PARALLEL OPTIMIZATION TECHNOLOGY FOR ATOMIC-MOLECULAR MORSE CLUSTERS

В статье рассматриваются специализированные вычислительные технологии и алгоритмы, используемые для поиска низкопотенциальных атомно-молекулярных кластеров. Проведенные вычислительные эксперименты продемонстрировали достаточно высокую конкурентоспособность новых алгоритмов по сравнению с классическими для функций рассматриваемого типа. С использованием разработанного программного комплекса получены рекордные результаты оптимизации атомно-молекулярных кластеров Морса рекордных размерностей. The paper deals with specialized computing technology and algorithms used for finding low-potential atomic-molecular clusters. The performed computational experiments demonstrated a rather high competitiveness of the new algorithms in comparison with the classical methods for the considerable functions. Using the developed software, the applied problem of molecular docking was solved. Using the developed software package, record results for optimization of atomic-molecular Morse clusters of large dimensions have been obtained.

New Algorithm to Solve Mixed Integer Quadratically Constrained Quadratic Programming Problems Using Piecewise Linear Approximation

Techniques and methods of linear optimization underwent a significant improvement in the 20th century which led to the development of reliable mixed integer linear programming (MILP) solvers. It would be useful if these solvers could handle mixed integer nonlinear programming (MINLP) problems. Piecewise linear approximation (PLA) is one of most popular methods used to transform nonlinear problems into linear ones. This paper will introduce PLA with brief a background and literature review, followed by describing our contribution before presenting the results of computational experiments and our findings. The goals of this paper are (a) improving PLA models by using nonuniform domain partitioning, and (b) proposing an idea of applying PLA partially on MINLP problems, making them easier to handle. The computational experiments were done using quadratically constrained quadratic programming (QCQP) and MIQCQP and they showed that problems under PLA with nonuniform partition resulted in more accurate solutions and required less time compared to PLA with uniform partition.

Software tool for evaluation of reliability and survivability of complex technical system based on logical-probabilistic methodology

The paper presents solutions for estimation and analysis of complex system (CS) reliability and survivability indicators based on the logical-probabilistic approach. Modified logical-probabilistic method and software tool for evaluating the reliability and survivability of onboard equipment (OE) of small satellites were developed (SS). The correctness of the suggested method and software tool was shown by computational experiments on some systems of CS SS similar to Belarusian SS, and later compared with the “Arbitr” software complex results.

Improving the dependability of light vented foundations exposed to vibration load on frost soils

Aim. Today, dynamically-loaded foundations of process equipment often prove to be oversized with significantly overestimated values of stiffness, mass and material consumption. Therefore, reducing the costs and time of construction of gas pipeline facilities, especially on permafrost, is of relevance to PJSC Gazprom. One of the primary ways of solving this problem is installing gas pumping equipment on light vented support structures. The disadvantage of such structures is the low vibration rigidity. A method [1] is proposed for improving the vibration rigidity of a foundation subjected to vibration load. The simulation aims to improve the dependability of light vented foundations by studying vibration displacements of foundations with attached reinforced concrete panels depending on the thermal state of frost soils, parameters of the attached panels and connectors. Methods. Vibration displacements of a foundation with an attached device were identified using the finite element method and the improved computational model of the foundation – GCU – soil system. Results. Computational experiments identified the vibration displacements of the foundation in the cold and warm seasons for the following cases of reinforced concrete plates attached to the foundation: symmetrical and non-symmetrical; at different distances; through connectors with different stiffness parameters; with additional weights; frozen to the ground. Conclusions were made based on the results of simulation of vibration displacements of foundations with an attached device in cold and warm seasons. Conclusion. The presented results of computational experiments aimed at improving the vibration rigidity of light foundations by using method [1] show sufficiently good indicators of reduced vibration displacements of the foundation. Thus, in the case of symmetrical connection of four reinforced concrete panels in summer, the reduction of vibration displacements is 42.4%, while increased stiffness of the connectors, attachment of additional weights and freezing of reinforced concrete panels into the ground will allow reducing the vibration displacements of the foundation up to 2.5 times. However, it should be noted, that applying the findings in the process of development of project documentation and construction of foundations requires R&D activities involving verification and comparison of the obtained results of numerical simulation with a natural experiment.

