Pub Date : 2017-12-25DOI: 10.24108/mathm.0617.0000090
Максим Константинович Сахаров, А. В. Поноренко
In solving practically significant problems of global optimization, the objective function is often of high dimensionality and computational complexity and of nontrivial landscape as well. Studies show that often one optimization method is not enough for solving such problems efficiently - hybridization of several optimization methods is necessary. One of the most promising contemporary trends in this field are memetic algorithms (MA), which can be viewed as a combination of the population-based search for a global optimum and the procedures for a local refinement of solutions (memes), provided by a synergy. Since there are relatively few theoretical studies concerning the MA configuration, which is advisable for use to solve the black-box optimization problems, many researchers tend just to adaptive algorithms, which for search select the most efficient methods of local optimization for the certain domains of the search space. The article proposes a multi-memetic modification of a simple SMEC algorithm, using random hyper-heuristics. Presents the software algorithm and memes used (Nelder-Mead method, method of random hyper-sphere surface search, Hooke-Jeeves method). Conducts a comparative study of the efficiency of the proposed algorithm depending on the set and the number of memes. The study has been carried out using Rastrigin, Rosenbrock, and Zakharov multidimensional test functions. Computational experiments have been carried out for all possible combinations of memes and for each meme individually. According to results of study, conducted by the multi-start method, the combinations of memes, comprising the Hooke-Jeeves method, were successful. These results prove a rapid convergence of the method to a local optimum in comparison with other memes, since all methods perform the fixed number of iterations at the most. The analysis of the average number of iterations shows that using the most efficient sets of memes allows us to find the optimal solution for the less number of iterations in comparison with the less efficient sets. It should be additionally noted that there is no dependence of the total number of the algorithm iterations on the number of memes used. The study results demonstrate that the Hooke-Jeeves method proved to be the most efficient for the chosen functions, since its presence in a set of memes allows a significantly improving quality of the solution obtained. At the same time, the results of statistical tests show that the use of additional methods in a set of memes often has no significant effect on the results of the algorithm.
{"title":"Исследование эффективности мульти-меметического алгоритма эволюции разума","authors":"Максим Константинович Сахаров, А. В. Поноренко","doi":"10.24108/mathm.0617.0000090","DOIUrl":"https://doi.org/10.24108/mathm.0617.0000090","url":null,"abstract":"In solving practically significant problems of global optimization, the objective function is often of high dimensionality and computational complexity and of nontrivial landscape as well. Studies show that often one optimization method is not enough for solving such problems efficiently - hybridization of several optimization methods is necessary. One of the most promising contemporary trends in this field are memetic algorithms (MA), which can be viewed as a combination of the population-based search for a global optimum and the procedures for a local refinement of solutions (memes), provided by a synergy. Since there are relatively few theoretical studies concerning the MA configuration, which is advisable for use to solve the black-box optimization problems, many researchers tend just to adaptive algorithms, which for search select the most efficient methods of local optimization for the certain domains of the search space. The article proposes a multi-memetic modification of a simple SMEC algorithm, using random hyper-heuristics. Presents the software algorithm and memes used (Nelder-Mead method, method of random hyper-sphere surface search, Hooke-Jeeves method). Conducts a comparative study of the efficiency of the proposed algorithm depending on the set and the number of memes. The study has been carried out using Rastrigin, Rosenbrock, and Zakharov multidimensional test functions. Computational experiments have been carried out for all possible combinations of memes and for each meme individually. According to results of study, conducted by the multi-start method, the combinations of memes, comprising the Hooke-Jeeves method, were successful. These results prove a rapid convergence of the method to a local optimum in comparison with other memes, since all methods perform the fixed number of iterations at the most. The analysis of the average number of iterations shows that using the most efficient sets of memes allows us to find the optimal solution for the less number of iterations in comparison with the less efficient sets. It should be additionally noted that there is no dependence of the total number of the algorithm iterations on the number of memes used. The study results demonstrate that the Hooke-Jeeves method proved to be the most efficient for the chosen functions, since its presence in a set of memes allows a significantly improving quality of the solution obtained. At the same time, the results of statistical tests show that the use of additional methods in a set of memes often has no significant effect on the results of the algorithm.","PeriodicalId":436153,"journal":{"name":"Matematika i Matematičeskoe Modelirovanie","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115843895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.7463/MATHM.0416.0850749
