# Mikhail V. GoubkoInstitute of Control Sciences | IPU · Mathematical analysis of multi-agent systems

Mikhail V. Goubko

Dr Sc., Professor of RAS

## About

146

Publications

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Introduction

STRUCTURING THE BETTER WORLD...
I develop mathematical methods for structure optimization in complex systems and apply them to computer science, chemistry, economics, business administration, and engineering.

Additional affiliations

January 2017 - present

January 2015 - present

January 2015 - present

## Publications

Publications (146)

We propose a two-step algorithm for optimal controlled islanding that partitions a power grid into islands of limited volume while optimizing several criteria: high generator coherency inside islands, minimum power flow disruption due to teared lines, and minimum load shedding. Several spectral clustering strategies are used in the first step to lo...

The optimal connecting network problem generalizes many models of structure optimization known from the literature, including communication and transport network topology design, graph cut and graph clustering, structure identification from data, etc. For the case of connecting trees with the given sequence of vertex degrees, the cost of the optima...

For modern energy markets it is typical to use dynamic real-time pricing schemes even for residential customers. Such schemes are expected to stimulate rational energy consumption by the end customers, provide peak shaving and overall energy efficiency. But under dynamic pricing planning a household’s energy consumption becomes complicated. So auto...

It is known from algebraic graph theory that if L is the Laplacian matrix of some tree G with a vertex degree sequence d=(d_1, ..., d_n)^\top and D is its distance matrix, then LD+2*I=(2*\vec{1}-d)\vec{1}^T, where \vec{1} is an all-ones column vector. We prove the converse proposition: if this identity holds for the Laplacian matrix of some graph G...

Several novel mixed-integer linear and bilinear formulations are proposed for the optimum communication spanning tree problem. They implement the distance-based approach: graph distances are directly modeled by continuous, integral, or binary variables, and interconnection between distance variables is established using the recursive Bellman-type c...

Three novel approximate dynamic programming algorithms based on the temporal, spatial, and spatiotemporal decomposition are proposed for the economic dispatch problem (EDP) in a distribution energy system with complex topology and many non-dispatchable renewable energy sources and energy storage systems (ESS). Computational efficiency of the propos...

Modern trend in operation and development of energy systems is to rely on data both in low-level control and strategic decisions. So, there is an urgent need in real-life data available for researchers and practioneers. We collected and published online data on real-time functioning of the energy grid of the Trapeznikov Institute of Control Science...

Three novel approximate dynamic programming algorithms based on the temporal, spatial, and spatiotemporal decomposition are proposed for the economic dispatch problem (EDP) in a distribution energy system with complex topology and many non-dispatchable renewable energy sources and energy storage systems (ESS). Computational efficiency of the propos...

It is known from algebraic graph theory that if L is the Laplacian matrix of some tree G with a vertex degree sequence d=(δ1,…,δn)⊤ and D is its distance matrix, then LD+2I=(2⋅1−d)1⊤, where 1 is an all-ones column vector. We prove the converse proposition: if this identity holds for the Laplacian matrix of some graph G with a degree sequence d and...

A method is developed for predicting the sorption parameters of polymers (the infinite dilution solubility coefficient of gases S and the Henry law equilibrium constant kD of double sorption models) of most light gases in glassy polymers on the basis of a computer model of a polymer chain segment. From the molecular dynamic model of conformations o...

The optimal connecting network problem generalizes many models of structure optimization known from the literature, including communication and transport network topology design, graph cut and graph clustering, etc. For the case of connecting trees with the given sequence of vertex degrees the cost of the optimal tree is shown to be bounded from be...

This is a part 1 (of 3) of a plenary talk made at the School and Conference «Large-Scale Systems Control», Perm, Russia, Sep 5, 2017, translated from Russian to English.
A problem of user experience for smart climate control in common areas (shops, classrooms, offices) is solved using a median voter scheme.

Электроэнергетическая система характеризуется как сложная многоуровневая распределенная организационно-техническая система. Отмечается важность ”умного подхода” к учету человеческого фактора при разработке и внедрении механизмов управления электроэнергетической системой. Приводится несколько задач управления в электроэнергетике, требующих корректны...

The Wiener index is maximized over the set of trees with the given vertex weight and degree sequences. This model covers the traditional "unweighed" Wiener index, the terminal Wiener index, and the vertex distance index. It is shown that there exists an optimal caterpillar. If weights of internal vertices increase in their degrees, then an optimal...

We propose a Bayesian learning algorithm to estimate the comfort level function of a residential appliance user from the history of her actions in different situations. In numeric experiments with datasets generated from a simulation model of a rational consumer interacting with small home appliances, our algorithm outperforms popular contemporary...

A method is proposed to support management policy design and verification in complex cyber-physical & human systems (CPHS). A hierarchy of interconnected formal models is built to provide the multi-faceted view of the conflict situation lying in the core of a certain management problem. Game-theoretical analysis reveals the problem and mechanism de...

