# Mikhail PosypkinFederal Research Center “Computer Science and Control” of Russian Academy of Sciences

Mikhail Posypkin

PhD, D. Sc.

## About

101

Publications

8,883

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

721

Citations

Citations since 2017

Introduction

Additional affiliations

November 2015 - present

**Federal Research Center “Computer Science and Control” of Russian Academy of Sciences**

Position

- Head of Department

January 2013 - November 2015

## Publications

Publications (101)

Restoration of the 3D structure of a protein from the sequence of its amino acids (“folding”) is one of the most important and challenging problems in computational biology. The most accurate methods require enormous computational resources due to the large number of variables determining a protein’s shape. Coarse-grained models combining several p...

The problem of approximating and visualizing the solution set of systems of nonlinear inequalities can be frequently met in practice, in particular, when it is required to find the working space of some robots. In this paper, a method using Peano-Hilbert space-filling curves for the dimensionality reduction has been proposed for functions satisfyin...

Reliable bounding of a function’s range is essential for deterministic global optimization, approximation, locating roots of nonlinear equations, and several other computational mathematics areas. Despite years of extensive research in this direction, there is still room for improvement. The traditional and compelling approach to this problem is in...

Parallel robots are mechanical systems with numerous applications in manufacturing, medicine, space industry, etc. Such robots are characterized by closed kinematic chains ensuring robustness and maneuverability. The design of a fully functional parallel robot is a time-consuming task as an engineer needs to enumerate and compare many variants in o...

The article considers approximation of solution sets to indeterminate systems for non-linear equations. We developed a method to obtain inner and outer approximations of such sets. The method uses interval analysis techniques and relies on the Krawczyk operator and its modification based on the Baumann bicentered interval extension. We developed so...

In this paper we study the question of parallelization of a variant of Branch-and-Bound method for solving of the subset sum problem which is a special case of the Boolean knapsack problem. The following natural approach to the solution of this question is considered. At the first stage one of the processors (control processor) performs some number...

The paper addresses the problem of constructing lower and upper estimators for univariate functions. This problem is of crucial importance in global optimization, where such bounds are used to reduce the search area. We propose to use piecewise linear estimators for bounding univariate functions and show how such estimators can be derived from the...

Increasing the number of computational cores is a primary way of achieving the high performance of contemporary supercomputers. However, developing parallel applications capable to harness the enormous amount of cores is a challenging task. It is very important to understand the principle limitations of the scalability of parallel applications impo...

An easily implementable recursive parallelization strategy for solving the subset sum problem by the branch-and-bound method is proposed. Two different frontal and balanced variants of this strategy are compared. On an example of a particular case of the subset sum problem we show that the balanced variant is more effective than the frontal one. Mo...

One of the most actual and complex problems of medicine and neurology is the rehabilitation of patients. Robotic systems currently occupy an important place in the comprehensive rehabilitation of neurological patients with severe motor impairment of various etiologies, as well as the most socially significant and common neurological diseases. The a...

The backtracking is a basic combinatorial search algorithm. As many other deterministic methods it suffers from the high complexity. Fortunately the high performance computing can efficiently cope with this issue. It was observed that the structure of the search tree can dramatically affect the efficiency of a parallel search. We study the complexi...

This book constitutes the refereed proceedings of the 10th International Conference on Optimization and Applications, OPTIMA 2019, held in Petrovac, Montenegro, in September-October 2019.
The 35 revised full papers presented were carefully reviewed and selected from 117 submissions. The papers cover such topics as optimization, operations research...

We consider a concept of so called point-dependent Lipschitz constant. In contrast to the standard Lipschitz the value of the point-dependent Lipschitz constant can vary within the given interval. This allows us to construct a better piece-wise approximation of the objective function and as a consequence obtain a faster finding globally optimal sol...

This book constitutes the refereed proceedings of the 9th International Conference on Optimization and Applications, OPTIMA 2018, held in Petrovac, Montenegro, in October 2018.
The 35 revised full papers and the one short paper presented were carefully reviewed and selected from 103 submissions. The papers are organized in topical sections on mathe...

