This monograph introduces a novel multiset-based conceptual, mathematical and knowledge engineering paradigm, called multigrammatical framework (MGF), used for planning and scheduling in resource-consuming, resource-producing (industrial) and resource-distributing (economical) sociotechnological systems (STS). This framework is meant to enable smart operation not only in a “business-as-usual” mode, but also in extraordinary, highly volatile or hazardous environments. It is the result of convergence and deep integration into a unified, flexible and effectively implemented formalism operating on multisets of several well-known paradigms from classical operations research and modern knowledge engineering, such as: mathematical programming, game theory, optimal scheduling, logic programming and constraint programming.
The mathematical background needed for MGF, its algorithmics, applications, implementation issues, as well as its nexus with known models from operations research and theoretical computer science areas are considered. The resilience and recovery issues of an STS are studied by applying the MGF toolkit and on paying special attention to the multigrammatical assessment of resilience of energy infrastructures. MGF-represented resource-based games are introduced, and directions for further development are discussed. The author presents multiple applications to business intelligence, critical infrastructure, ecology, economy and industry.
This book is addressed to scholars working in the areas of theoretical and applied computer science, artificial intelligence, systems analysis, operations research, mathematical economy and critical infrastructure protection, to engineers developing software-intensive solutions for implementation of the knowledge-based digital economy and Industry 4.0, as well as to students, aspirants and university staff. Foundational knowledge of set theory, mathematical logic and routine operations on data bases is needed to read this book. The content of the monograph is gradually presented, from simple to complex, in a well-understandable step-by-step manner. Multiple examples and accompanying figures are included in order to support the explanation of the various notions, expressions and algorithms.
Author(s): Igor A. Sheremet
Publisher: Springer
Year: 2022
Language: English
Pages: 467
City: Cham
Preface
Acknowledgments
Contents
Chapter 1: Introduction
Chapter 2: Sociotechnological Systems and Associated Problems
2.1 Classes of Sociotechnological Systems
2.2 Resource-Consuming Sociotechnological Systems
2.3 Resource-Producing (Industrial) Sociotechnological Systems and Smart Industry
2.4 Resource-Distributing (Economical) Sociotechnological Systems
2.5 Resilience and Recovery of Sociotechnological Systems
Chapter 3: Syntax, Semantics, and Mathematical Properties of Multiset Grammars
3.1 Multisets, Multiset Grammars, and Filtering Multiset Grammars
3.1.1 Basic Notions and Definitions
3.1.2 Filters
3.1.3 Multiset Grammars and Filtering Multiset Grammars
3.2 Temporal Multiset Grammars
3.2.1 Temporal Multisets, Temporal Rules, and Manufacturing Devices
3.2.2 Mathematical Semantics of TMGs
3.2.3 Filtering Temporal Multiset Grammars
3.2.4 Self-Generating TMGs and Filtering Self-Generating TMGs
3.3 Metagrammatical Extensions of Multiset Grammars
3.3.1 Multiset Metagrammars
3.3.2 Unitary Multiset Metagrammars
3.3.3 Temporal Multiset Metagrammars and Self-Generating Temporal Multiset Metagrammars
