subclass of tasks in the form of pseudobulous optimization with disjunctive normal shape (\textit{DNS}) constraints to which the task is reduced mTSP. Problems in this form are polynomially solvable and allow to combine knowledge about network structure, requirements to pass routes by agents (search procedures) and efficient algorithms of logical inference on constraints in the form of \textit{DNS}. This approach is the theoretical justification for the development of multi-agent system management leading to a solution mTSP. Within the framework of intellectual planning, using resources and capabilities, and taking into account the constraints for each agent on the selected clusters of the network, the construction of a common solution for the whole complex network is achieved.

Ulugbek Yu. Tuliev ◽  
Musulmon Ya. Lolaev ◽  

Reducing the dimension of the feature space for describing thematic documents is considered. Descriptions of documents are presented in the form of an “object-property” table, for the formation of which thematic dictionaries were developed with a volume of no more than 100 keywords for each subject area. The correctness of the formation of dictionaries is proved in the framework of the problem of the pattern recognition with disjoint classes. Results of the analysis of the topological properties of the feature space by the values of the compactness measures are used as a research tool. The values of the compactness measures are the quantitative estimation of structures in relations between objects for each class and for the sample as a whole. The structure of relationships is investigated through the division of the class objects into disjoint groups. A path always may be created based on binary relation of connectedness between any two objects of a group. The choice of the space for the description of documents is made by solving the problem of conditional optimization using the Lagrange method. The condition for the formation of an ordered sequence of features is determined. Applying of an ordered sequence is considered as a method to reduce the combinatorial complexity of the selection algorithms. When removing uninformative features from the description of documents, the value of the measure of the compactness of the sample reaches its maximum. A visual representation of the complexity of the configuration of groups and the connectivity of objects from their composition is given.

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