Mathematical optimization theory and operations research : recent trends : 21st International Conference, MOTOR 2022, Petrozavodsk, Russia, July 2-6, 2022, Revised selected papers

This book constitutes refereed proceedings of the 21st International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2022, held in Petrozavodsk, Russia, in July 2022. The 21 full papers and 3 short papers presented in this volume were carefully reviewed and selected from a total of 88 submissions. The papers in the volume are organised according to the following topical headings: ​invited talks; integer programming and combinatorial optimization; mathematical programming; game theory and optimal control; operational research applications. Preface Organization Contents Invited Talks Three Efficient Methods of Approximate Solution of NP-Hard Discrete Optimization Problems. (Illustrated by Applications to Scheduling Problems) 1 Introduction 2 Uniformization Problems 3 Two Algorithms of Finding Uniform Distributions of One-Component Items Under Distribution Restrictions 3.1 The ``short'' Approximation Algorithm for Solving the Problems "426830A P"026A30C Mk"026A30C Cmax"526930B and "426830A Q"026A30C Mk"026A30C Cmax"526930B 3.2 The Method of Finding Balanced Restrictions on the Set of Feasible Solutions. (``Long Approximation'' for "426830A Q"026A30C Mk"026A30C Cmax"526930B .) 4 Problems of Multidimensional Uniformization and the Method of Compact Vector Summation 5 Conclusion References Recent Advances in Sphere Packing Problems 1 Introduction 2 Formulation of Sphere Packing Problem 3 Multi-objective Optimization Approach to Sphere Packing Problem 4 Game Theory Approach to Sphere Packing Problem 5 Optimal Control Sphere Packing 6 Applications 6.1 Mathematical Model of Flotation Process ch2ENK8 6.2 Profit Analysis ch2ENK6 7 Conclusion References Integer Programming and Combinatorial Optimization Genetic Algorithm for the Variable Sized Vector Bin-Packing Problem with the Limited Number of Bins 1 Introduction 2 Problem Formulation 3 Genetic Algorithm 3.1 Solutions Representation 3.2 Crossover and Mutation Operators 4 Experimental Evaluation 5 Conclusions References An Approximation Algorithm for Graph Clustering with Clusters of Bounded Sizes 1 Introduction 2 Graph Clustering Problems 3 The Graph Clustering Problem with Clusters of Bounded Sizes 4 An Approximation Algorithm for Problem GCs 5 Conclusion References Approximation Non-list Scheduling Algorithms for Multiprocessor System 1 Introduction 2 Approximation Algorithm CP/IIT 3 Computational Experiments 4 Conclusions References Approximate Algorithms for Some Maximin Clustering Problems 1 Introduction 2 Generalized Problem 3 Algorithm for Problem with Fixed Centers 4 Algorithm for Problem with Centers from the Input Set 5 Algorithm for Problem with Geometric Centers 6 Conclusion References Parameter Analysis of Variable Neighborhood Search Applied to Multiprocessor Scheduling with Communication Delays 1 Introduction 2 Motivation and Related Work 3 Description of MSPCD and VNS Implementation 3.1 Problem Description 3.2 Variable Neighborhood Search Algorithm and Its Parameters 4 Empirical Study of the VNS Parameters 4.1 Previous Study 4.2 New Study 4.3 Experimental Methodology 4.4 Results 5 Conclusion References Competitive Location Strategies in the (rp)-Centroid Problem on a Plane with Line Barriers 1 Introduction 2 Definitions, Properties, and Problem Formulation 3 (11)-Centroid Problem with Line Barriers 4 (rXp-1+1)-Centroid Problem with Line Barriers 5 Conclusion References Cascade Merge of Aircraft Flows as Mixed Integer Linear Programming Problem 1 Introduction 2 Problem Formalization 2.1 Input Data 2.2 Optimality Criteria 2.3 Aircraft Order Change Assumption 2.4 Arrival Instant Variables and Constraints 2.5 Taking into Account Aircraft Order and Safety Constraints 2.6 Optimization Problem 3 Numerical Results 3.1 Model Examples 3.2 Statistical Tests 4 Sequential Solution of MILP Problem 4.1 Numerical Results 5 Conclusion References The Gap Between Cooperative