3.4 Mathematical Properties of Multiset Grammars and Multiset Metagrammars
3.4.1 Interconnections Between Classes of Multiset Grammars
3.4.2 Properties of Multiset Grammars
3.4.3 Properties of Filtering Multiset Grammars
3.4.4 Properties of Unitary Multiset Grammars and Filtering UMGs
3.4.5 Properties of Metagrammatical Extensions
3.5 Descriptional Extensions of the Basic Multigrammatical Toolkit
3.5.1 Rational Multiplicities
3.5.2 Negative Multiplicities
3.5.3 Composite Names of Objects
3.5.4 Multifunctional Manufacturing Devices
Chapter 4: Basic Algorithmics of Multiset Grammars and Metagrammars
4.1 Unitary Multiset Grammars
4.1.1 Acyclic Non-variative UMGs
4.1.2 Acyclic Variative UMGs
4.1.3 Acyclic Variative Filtering UMGs
4.2 Unitary Multiset Metagrammars
4.2.1 Algorithm for a Direct Implementation of UMMGs´ Mathematical Semantics
4.2.2 Basic Idea for the Improvement of UMMGs´ Algorithmics
4.2.3 Macroset Representation of Polynomials and Variable-Containing Multiplicities
4.2.4 Operations on Macroset-Represented Polynomials and Variable-Containing Multiplicities
4.2.5 Operations on Multisets with Interval Multiplicities
4.2.6 Improved Algorithm for STMS Generation
4.2.7 Implementation of Acyclic and Cyclic Variative UMMGs
4.3 Filtering Multiset Grammars
4.3.1 Primary Multi-agent Implementation
4.3.2 Reduction of Inter-agent Exchange
4.4 Key Issues of Algorithmics of Filtering Temporal MGs
4.4.1 ``Bottom-Up´´ Generation of Schedules
4.4.2 ``Top-Down´´ Generation of Schedules
4.4.3 Terminalization
Chapter 5: Resource-Consuming Sociotechnological Systems
5.1 Multigrammatical Representation of RCSs
5.1.1 Organizational Systems
5.1.2 Organizational-Technological Systems
5.1.3 Resource-Consuming Organizational-Technological Systems
5.1.4 Alternative Ways to Apply UMGs to the Representation of RCSs
5.1.5 Application of UMGs to Representation of Non-hierarchical RCSs
5.2 RCS Analysis
5.2.1 Assessment of Sufficiency of Amounts of Resources Available to an RCS
5.2.2 Assessment of the Cost of an Additional Supply
5.2.3 Assessment of the Maximal Period of Time of RCS Operation Given Available Amounts of Resources
5.2.4 Assessment of Variations of Amounts of Resources Consumed by an RCS
5.2.5 Assessment of Feasibility of Restructuring Decisions
5.3 RCS Synthesis
5.3.1 Approaches to RCS Synthesis
5.3.2 Direct FUMG/UMMG Application to RCS Synthesis
5.3.3 Variative FUMGs with a Problem-Oriented Mathematical Semantics and Their Application to RCS Synthesis
Chapter 6: Industrial Sociotechnological Systems
6.1 UMG-Based Representation of Industrial Systems and Associated Tasks
6.1.1 UMG-Based Representation of ISs
6.1.2 Assessment of Order Feasibility
6.1.3 Assessment of Amounts of Resources to Be Acquired to Allow Completion of Initially Non-feasible Orders
6.1.4 Assessment of Partial Order Completion in the Case of an Insufficient Resource Base
6.1.5 Assessment of Ecological Damage Which May Be Caused by ISs During Their Operation and Order Feasibility Under Ecological...
6.1.6 Technique of Competition Modeling
6.2 TMG-Based Representation of Industrial Systems and IS Scheduling
6.2.1 TMG-Based Representation of ISs MPR, Bottom-Up Assessment of Order Feasibility, and Ecological Issues Modeling
6.2.2 Top-Down Assessment of Order Feasibility for a TMG-Based Representation of ISs MPR
6.2.3 Assessment of Additional Amounts of Resources to Be Acquired and the Time Period Necessary for Completion of Initially N...