Combining Polyhedral Approaches and Stochastic Dual Dynamic Integer Programming for Solving the Uncapacitated Lot-Sizing Problem Under Uncertainty

We study the uncapacitated lot-sizing problem with uncertain demand and costs. The problem is modeled as a multistage stochastic mixed-integer linear program in which the evolution of the uncertain parameters is represented by a scenario tree. To solve this problem, we propose a new extension of the stochastic dual dynamic integer programming algorithm (SDDiP). This extension aims at being more computationally efficient in the management of the expected cost-to-go functions involved in the model, in particular by reducing their number and by exploiting the current knowledge on the polyhedral structure of the stochastic uncapacitated lot-sizing problem. The algorithm is based on a partial decomposition of the problem into a set of stochastic subproblems, each one involving a subset of nodes forming a subtree of the initial scenario tree. We then introduce a cutting plane–generation procedure that iteratively strengthens the linear relaxation of these subproblems and enables the generation of an additional strengthened Benders’ cut, which improves the convergence of the method. We carry out extensive computational experiments on randomly generated large-size instances. Our numerical results show that the proposed algorithm significantly outperforms the SDDiP algorithm at providing good-quality solutions within the computation time limit. Summary of Contribution: This paper investigates a combinatorial optimization problem called the uncapacitated lot-sizing problem. This problem has been widely studied in the operations research literature as it appears as a core subproblem in many industrial production planning problems. We consider a stochastic extension in which the input parameters are subject to uncertainty and model the resulting stochastic optimization problem as a multistage stochastic integer program. To solve this stochastic problem, we propose a novel extension of the recently published stochastic dual dynamic integer programming (SDDiP) algorithm. The proposed extension relies on two main ideas: the use of a partial decomposition of the scenario tree and the exploitation of existing knowledge on the polyhedral structure of the stochastic uncapacitated lot-sizing problem. We provide the results of extensive computational experiments carried out on large-size randomly generated instances. These results show that the proposed extended algorithm significantly outperforms the SDDiP at providing good-quality solutions for the stochastic uncapacitated lot-sizing problem. Although the paper focuses on a basic lot-sizing problem, the proposed algorithmic framework may be useful to solve more complex practical production planning problems.

Wavelet filtering for solving the problem of selecting the outlines and analysis of the measurement results in the background of noise

Currently, the issue of developing new modern algorithms and methods is quite relevant, which will allow in an automated mode to analyze images (signals and the results of their measurements) against a background of noise. This task is relevant in the analysis and modeling of dynamic processes and objects, in the search for methods for automating their control. For the process of automating the processing of the results of computational experiments, it is important to implement the calculation of the derivatives of the first and second order against the background of noise.

CONDITIONS OF MONOTONE APPROXIMATION OF RAMSEY CURVES AND THEIR MODIFICATIONS

The algorithm for approximating the experimental data of the Ramsey curve and its modifications has been developed, which provides a monotonic increase of the approximating function in the interval [0;\infty) and an existence of a given number of inflection points. The Ramsey curve belongs to the family of logistic curves that are widely used in modeling of limited increasing processes in various subject fields. The classical Ramsey curve has two parameters and has a left constant asymmetry. It is also known that its three-parameter modification provides the possibility of displacement along the axes of ordinate. The extensive practical use of the Ramsey curve with both two and more parameters for approximating experimental dependences is restrained by the frequent loss by this curve of the logistic shape when approximating without additional restrictions on the relationships between its parameters. The article discusses modifications of the Ramsey curve with three and five parameters. The first and second derivatives of the studied modifications of the Ramsey function have a special structure. They are products of polynomial and exponential functions. This allows using Sturm's theorem on the number of polynomial roots in a given interval to control the shape of the approximating curve. It has been shown that with an increase in the number of parameters for the modified curve, the number of possible combinations of restrictions on the values of the parameters ensuring the preservation of its like shape increases significantly. The solution to the approximation problem in this case consists of solving a sequence of conditional global optimization problems with different constraints and choosing a solution that provides the smallest approximation error. Also, the studies of the accuracy of estimating the parameters of the Ramsey curve in accordance with the accuracy of the experimental data have been carried out. In order to simulate the presence of measurement errors, the values of a normally distributed random variable with a mathematical expectation equal to zero and different values of the standard deviation for different series of computational experiments were added to the values of the deterministic sequence. Computational experiments have shown a significant sensitivity of the values of the Ramsey function parameters to the measurement accuracy of experimental data.

On the node reliability of Harary graphs: an analysis through real-world topologies

The literature on network reliability shows that Harary networks are designed so that the link reliability is maximum in many cases. The following question: ``what are the best topology networks in maximizing node reliability?'' is still open. In this paper, we performed computational experiments with eleven real-world networks and their corresponding Harary graphs. The node reliability of both sets of networks was computed. Computational results point out that the Harary network has a topology with high node reliability if compared to the real-world networks studied.