The paper proposes an implementation of the Branch-and-Bound method for an enterprise grid based on the BOINC infrastructure. The load distribution strategy and the overall structure of the developed system are described with special attention payed to some specific issues such as incumbent updating and load distribution. The implemented system was...

Increasing the number of computational cores is a primary way of achieving high performance of contemporary supercomputers. However, developing parallel applications capable to harness the enormous amount of cores is a challenging task. Thus, studying the scalability of parallel algorithms (the growth order of the number of processors required to a...

The paper addresses the problem of constructing lower and upper bounding functions for univariate functions. This problem is of a crucial importance in global optimization where such bounds are used by deterministic methods to reduce the search area. It should be noted that bounding functions are expected to be relatively easy to construct and mani...

Рассматривается легко реализуемая на практике стратегия распараллеливания при решении задачи о сумме подмножеств методом ветвей и границ, называемая рекурсивной стратегией распараллеливания. Сравниваются два различных варианта этой стратегии: фронтальный и сбалансированный. На примере частного случая задачи о сумме подмножеств показано, что сбаланс...

In this paper we propose a method for solving systems of nonlinear inequalities with predefined accuracy based on nonuniform covering concept formerly adopted for global optimization. The method generates inner and outer approximations of the solution set. We describe the general concept and three ways of numerical implementation of the method. The...

USPEX is a world-leading software for computational material design. In essence, USPEX splits simulation into a large number of workunits that can be processed independently. This scheme ideally fits the desktop grid architecture. Workunit processing is done by a simulation package aimed at energy minimization. Many of such packages are proprietary...

The paper is concerned with estimating the computational complexity of the branch-and-bound method for the subset sum problem. We study the relationship between the way of decomposition of subproblems and the number of the method steps. The standard variant of the branch-and-bound method for the subset sum problem with binary branching is considere...

A volunteer computing project aimed at solving computationally hard inverse problems in underwater acoustics is described. This project was used to study the possibilities of the sound speed profile reconstruction in a shallow-water waveguide using a dispersion-based geoacoustic inversion scheme. The computational capabilities provided by the proje...

The paper considers the implementation and verification of a test suite containing 150 benchmarks for global deterministic box-constrained optimization. A C++ library for describing standard mathematical expressions was developed for this purpose. The library automate the process of generating the value of a function and its’ gradient at a given po...

A gapped repeat is a factor of the form uvu where u and v are nonempty words. The period of the gapped repeat is defined as |u|+|v|. The gapped repeat is maximal if it cannot be extended to the left or to the right by at least one letter with preserving its period. The gapped repeat is called α-gapped if its period is not greater than α|u|. A δ-sub...

The problem of crystal structure prediction is very old and does, in fact, constitute the central problem of theoretical crystal chemistry. In this paper, we discuss the popular USPEX evolutionary algorithm for crystal structure prediction. Here we present the distributed computing implementation of USPEX based on a popular BOINC volunteer computin...

The problem of approximating the set of all solutions to a system of nonlinear inequalities is studied. A method based on the concept of nonuniform coverings is proposed. It allows one to obtain an interior and exterior approximation of this set with a prescribed accuracy. The efficiency of the method is demonstrated by determining the workspace of...

A new concept of a multitask distributed heterogeneous computing system is proposed. The basic principles of such system are that it uses only idle supercomputer resources and does it as a common user; thus, it does not conflict with the administration policy in any way. The efficiency of the proposed concept is demonstrated by the example of the r...

We obtain an exact upper bound on the complexity of solving the Subset Sum problem with a variation of the branch-and-bound method of a special form. Complexity is defined as the number of subproblems considered in the process of solving the original problem. Here we reduce the enumeration by using the domination relation. We construct an instance...

This paper presents a new numerical approach to manipulator workspace assessment. The method is based on the non-uniform covering concept in which the workspace is a solution for the system of non-linear inequalities with Lipschitz continuous functions. The illustrative example shows the performance of the approach and indicates the precision of th...