6.2.4 Multi-order Scheduling
6.3 Operational Interconnections Between Resource-Consuming and Industrial Systems
Chapter 7: Economical Sociotechnological Systems and Economical Combinatorics
7.1 Exchange Economical Systems
7.1.1 Basic Scheme of an Exchange and Its Representation by Filtering Multiset Grammars
7.1.2 Direct Exchange ESs
7.1.3 Cooperative Exchange ESs
7.1.4 Broker Exchange ESs
7.2 Lending Economical Systems
7.2.1 Representation of Loans
7.2.2 Formal Definition of Loan Implementation
7.2.3 Formal Definition of an LES Schedule
7.3 Producing Economical Systems
7.3.1 Representation of PES Resource Bases and Manufacturing Technological Bases
7.3.2 Schedules of Economical Systems Operating on Passive Resources
7.4 Mixed Economical Systems
7.4.1 Exchange and Lending Economical Systems
7.4.2 Exchange and Producing Economical Systems
7.4.3 Lending and Producing Economical Systems
7.4.4 Exchange, Lending, and Producing Economical Systems
Chapter 8: Resilience and Recovery of Sociotechnological Systems
8.1 Closed Industrial Systems
8.1.1 UMG-Based Analysis of IS Vulnerability
8.1.2 UMG-Based Assessment of Partial Order Completion by a Vulnerable IS
8.1.3 TMG-Based Analysis of IS Resilience
8.1.4 TMG-Based Assessment of Partial Order Completion by a Vulnerable IS
8.2 Open Industrial Systems
8.2.1 UMG-Based Analysis of Recoverability of Vulnerable ISs
8.2.2 UMG-Based Analysis of Supportability of Vulnerable ISs
8.2.3 TMG-Based Analysis of Supportability of Vulnerable ISs
8.2.4 TMG-Based Analysis of Recoverability of Vulnerable ISs
8.2.5 TMG-Based Assessment of the Contribution of Non-interrupted Manufacturing Devices to the Supportability of Vulnerable ISs
8.3 Cascade Effects
8.3.1 Passive Cascade Effects
8.3.2 Active Cascade Effects
8.4 Energy Infrastructures
8.4.1 Basic Graph Representation of Energy Infrastructures
8.4.2 Basic Multigrammatical Representation of Energy Infrastructures
8.4.3 Cyclicity of FUMGs Representing Energy Infrastructures and Their Finitarization
8.4.4 Criteria of Vulnerability of an Energy Infrastructure to a Destructive Impact
8.4.5 Modeling Reservation and Recovery of Energy Infrastructures
8.4.6 Modeling Rechargeable Power Storages and Their Application
8.4.7 Further Tasks
Chapter 9: Resource-Based Games
9.1 Multigrammatical Representation of Classic Games
9.1.1 Multigrammatical Representation of Classic Games with Sequential Moves
9.1.2 Multigrammatical Representation of Classic Games with Simultaneous Moves
9.2 Resource-Based Antagonistic Games
9.2.1 Primary Definitions
9.2.2 Multigrammatical Representation of Antagonistic RBGs
9.2.3 Multigrammatical Representation of Extensions of Antagonistic RBGs
9.3 Cooperative and Coalitional Resource-Based Games
9.3.1 Cooperative RBGs
9.3.2 Multi-player Cooperative RBGs and Coalitional RBGs
9.4 Distributed Resource-Based Games
9.4.1 Antagonistic Distributed RBGs with Sequential Moves
9.4.2 Distributed RBGs with Simultaneous Moves
9.4.3 Cooperative and Coalitional Distributed RBGs
Chapter 10: Multigrammatical Representation of Classic Problems of Operations Research
10.1 Shortest Path, Traveling Salesman, and Maximal Flow Problems
10.1.1 Shortest Path Problem (SPP)
10.1.2 Traveling Salesman Problem (TSP)
10.1.3 Maximal Flow Problem (MFP)
10.2 Assignment, Optimal Pair Matching, and Transportation Problems
10.2.1 Assignment Problem
10.2.2 Optimal Pair Matching Problem
10.2.3 Transportation Problem
10.3 Integer Linear Programming and Its Particular Cases
10.3.1 Integer Linear Programming
10.3.2 Knapsack Problem
10.3.3 Multiobjective Boolean Programming
10.3.4 Multigrammatical Representation of an ILP Problem Reduced to a Problem of Boolean Programming
10.4 Correspondence of Unitary Multiset Metagrammars and Multiobjective Problems of Discrete Polynomial Programming
Chapter 11: Interconnections Between Multiset Grammars and Models of Computation
11.1 Vector Addition and Substitution Systems
11.1.1 Vector Addition Systems
11.1.2 Vector Substitution Systems
11.2 Production Functions
11.3 Petri Nets
11.4 String-Operating Grammars and ``Set-of-Strings´´ Databases
Chapter 12: Implementation Issues and Future Developments
12.1 Operation of MGF-Centered Smart Industrial STSs
12.2 Creation and Maintenance of Multigrammatical Knowledge Bases
12.3 Future Developments of the Multigrammatical Framework
12.3.1 Applications
12.3.2 Mathematical Background
12.3.3 Implementation
Chapter 13: Conclusion
Acronyms
References
Index
