I. V. Sergienko’s research while affiliated with V.M. Glushkov Institute of Cybernetics and other places

Introduction. The quadratic assignment problem is a well-established NP-hard problem in combinatorial optimization with applications in diverse fields like economics, archaeology, and chemistry. Due to its complexity, research on efficient solution methods remains active, including efforts for parallelization on multiprocessor computing systems. However, effective parallel algorithms are crucial to fully leverage these computational resources. In this context, algorithm unions (portfolios and teams) play a significant role in achieving parallel execution for solving such problems. Research objectives. This work investigates the application of portfolios constructed from modifications of the repeated iterated tabu search algorithm to the quadratic assignment problem. The effectiveness of these portfolios was evaluated through experimental computations. Results. The portfolios, derived from modifications of the repeated iterated tabu search algorithm, were applied to the quadratic assignment problem. For the most demanding test instances, the proposed algorithms were evaluated on the SCIT-4 supercomputer, alongside previously published results from the authors, confirming their competitive performance. Additionally, we assessed the parallel efficiency of these portfolios in solving instances of the quadratic assignment problem. The results demonstrate their ability to accelerate the optimization process (with speedup dependent on problem size and utilized processors), enabling the solution of large-scale problems. Conclusions. The conducted studies demonstrate that employing algorithm portfolios significantly accelerates the solution process for the quadratic assignment problem. Analysis of the results reveals a near-linear speedup factor achieved by the portfolio. For the challenging test instance tai100a, a new best solution value of 21040996 was obtained using a portfolio of 16 algorithms. Keywords: quadratic assignment problem, algorithm portfolios, experimental research, algorithm portfolios efficiency.

Physical and medical rehabilitation in Ukraine has been experiencing a period of intensive development in recent years. The focus of the monograph is on one of the most urgent medical challenges globally – the rising incidence and mortality rates of oncological diseases, which rank second only to heart diseases both in Ukraine and worldwide. Breast cancer remains the most prevalent malignancy, thus the work places a special emphasis on it. Information and communication technologies have significantly contributed to the development of the field of rehabilitation medicine, particularly its telerehabilitation sector. A distinctive feature of the proposed information technology and the corresponding system architecture is the integration of artificial intelligence methods with precise mathematical optimization techniques for methodologies and the entire telerehabilitation process. The book is intended for specialists in the field of applied intelligent technologies in medicine, as well as professionals in healthcare and rehabilitation, including tele- and psychological rehabilitation.

This paper considers algorithm unions (portfolios and teams) of optimization algorithms, their properties, and their impact on the acceleration of the optimization process. The authors have investigated the application of unions of global equilibrium search algorithms to specific discrete optimization problems and various information exchange schemes within algorithm teams. They devoted significant attention to experimental research of developed portfolios and algorithm teams in real-time mode using the multi-processor computing complex SCIT-4 at the V. M. Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine and to their comparative analysis. The authors have obtained estimates of the efficiency of algorithm unions, indicating that the team approach has significant advantages over algorithm portfolios.

This paper considers the planning of logistics missions of hybrid transport systems, which include a car or other vehicle that can move from a base to other locations along a designated route, carrying one unmanned aerial vehicle (UAV). A meaningful formulation and mathematical models of optimization problems of distributing objects to bases, selecting bases, and generating UAV routes during the inspection of maintenance of a given set of objects in the presence of flight resource constraints are proposed. We have developed an algorithm based on ant colony optimization to solve the resulting combinatorial optimization problems. We present the results of a computational experiment.

Introduction. The significance of methods and algorithms for solving discrete optimization problems in mathematical supporting computer technologies of diverse levels and objectives is increasing. Consequently, the efficacy of discrete optimization methods deserves particular attention, as it drives the advancement of techniques capable of solving complex real-world problems. This paper introduces the Global Equilibrium Search (GES) method as a highly effective approach for solving Boolean programming problems, thus contributing to the field's progress and applicability. Purpose. We describe the successful application of the approximate probabilistic GES method for effectively solving various Boolean programming problems. Results. This paper explores the application of sequential GES algorithms for solving Boolean linear, Boolean quadratic programming, and other related problems with their specific characteristics. In our study, we conducted a comparative analysis to assess the effectiveness of GES algorithms by evaluating them against state-of-the-art approaches. Additionally, to parallelize the optimization process for discrete programming problems, we introduced algorithm unions, specifically portfolios, and teams. The efficiency of GES algorithm portfolios and teams is investigated by solving the maximum weighted graph cut problem, with subsequent comparisons to identify distinctions between them. Conclusions. Based on the accumulated experience of applying GES algorithms and their modifications to solve discrete optimization problems, this study establishes the GES method as the leading approximate approach for Boolean programming. The results demonstrate the GES algorithm unions experience a significant boost in the optimization process speed, whereas algorithm teams demonstrate higher efficiency.

The authors consider classes of functions that can be exactly reconstructed using the D’Alembert formula generalized by O. M. Lytvyn in 1989. This formula as a special case is known to yield the Taylor polynomial of the expansion of functions in one variable but, unlike the Taylor polynomial, it retains the same differentiability class to which the approximated function belongs, even if its partial derivatives of sth order (s = 1, 2, ⋯ N) do not belong to the same differentiability class. In such case, the system of parametersβ1, β0, ⋯ βN is used. The authors propose a method for the optimal choice of these parameters and provide and prove several theorems related to classes of functions that can be exactly reconstructed by the generalized D’Alembert operators.

Introduction. Solving large-scale discrete optimization problems requires the processing of large-scale data in a reasonable time. Efficient solving is only possible by using multiprocessor computer systems. However, it is a daunting challenge to adapt existing optimization algorithms to get all the benefits of these parallel computing systems. The available computational resources are ineffective without efficient and scalable parallel methods. In this connection, the algorithm unions (portfolios and teams) play a crucial role in the parallel processing of discrete optimization problems. The purpose. The purpose of this paper is to research the efficiency of the algorithm portfolios by solving the weighted max-cut problem. The research is carried out in two stages using stochastic local search algorithms. Results. In this paper, we investigate homogeneous and non-homogeneous algorithm portfolios. We developed the homogeneous portfolios of two stochastic local optimization algorithms for the weighted max-cut problem, which has numerous applications. The results confirm the advantages of the proposed methods. Conclusions. Algorithm portfolios could be used to solve well-known discrete optimization problems of unprecedented scale and significantly improve their solving time. Further, we propose using communication between algorithms, namely teams and portfolios of algorithm teams. The algorithms in a team communicate with each other to boost overall performance. It is supposed that algorithm communication allows enhancing the best features of the developed algorithms and would improve the computational times and solution quality. The underlying algorithms should be able to utilize relevant data that is being communicated effectively to achieve any computational benefit from communication. Keywords: Discrete optimization, algorithm portfolios, computational experiment.

The authors have obtained and analyzed the expansions of weighted pseudoinverses with mixed weights (one of the weight matrices is positive definite and the other is nonsingular indefinite) into matrix power series with positive exponents. Iterative methods for calculation of weighted pseudoinverces with mixed weights have been generated and investigated on the basis of the obtained expansions of weighted pseudoinverses. Different variants of weighted pseudoinverces with mixed nonsingular weights are analyzed and developed into matrix power series.

For every disease, there is a certain set of genes whose mutations increase the risk of illness development. DNA sequencing of sick and healthy individuals results in the determination of genes related to certain diseases. Efficient procedures are described in order to determine point mutations in gene sequences of the examined patients. The optimal Bayesian procedure is used to determine risk groups for certain diseases, including the ones that underlie COVID-19.