The Branch and Bound method (B&B) is an efficient and well-known technique to solve combinatorial optimization problems. However for real-life problems B&B can consume tremendous amount of resources thereby making reasonable the use of parallel and distributed systems. In this paper we discuss an efficient implementation of B&B method on desktop gr...

A two-dimensional model of a multilayer material and a procedure for simulating its properties based on global optimization methods are proposed. This model is applied for the case of a two-dimensional crystal. Global minima of the interaction energy of the material’s atoms are found, and geometric characteristics of its corresponding equilibrium s...

This paper presents various methods for the determination of the workspace of parallel robots. Different types of workspaces are defined, and algorithms for calculating them are presented. We propose a universal method of approximating the working space of a robot by reducing to finding the solution set of system of nonlinear inequalities. The meth...

We obtained an exact upper bound for the complexity of solving subset sum problem with the special kind of branch and bound algorithm. Complexity is defined as the number of steps of the algorithm. The dominance relation and cardinality bound is used to reduce the number of iterations. We constructed an example of the subset sum problem that has th...

The paper considers the problem of finding the structure of a fragment of two-dimensional crystal lattice with the minimal energy. Atoms in a lattice reside on parallel lines (layers). The interatomic distances are the same within one layer but can differ for distinct layers. The energy of the piece of material is computed using so-called potential...

The subset sum problem is a particular case of the Boolean knapsack problem where each item has the price equal to its weight. This problem can be informally stated as searching for most dense packing of a set of items into a box with limited capacity. Recently, coarse-grain parallelization approaches to Branch-and-Bound (B&B) method attracted some...

The Branch-and-Bound method is known as one of the most powerful but very resource consuming global optimization methods. Parallel and distributed computing can efficiently cope with this issue. The major difficulty in parallel B&B method is the need for dynamic load redistribution. Therefore design and study of load balancing algorithms is a separ...

Paper deals with the non-uniform covering method that is aimed at deterministic global optimization. This method finds a feasible solution to the optimization problem numerically and proves that the obtained solution differs from the optimal by no more than a given accuracy. Numerical proof consists of constructing a set of covering sets - the cove...

The Branch-and-Bound (B&B) is a fundamental algorithmic scheme for a large variety of global optimization methods. For many problems B&B requires the amount of computing resources far beyond the power of a single-CPU workstation thus making parallelization almost inevitable. The approach proposed in this paper allows one to evaluate load balancing...

When designing electronic circuits, we often need to solve discrete optimization problems. One of the basic methods for solving such problems is the method of dynamic programming. The paper is devoted to a comparative study of different versions of the dynamic programming method for the knapsack problem. The formulation of the problem and various v...

We study the computational complexity of one of the particular cases of the
knapsack problem: the subset sum problem. For solving this problem we consider
one of the basic variants of the Branch-and-Bound method in which any
sub-problem is decomposed along the free variable with the maximal weight. By
the complexity of solving a problem by the Bran...

A strictly defined notion of an approximate solution for a multicriteria optimization problem with functional constraints and a deterministic method for obtaining such approximations are presented. Unlike traditional algorithms for constrained multicriteria optimization the proposed method not only generates an approximation but also proves its acc...

INTRODUCTION At present, the development and application of optimization methods seems to be an especially prom ising approach to the important task of predictive computer simulation of crystalline structures with the use of multiscale techniques (see [1, 2]). In this approach, results of the firsttprinciple simulation [3, 4] of atomic structures a...

The paper describes a method for solving multi-objective optimization problems with box constraints. Unlike existing approaches, the proposed method not only constructs a finite approximation of Pareto frontier, but also proves its -optimality. The paper gives a detailed explanation of basic theoretical concepts behind the method and describes the...

Application of the non-uniform coverage method to the multicriteria optimization problems was considered, and the concept of the ɛ-Pareto set was formulated and studied. An algorithm to construct a ɛ-Pareto set with a guaranteed accuracy ɛ was described. Efficient implementation of this approach was described, and the results of experiments were pr...

The Berkeley Open Infrastructure for Network Computing (BOINC) is an opensource middleware system for volunteer and desktop grid computing. In this paper we propose BNBTEST, a BOINC version of distributed branch and bound method. The crucial issues of distributed branch-and-bound method are traversing the search tree and loading balance. We develop...