In coming years residential consumers will face real-time electricity tariffs with energy prices varying day to day, and effective energy saving will require automation - a recommender system, which learns consumer's preferences from her actions. A consumer chooses a scenario of home appliance use to balance her comfort level and the energy bill. W...

We propose a Bayesian learning algorithm to estimate the comfort level function of a residential appliance user from the history of her actions in different situations. In numeric experiments with datasets generated from a simulation model of a rational consumer interacting with small home appliances, our algorithm outperforms popular contemporary...

Infinite dilution gas solubility coefficients in glassy polymers of diverse chemical structure are predicted on the basis of a simple computational model of short polymer chain conformations. In contrast to existing models that describe the infinite dilution solubility coefficient S of various gases in certain polymers or S for the particular gas i...

Infinite dilution gas solubility coefficients in glassy polymers of diverse chemical structure are predicted on the basis of a simple computational model of short polymer chain conformations. In contrast to existing models that describe the infinite dilution solubility coefficient S of various gases in certain polymers or S for the particular gas i...

Recently developed computer-aided design (CAD) tools automate design of rational hierarchical user menu structures. Proper choice of the optimization criterion is the key factor of success for such a CAD tool. We suggest user preference share as a novel metric of menu layout performance. It has clear economic grounds and is sound for management. We...

In 1997 Klav\v{z}ar and Gutman suggested a generalization of the Wiener index
to vertex-weighted graphs. We minimize the Wiener index over the set of trees
with the given vertex weights' and degrees' sequences and show an optimal tree
to be the, so-called, Huffman tree built in a bottom-up manner by sequentially
connecting vertices of the least wei...

We find simple saturated alcohols with the given number of carbon atoms and
the minimal normal boiling point. The boiling point is predicted with a
weighted sum of the generalized first Zagreb index, the second Zagreb index,
the Wiener index for vertex-weighted graphs, and a simple index caring for the
degree of a carbon atom being incident to the...

We consider a problem of a rational organizational structure for change management support being an important aspect of the strategic management process in a firm. We combine recent theoretical findings with experience in strategic consulting to suggest mathematical models of an organizational structure for change management based on a formal repre...

T he decision point concerning identity of a person is inevitable irrespective of the degree of reliability of the DNA identification and, therefore, accurate decision justification is of demand. Decision theory develops formal models of rational decision making under incomplete information and provides solid ground to recommendations on forensic D...

The precision of DNA identification with a certain locus set is typically measured with the frequency P of allele combination occurrence in a population. If the decision is made solely on the basis of DNA analysis results, there is always the non-zero probability of justice failure due to mistaken identity. Therefore, for every case in hand we have...

For a tree with the given sequence of vertex degrees the spectral radius of its terminal distance matrix is shown to be bounded from below by the the average row sum of the terminal distance matrix of the, so called, BFS-tree (also known as a greedy tree). This lower bound is typically not tight; nevertheless, since spectral radius of the terminal...

In recent years several computer-aided design (CAD) tool prototypes were developed for the design of hierarchical user menus. These CAD systems differ in optimization criteria used to compare menus. A traditional approach relates menu performance to the target item selection time, but is the faster always the better for a user? We elicit key factor...

Introduction to Theory of Control in Organizations explains how methodologies from systems analysis and control theory, including game and graph theory, can be applied to improve organizational management. The theory presented extends the traditional approach to management science by introducing the optimization and game-theoretical tools required...

Given a graph G, the atom-bond connectivity (ABC) index is defined to be ABC(G) = Sigma Euv is an element of E(G)root d(G)(u)+d(G)(v)-2/d(G)(u)d(G)(v), where E(G) is the edge set of graph G and d(G)(v) is the degree of vertex v in graph G. The paper [10] claims to classify tho trees with a fixed number of leaves which minimize the ABC index. Unfort...

A dynamic programming method is elaborated, enabling the characterization of trees with a given number of pendent vertices, for which a vertex-degree-based invariant (“topological index”) achieves its extremal value. The method is applied to the chemically interesting and earlier much studied such invariants: the first and second Zagreb index, and...

We derive sharp lower bounds for the first and the second Zagreb indices
($M_1$ and $M_2$ respectively) for trees and chemical trees with the given
number of pendent vertices and find optimal trees. $M_1$ is minimized by a tree
with all internal vertices having degree 4, while $M_2$ is minimized by a tree
where each "stem" vertex is incident to 3 o...

Efficiency of a control system is related to its structure (understood as a collection of links of different nature between the elements of the system). Complex control systems are often hierarchy-shaped. Typically, such an hierarchy follows from the control problem decomposition and coordination of local decisions by virtue of information transfer...

To solve problems of demand management in terms of smart energy systems (Smart grid), we need a mathematical model of active consumer decision-making. Existing models either do not consider important aspects of consumer behavior, or are too complex for use in multi-agent simulation. A mathematical model of an active consumer is proposed, based on w...

