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Solvability of Quasilinear Integral–Algebraic Equations

Journal of Mathematical Sciences (United States) 2024年第6期279卷 756-762页

作者： Bulatov, Mikhail Solovarova, Liubov Matrosov Institute for System Dynamics and Control Theory SB RAS 134 Lermontova St Irkutsk 664033 Russian Federation

We study quasilinear systems of integral equations that are linear with respect to the principal part and nonlinear with respect to the integral term. We formulate sufficient conditions for the local existence of a unique smooth solution to such a system in terms of matrix pencils and provide some examples. We study quasilinear systems of integral equations that are linear with respect to the principal part and nonlinear with respect to the integral term. We formulate sufficient conditions for the local existence of a unique smooth solution to such a system in terms of matrix pencils and provide some examples. © Springer Nature Switzerland AG 2024.

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A Three-Stage Numerical Approach to the Study of Extra-Large Atomic-Molecular Clusters 15th

A Three-Stage Numerical Approach to the Study of Extra-La...

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15th International Conference on Optimization and Applications, OPTIMA 2024

作者： Gornov, Alexander Anikin, Anton Sorokovikov, Pavel Zarodnyuk, Tatiana Matrosov Institute for System Dynamics and Control Theory of SB RAS Lermontov Str. 134 Irkutsk664033 Russia

ISBN: (纸本)9783031791185

The article discusses a novel approach for optimizing atomic-molecular structures in extra-large clusters, focusing on reducing computational complexity and applying parallel computing techniques. A three-stage computation process is outlined, offering benefits over traditional algorithms by efficiently navigating through multi-extremal optimization challenges. The software, based on this methodology, demonstrated high efficacy in solving complex molecular dynamics problems. When comparing the outcomes with experimental data, no significant deviations from the expected patterns in potential values were detected. The developed three-stage numerical approach proved instrumental in solving optimization tasks for extra-large atomic-molecular systems. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Molecular dynamics

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On a Global Search in Bilevel Optimization Problems with a Bimatrix Game at the Lower Level 23rd

On a Global Search in Bilevel Optimization Problems with ...

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23rd International Conference on Mathematical Optimization theory and Operations Research, MOTOR 2024

作者： Orlov, Andrei V. Matrosov Institute for System Dynamics and Control Theory of SB of RAS Irkutsk Russia

ISBN: (纸本)9783031627910

This paper addresses one class of bilevel optimization problems (BOPs) with an equilibrium at the lower level (in optimistic statement). Namely, we study BOPs with a convex quadratic optimization problem under linear constraints at the upper level and with a parametric non-normalized bimatrix game at the lower one, where we need to find a Nash equilibrium. In order to construct numerical methods for the problem in question, first, we transform the original bilevel problem into a single-level nonconvex optimization problem by replacing the lower level with its optimality conditions. Then we apply the Exact Penalization theory and Global Search theory (GST) to the resulting problem. According to the standard research of nonconvex problems by the GST, we construct the d.c. representations of all nonconvex functions from the original statement (into the differences of two convex functions), formulate the Global Optimality Conditions in terms of reduced penalized problem, and develop local and global search method taking into account the specific of problem in question. The main feature of the developed methods consists in the possibility of varying the penalty parameter within the methods themselves. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

关键词： Numerical methods

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Modeling Agent Behavior in Interacting Microgrids 10

Modeling Agent Behavior in Interacting Microgrids

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10th International Conference on Information Technology and Nanotechnology, ITNT 2024

作者： Bychkov, Igor Feoktistov, Alexander Chekan, Mikhail Matrosov Institute For System Dynamics And Control Theory Of Sb Ras Irkutsk Russia

ISBN: (纸本)9798350372939

We propose the agent-based approach to intellectualize data processing and analysis in modeling the operations of interconnected microgrids. Microgrids are modern energy systems with a large share of environmentally friendly and resource-saving equipment. The modeling of different aspects for the organization and operation of microgrids is relevant for their structural and parametric optimization. The study of these aspects in the interaction of microgrids deserves special attention. In this case, it becomes possible to take into account the synergistic effect in the distribution and consumption of electric power. We implement the modeling process using a multi-agent system. In this regard, we describe the structure of this system, methods of its construction, and goals and processes of agent operations. In addition, we provide a model of agent behavior developed based on the basis of a finite-state control machine. The advantages of the proposed approach are demonstrated on a model example of balancing generation and consumption of electric power. © 2024 IEEE.