A gapped repeat is a factor of the form uvu where u and v are nonempty words. The period of the gapped repeat is defined as |u| + |v|. The gapped repeat is maximal if it cannot be extended to the left or to the right by at least one letter with preserving its period. The gapped repeat is called α-gapped if its period is not greater than α|u|. A δ-s...

A deterministic global optimization algorithm for box-constrained problems is presented. The proposed approach is based on well-known non-uniform space covering technique. In the paper this approach is further elaborated. We propose a new techniques that enables a significant reduction of the search space by means of dropping parts of processed box...

The nonuniform covering method is applied to multicriteria optimization problems. The ɛ-Pareto set is defined, and its properties are examined. An algorithm for constructing an ɛ-Pareto set with guaranteed accuracy ɛ is described. The efficiency of implementing this approach is discussed, and numerical results are presented.

Работа посвящена применению метода неравномерных покрытий для решения задач многокритериальной оптимизации. Определяется множество ε-Парето и исследуются его свойства. Описан алгоритм построения множества εε-Парето с гарантированной заданной точностью εε. Обсуждаются вопросы эффективной реализации данного подхода и приводятся результаты эксперимент...

An algorithm for solving global optimization problems is developed. The objective and constraints are required to have gradients satisfying Lipschitz condition. The problem may contain both continuous and integer variables and the objective may be non-convex and multimodal. Improved lower bounds and new techniques to reduce the number of algorithm...

Many practically important combinatorial problems can be efficiently reducedto a problem of Boolean satisfiability (SAT). Therefore, the implementation ofdistributed algorithms for solving SAT problems is of great importance. In thisarticle we describe a technology for organizing desktop grid, which is meantfor solving SAT problems. This technology...

One of the possible realizations of the branch-and-bound method on multiprocessor systems with distributed memory, the front-end algorithm is addressed. The complexity of the front-end algorithm is studied for a family of Boolean knapsack problems with one constraint under the assumption that the number of processors is not limited. Formulas for th...

In logical cryptanalysis a problem of search of a secret key of a cryptographic system is formulated as a SAT problem, i.e. a problem of search of a satisfying assignment for some CNF. In this paper we consider some natural strategies for parallelization of these SAT problems. We apply coarse-grained approach which makes it possible to use distribu...

The nonuniform covering method for global optimization of functions of several variables is extended to nonlinear programs.
It is shown that this method can be used for solving problems that, in addition to conventional constraints, involve partial
integrality conditions. Estimates for the accuracy of the solution and for the number of steps requir...

The method of nonuniform coverings as applied to the global optimization of functions of several variables was proposed in Yu.G. Evtushenko [Zh. Vychisl. Mat. Mat. Fiz. 11, 1390–1403 (1971; Zbl 0233.90007)]. Various versions of the method were implemented as software codes and were used for computations on multiprocessor systems. This paper gives a...

In this article we consider the inversion problem for polynomially computable
discrete functions. These functions describe behavior of many discrete systems
and are used in model checking, hardware verification, cryptanalysis, computer
biology and other domains. Quite often it is necessary to invert these
functions, i.e. to find an unknown preimage...

Motivation: Computer modeling of protein-ligand interactions is one of the most important phases in a drug design process. The core part of this modeling is a resolution of a global unconstrained optimization problem. This paper presents a comparative computational experiments aimed at studying the efficiency of the different optimization methods a...

We study parallel complexity of the branch-and-bound method for optimization problems. We consider a standard implementation
scheme for the branch-and-bound method on a parallel system, in which first only one processor is working, and then the resulting
subtasks are given out to other processors. For this scheme, we give a lower bound on the paral...

This paper is devoted to questions concerning the complexity of solution of the problem on one-dimensional Boolean knapsack by the branch and bound method. For this complexity, we obtain two upper bounds. We separate the special case of the knapsack problem where the complexity is polynomially bounded by the dimension of the problem. We also obtain...