Array Ю. Баркин
The paper deals with development of the theory of perturbed rotational motion of a celestial body with variable geometry of the masses. Its main task is to study the impact of annual and semi-annual variations of the Earth's mass geometry (a component of its inertia tensor), as well as a component of its relative angular momentum, on the movement of the Earth's poles and its axial rotation. The body is considered to be a free (isolated), and the problem formulation corresponds to the classical Liouville problem on rotation of a variable body. Euler conical movement of the axially symmetric body with an arbitrary constant half-angle is assumed as the unperturbed motion. In the classical theory of the Earth's rotation this angle is usually assumed to be zero. In the last 20 years, accuracy to determine the Earth rotation parameters owing to using methods of space geodesy and method of Very Long Baseline Interferometry (VLBI) has increased by about three orders of magnitude and has made about i.e., in angle measure it is about 10 - 20 arc-microseconds. According to experts, the theory of the Earth's rotation with such precision is not created yet. The paper is focused just on the new dynamic studies of the Earth rotation at a higher level of accuracy than has been done in previous studies, using a new approach to the problem, based on the new forms of the equations of motion (in the Andoyer variables) and the analytical methods of perturbation theory (small parameter method). The problem of perturbed rotational motion with variable geometry and variable mass relative angular momentum in the first approximation is solved in Andoyer variables and projections of the angular velocity of the planet rotation. The analytical solution allows us to run applications to study dynamic effects from above factors for various bodies in the solar system, including the Earth. The solution allowed us to obtain the following parameters of the fundamental effects in the Earth's rotation: the annual and semi-annual fluctuations of the axis pole of Earth's rotation, annual and semiannual variations in the axial Earth's rotation. The theoretical values of the parameters are in good agreement with modern observation data of the Earth's rotation and the cyclical variations in the geo-potential coefficients.
{"title":"Динамические эффекты во вращении Земли, вызванные годовыми и полугодовыми циклическими перераспределениями масс планеты","authors":"Array Ю. Баркин","doi":"10.7463/MATHM.0416.0850749","DOIUrl":"https://doi.org/10.7463/MATHM.0416.0850749","url":null,"abstract":"The paper deals with development of the theory of perturbed rotational motion of a celestial body with variable geometry of the masses. Its main task is to study the impact of annual and semi-annual variations of the Earth's mass geometry (a component of its inertia tensor), as well as a component of its relative angular momentum, on the movement of the Earth's poles and its axial rotation. The body is considered to be a free (isolated), and the problem formulation corresponds to the classical Liouville problem on rotation of a variable body. Euler conical movement of the axially symmetric body with an arbitrary constant half-angle is assumed as the unperturbed motion. In the classical theory of the Earth's rotation this angle is usually assumed to be zero. In the last 20 years, accuracy to determine the Earth rotation parameters owing to using methods of space geodesy and method of Very Long Baseline Interferometry (VLBI) has increased by about three orders of magnitude and has made about i.e., in angle measure it is about 10 - 20 arc-microseconds. According to experts, the theory of the Earth's rotation with such precision is not created yet. The paper is focused just on the new dynamic studies of the Earth rotation at a higher level of accuracy than has been done in previous studies, using a new approach to the problem, based on the new forms of the equations of motion (in the Andoyer variables) and the analytical methods of perturbation theory (small parameter method). The problem of perturbed rotational motion with variable geometry and variable mass relative angular momentum in the first approximation is solved in Andoyer variables and projections of the angular velocity of the planet rotation. The analytical solution allows us to run applications to study dynamic effects from above factors for various bodies in the solar system, including the Earth. The solution allowed us to obtain the following parameters of the fundamental effects in the Earth's rotation: the annual and semi-annual fluctuations of the axis pole of Earth's rotation, annual and semiannual variations in the axial Earth's rotation. The theoretical values of the parameters are in good agreement with modern observation data of the Earth's rotation and the cyclical variations in the geo-potential coefficients.","PeriodicalId":436153,"journal":{"name":"Matematika i Matematičeskoe Modelirovanie","volume":"147 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123281397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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