关键词： Balancing

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dynamics of Bipartite Logical Networks 47

Dynamics of Bipartite Logical Networks

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47th ICT and Electronics Convention, MIPRO 2024

作者： Oparin, G.A. Bogdanova, V.G. Pashinin, A.A. Matrosov Institute For System Dynamics And Control Theory Of Sb Ras Irkutsk Russia

ISBN: (纸本)9798350382495

Based on the Boolean constraints method several problems of qualitative analysis of bipartite logical networks are solved. The dynamics of the trajectories behavior of these networks is studied over a finite time interval. A method is proposed for splitting a bipartite trajectory into two independent trajectories based on deterministic block-sequential updating of the state vectors of each part. Conditions for the existence, isolation and attraction of cyclic trajectories of a given length are obtained as Boolean constraints. The solvability of such equations reduces to the well-known Boolean satisfiability problem, effectual algorithms for solving which provide dynamic analysis for systems with high dimensionality of the state vector over large discrete time intervals. The program modules implementation for building Boolean constraints and checking their feasibility in the form of microservices ensures their reuse, simplification of deployment, updating, and high scalability in the cloud environment. Multi-agent computation management in an applied microservices package provides the non-procedural problem formulation on a distributed model of the subject area, forms and executes a scheme for solving it, and automates the additional resources provision. The practical significance of the obtained results consists in providing the opportunity for a more detailed study of dynamics of the molecular features of gene regulation networks. © 2024 IEEE.

关键词： Trajectories

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Numerical Investigation of the Swarm Intelligence Algorithm Obtained Using ChatGPT for Univariate Global Optimization 23rd

Numerical Investigation of the Swarm Intelligence Algorithm ...

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23rd International Conference on Mathematical Optimization theory and Operations Research, MOTOR 2024

作者： Sorokovikov, Pavel Gornov, Alexander Zarodnyuk, Tatiana Matrosov Institute for System Dynamics and Control Theory of SB RAS Lermontov Str. 134 Irkutsk664033 Russia

ISBN: (纸本)9783031733642

This paper explores the possibility of designing an efficient global optimization algorithm using an artificial intelligence chatbot, ChatGPT. The main idea is to use the swarm intelligence metaheuristic method, which operates on a set of particles in a swarm, to solve non-local univariate search problems. Testing was carried out on a set of one-dimensional non-convex functions with varying numbers of local optima. The results demonstrate that this algorithm can be used to solve multi-extremal optimization problems. The paper presents the results of a numerical study on the properties of this algorithm in comparison with the Piyavsky method, the Strongin method, and a combination of the Strongin with the Parabolas methods. The performed computational experiments testify to the suitability of the obtained swarm intelligence algorithm for solving univariate non-local search problems. This approach can also be useful for solving auxiliary optimization problems and for developing multimethod computational technologies. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

关键词： Optimization algorithms

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Binary Dynamic Models of Structural Synthesis of Programs 46

Binary Dynamic Models of Structural Synthesis of Programs

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46th ICT and Electronics Convention, MIPRO 2023

作者： Oparin, G.A. Bogdanova, V.G. Pashinin, A.A. Matrosov Institute for System Dynamics and Control Theory of SB RAS Irkutsk Russia

ISBN: (纸本)9789532331042

In this paper, we propose a matrix-vector Boolean differential model for constructing plans of computational actions in solving non-procedural problems on a computational model of a modular software system. The conditions of the problem of structural synthesis of a program from pre-implemented modules are formulated as a system of Boolean differential equations, the solutions of which, under given initial conditions (consistent with the non-procedural formulation of the problem), determine the solvability of the problem and give constructive plans for its solution (including parallel ones). The proposed method of structural synthesis is focused on high-dimensional models. It allows highly efficient software implementation due to the high parallelism of performing vector-matrix operations on binary vectors at the level of machine instructions. The developed model is used for planning computations in packages of applied microservices based on the HPCSOMAS-MSC platform. © 2023 MIPRO Croatian Society.