The paper describes the design and implementation of BNB-Solver, an object-oriented framework for
discrete and continuous parallel global optimization. The framework supports exact branch-and-bound algorithms,
heuristic methods and hybrid approaches. BNB-Solver provides a support for distributed and shared
memory architectures. The implementation f...

Parallel implementations of a combined branch-and-bound algorithm for the knapsack problem with one constraint are considered.
By the combined algorithm we mean an algorithm in which two methods of branching are implemented, the method based on an estimate
of the upper bound and the method of one-sided branching based on the vector. An approach com...

The paper presents IARnet toolkit, a set of high-level tools and services simplifying integration of software resources into
a distributed computing environment and development of distributed applications involving dynamic discovery and composition
of resources. A case study of using IARnet for solving large scale discrete optimization problems is...

A scheme for the parallel implementation of the combined branch-and-bound method and heuristic algorithms is proposed. Results
of computations for the one-dimensional Boolean knapsack problem are presented that demonstrate the efficiency of the proposed
approach. The main factors that affect the speedup of the solution when local optimization is us...

The efficiency of parallel implementations of the branch-and-bound method in discrete optimization problems is considered.
A theoretical analysis and comparison of two parallel implementations of this method is performed. A mathematical model of
the computation process is constructed and used to obtain estimates of the maximum possible speedup. Exa...

Efficient parallel implementation of the branch-and-bound method in discrete optimization problems is considered. A description of particular algorithms and of their implementation is given. Based on experimental data, conclusions concerning the efficiency of those algorithms are drawn and factors affecting their performance are investigated.

mpF is a new parallel extension of Fortran 90. It was developed on base of experience of development and use of the mpC parallel
programming language. The paper compares programming models of mpC and mpF.

In this paper, we present a new parallel Fortran extension called mpF. The language based on both data and task parallelism
allows explicit specification of data and computations distribution. We discuss some reasons for the language design and demonstrate
the basic mpF features on an example of the parallel matrix multiplication algorithm SUMMA. T...

Compilers are used for creating executable modules for programs written in high-level languages; therefore, the presence of errors in a compiler is a serious danger for the quality of the software developed with the use of this compiler. As in the case of any other software, testing is one of the most important methods of quality control and error...

A technique for an automated test generation for compilers, which is based on formal specifications of the programming language, is suggested. The technique makes it possible to generate tests correct from the dynamic semantics standpoint that do not depend on specific features (undefined or implementation-specific) of the semantics (the so-called...

A parallel implementation is suggested for the supernova explosion model with large-scale convective instability developed by a scientific team at the Keldysh Institute of Applied Mathematics, Russian Academy of Sciences (IPM RAN). The parallel algorithm is described, its scalability is estimated theoretically, and some theoretical and numerical re...

UMLдиаграмм действий. Метод заключается в построении обхода графа состояний системы с применением неизбыточного алгоритма обхода [1, 2] и компиляции построенного обхода в тестовый набор.

The paper presents a novel approach to automated compiler test suite generation based on the source level specification. Several coverage criteria are introduced. The application of the proposed methodology to testing the realistic programming language is discussed.

State Machines [4] formalism for modeling mpC expressions semantics. The formal specification is implemented using the ASM-based Montages frame- work [6] - a new method for giving the semantics of a programming language.

The paper presents an approach to automatic compiler test suite generation based on formal language specification. The language specification implemented using ASM formalism is discussed. The practical results for mpC parallel programming language compiler are presented.

State Machines [4] formalism for modeling mpC expressions semantics.The formal specification is implemented using the ASM-based Montages frame-work [6] - a new method for giving the semantics of a programming language.

In the paper, an accurate and detailed description of the programming language C[] is given. Unlike previous publications on the language, this paper gives a formal definition of a vector, which is used for the description of the semantics of basic constructs. The language updates that appeared after the first publication are discussed. Other vecto...

The paper presents a language for portable parallel computing on heterogeneous networks and experience of its use for solving scientific problems.

The paper presents mpC Parallel Applications Development Environment aimed at building parallel applications on a network of computers. The proposed approach enables to specify parallel application's building process for a general network con guration.