While the problem of hierarchical menu design is very common in user interface design, existing approaches lack either semantic aspects or optimization techniques. We suggest a semantic-aware mathematical model of hierarchical menu optimization and algorithms developed on the basis of this theory. These algorithms are implemented in the ready-to us...

Настоящий выпуск журнала «Управление большими системами: сборник трудов» посвящен применению наукометрических и экспертных методов к задачам оценки эффективности научно-исследовательской деятельности – как отдельных ученых, организаций, институтов, научных направлений, так и науки страны в целом. Эта тема приобрела особую актуальность в последние г...

To solve problems of demand management in terms of smart energy systems (Smart grid), we need a mathematical model of active consumer decision-making. Existing models either do not consider important aspects of consumer behavior, or are too complex for use in multi-agent simulation. A mathematical model of an active consumer is proposed, based on w...

Problems of control mechanisms integration are formulated and discussed in the framework of mechanism design for organizational behavior control. Unified schemes for control mechanisms description and design are proposed. An example of the integrated production cycle optimization mechanism is considered.

Basics are surveyed of a version of mechanism design theory tailored to solve management problems. The concept of a mechanism of organizational behavior control is introduced. Methodological grounds of the theory are discussed along with mechanisms classification. Mechanism implementation process is characterized. Also, basic mechanisms are sketche...

The first Zagreb index M 1 of a graph G is equal to the sum of squares of the vertex degrees of G. In a recent work [Goubko, MATCH Com-mun. Math. Comput. Chem. 71 (2014), 33–46], it was shown that for a tree with n 1 pendent vertices, the inequality M 1 9 n 1 −16 holds. We now provide an alternative proof of this relation, and characterize the tree...

Mechanism Design (MD) is a branch of game theory which deals with conflict situations involving a principal and a set of active agents (usually in the presence of asymmetric information). Mechanism design theory delivers a solution to many management problems in the form of a control mechanism, (i.e., a formalized routine of decision-making). Forma...

We survey basics of a version of the mechanism design theory tailored to solve management problems, and introduce the core concept of a mechanism of organizational behavior control. We discuss methodological grounds of the theory, give classification of mechanisms, and characterize the mechanism implementation process. Finally, we sketch basic mech...

A mathematical model is proposed to optimize the structure of hierarchical menus and directories. The model considers each element popularity. The problem of discrete optimization is solved regarding the choice of menu structure minimizing the average search time. It is demonstrated that optimal menu panels should provide the user with identical nu...

Анализируется место теории управления организационными системами (исторически берущей свое начало в теории активных систем) в системе научных и научно-практических направлений, исследующих организационное управление. Для этого выбирается единая система классификаций, кратко перечисляются современные научные направления, исследующие проблемы теории...

We suggest the mathematical model for strategic management control structures formation in firms. This model generalizes the applied technique, which was successfully used in the course of Russian manufacturing companies’ reorganization. The general problem of organization structure is formulated. In the case of symmetric projects the problem is re...

While an extensive body of literature investigates problems of decision trees growing, just a few study lower-bound estimates for the expected classification cost of decision trees, especially for varying costs of tests. In this paper the new lower-bound estimate is proposed. Computation of the estimate is reduced to solving a series of set-coverin...

The problem of rational organizational structure formation is considered. The problem is reduced to the discrete optimization
problem of searching a hierarchy of managers that minimizes certain criterion (normally, the cost of hierarchy maintenance).
Cost functions which can be written as a sum of homogenous function are analyzed. The conditions ar...

We propose an automated routine for hierarchical menu structure optimization. A computer advice-giving system founded on the mathematical model of menu navigation directs the designer-driven process of sequential enhancement, while menu designer caters for the semantic quality of menu labels and groupings used. The mathematical model employs the fr...

Предлагается математическая модель оптимизации структуры иерархических меню и каталогов. Каждому элементу меню ставится в соответствие его популярность и решается задача дискретной оптимизации – выбора структуры меню, минимизирующей среднее время поиска. Доказывается, что все панели оптимального меню должны предлагать пользователю одинаковое количе...

A mathematical model is proposed to optimize the structure of hierarchical menus and directories. The model considers each element popularity. The problem of discrete optimization is solved regarding the choice of menu structure minimizing the average search time. It is demonstrated that optimal menu panels should provide the user with identical nu...

The problem of rational organization structure (hierarchy of organizational control) is considered as a discrete
optimization problem, the one of managers' maintenance cost minimization by building an admissible hierarchy over a given set of workers. For the case of the, so-called, uniform cost function of a manager a lower-bound estimate of the op...

Учебник представляет собой вводный курс по теории управления организационными системами, рассчитанный на студентов ВУЗов и аспирантов инженерных, управленческих и экономических специальностей.
Приводится общая модель управления организационными системами и технология решения соответствующих задач управления. Достаточно подробно рассматриваются след...

Описываются два недавно завершенных Интернет-опроса – организация и технические детали. Сравнивается эффективность альтернативных подходов, приводятся рекомендации.