关键词： Differential equations

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Efficient Heuristics for a Partial Set Covering Problem with Mutually Exclusive Pairs of Facilities 1

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7th International Conference on Optimization, Simulation and control, COSC 2022

作者： Belykh, Aleksander Gruzdeva, Tatyana Ushakov, Anton Vasilyev, Igor Matrosov Institute for System Dynamics and Control Theory of SB RAS Irkutsk Russia

ISBN: (数字)9783031412295

ISBN: (纸本)9783031412288

Set cover problems are among the most popular and well-studied models in facility location. In this paper, we address an extension of the set covering and partial set covering problems. We suppose that a set of customers to be served is divided into two non-overlapped subsets: "mandatory" customers who must always be covered and "optional" customers who do not require obligatory coverage. To avoid a trivial solution that covers only customers from H, we suppose that the number of covered optional customers must be at least larger than a pre-defined threshold In the real world, local laws may prohibit location of a large number of facilities in some places to reduce harm to people and/or nature. To reflect that fact our problem involves pairs of facilities that are mutually exclusive, hence if a facility from such a pair is located, another one is prohibited. We formulate this problem as an integer linear program and develop and implement several fast heuristic approaches capable of finding high-quality solutions of large-scale problem instances arisen in real-life settings. In particular, we develop a hybrid heuristic involving a greedy algorithm and local search embedded into a variable neighborhood framework. We test our algorithms in a series of intensive computational experiments on both real-life problems and synthetically generated instances. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.

关键词： Location

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Semi-supervised K-Means Clustering via DC Programming Approach 22nd

Semi-supervised K-Means Clustering via DC Programming Appro...

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22nd International Conference on Mathematical Optimization theory and Operations Research, MOTOR 2023

作者： Gruzdeva, Tatiana V. Ushakov, Anton V. Matrosov Institute for System Dynamics and Control Theory of SB RAS 134 Lermontov str. Irkutsk664033 Russia

ISBN: (纸本)9783031353048

Though clustering is related to unsupervised machine learning and does not require any prior information on data items, in many real-life settings, there may be some expert knowledge on data labels or the properties of clusters known in advance. Obviously, such knowledge may be used to guide clustering process and improve the quality of found partitions. The clustering problems that involve some additional information on tags are called semi-supervised or constrained clustering problems. One distinguishes instance-level and cluster-level constraints usually formalized as the so-called must-link and cannot-link constraints or minimum/maximum cluster size. In this paper, we consider the constrained minimum sum-of-squares (k-means) clustering (MSSC) problem that incorporates both instance- and cluster-level constraints. As far as we know, such a semi-supervised MSSC problem has not been considered in the literature yet. We formulate this clustering problem and some of its particular cases as DC (difference of convex) optimization problems. Then, we develop a solution approach based on a special local search method. We carry out computational experiments on test problem instances demonstrating the efficiency of the proposed solution approach. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： K-means clustering

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On Active-Set Methods for Quadratic Problems with Positive Semidefinite Matrices 23rd

On Active-Set Methods for Quadratic Problems with Positive...

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23rd International Conference on Mathematical Optimization theory and Operations Research, MOTOR 2024

作者： Vasiliev, Igor Gruzdeva, Tatiana Barkova, Mariia Boyarkin, Denis Iakubovskii, Dmitrii Matrosov Institute for System Dynamics and Control Theory of SB RAS 134 Lermontov str. Irkutsk664033 Russia Melentiev Energy Systems Research Institute of SB RAS 130 Lermontov str. Irkutsk664033 Russia

ISBN: (纸本)9783031733642

Quadratic programming problems (QP) arise in a vast variety of real-world applications in finance, engineering, operational research, and many other fields. A huge number of methods and their various modifications have been developed for solving convex QPs. One of the first algorithms popularized as the solution method for QPs was the active-set method. The main idea of the method is selection of a set of binding constraints (an active set) and then iteratively adaptation it by adding and dropping constraints from the index set. The dual active-set (DAS) method of Goldfarb and Idnani is still well-known to be efficient and numerically stable. Taking advantage of the fact that the unconstrained minimum of the objective function can be used as a starting point of the method, its implementation utilizes the Cholesky and QR factorizations and procedures for updating them. At the same time, it suffers from the restriction that it cannot be applied to problems with positive semidefinite objective matrices, whereas in practice optimization problems may often be of such structure. We propose an add-in to the method of Goldfarb and Idnani that allows solving problems with positive semidefinite matrices directly by the DAS algorithm with a warm-start where a good estimate of the optimal active set is used to start the algorithm. The proposed technique is based on the well-known possibility of representing any matrix, as a difference of two, positive definite ones and solving then a sequence of so-called partially linearized problems. It can be viewed as a particular case of the special local search method for DC minimization problems. A computational experiment to testing the proposed approach was carried out on QPs with positive semidefinite objective matrices from the Maros and Meszaros test set. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

关键词： Iterative methods

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