and Non-cooperative Solutions for the Public-Private Partnership Model 1 Introduction 2 Problem Formulation 3 Main Properties and Computation Complexity 4 Upper and Lower Bounds 5 Computational Experiments 5.1 Cooperative or Non-cooperative Cases for the High Point Relaxation 5.2 Tabu Search 6 Conclusions References Mathematical Programming Distributed Methods with Absolute Compression and Error Compensation 1 Introduction 1.1 Main Contributions 1.2 Preliminaries 2 Unified Analysis 3 Absolute Compression and Arbitrary Sampling 4 Absolute Compression and Variance Reduction 5 Numerical Experiments A Missing Proofs from Sect.2 A.1 Proof of Theorem 1 B Missing Proofs from Sects.3 and 4 B.1 Proof of Proposition 1 B.2 Proof of Proposition 2 References An Experimental Analysis of Dynamic Double Description Method Variations 1 Introduction 2 Double Description Method 3 Dynamic DDM Modifications 4 Computational Results 5 Conclusion References Conditions for the Fixed Points Existence of Locally Indecomposable Subhomogeneous Maps 1 Introduction and Basic Definitions 2 Indecomposability of a Matrix and Its Generalizations 3 Criteria for the Existence of Fixed Points for Subhomogeneous and Concave Maps 4 Conclusion References One Relaxed Variant of the Proximal Level Method 1 Introduction 2 Problem Settings 3 Minimization method 4 Convergence Research References Procedures for Updating Immersion Sets in the Cutting Method and Estimating the Solution Accuracy 1 Introduction 2 Problem Setting 3 Problem Solving Method 4 Method Discussion 5 Prove Convergence 6 Solution Accuracy Estimations References Game Theory and Optimal Control Synthesis of Motion Control of Rod Heating Sources with Optimization of Places for Measuring States 1 Introduction 2 Formulation of the Problem 3 Determination of Feedback Parameters 4 Numerical Experiments 5 Conclusion References Stability of Persons' Pareto Behavior with Respect to Different Mechanisms in Resource Allocation Game Experiments 1 Introduction 2 Resource Allocation Mechanisms 2.1 Resource Allocation Problem 2.2 Yang-Hajek Mechanism 2.3 ADMM Mechanism 3 Behavior Models 3.1 Rational Behavior 3.2 Pareto Efficiency Behavior 4 Experimental Data Analysis 4.1 Pareto Efficient Behavior Analysis 4.2 Rational Behavior Analysis 5 Persons' Rankings Analysis 6 Conclusion References Network Centralities Based on Non-additive Measures 1 Introduction 2 Network Centralities Based on Non-additive Measures 2.1 Non-additive Measures and the Choquet Integral 2.2 Node Centralities Expressed via the Choquet Integral 3 Applications 3.1 Node Centrality Based on the Relative Edge Density 3.2 Ranking of Nodes in a Chemical Space Network 3.3 Ranking of Nodes in a Transportation Network 4 Conclusion References Optimal Control of Output Variables Within a Given Range Based on a Predictive Model 1 Introduction 2 Problem Formulation 3 Optimization Approach to Control Design 4 Application to Linear Systems with Time Delay 5 Simulation Example 6 Conclusion References An Optimization Approach to the Robust Control Law Design for a Magnetic Levitation System 1 Introduction 2 Problem Formulation 2.1 Mathematical Model of the Magnetic Levitation System 2.2 Structure of the Dynamic Regulator 2.3 Problem Formulation of the Robust Control Law Synthesis 3 An Optimization Approach to the Robust Control Law Synthesis 3.1 Robust Stability Analysis of the Control System 3.2 Synthesis of Robust Control Law 4 Simulation Examples 5 Conclusion References Optimal Strategies of Consumers with Energy Storages in Electricity Market 1 Introduction 2 Consumer Model and Optimal Consumption Strategy 3 The Problem for Consumer with Energy Storage 4 Model with Random Factors 5 Optimal Consumer Strategy When the Energy Resale is Impossible 6 Conclusion References Operational Research Applications Variational Autoencoders for Precoding Matrices with High Spectral Efficiency 1 Introduction 2 Variational Autoencoder 3 Optimization Function 4 Problem Setup and Research Questions 5 Approach 6 Experimental Results 6.1 Generating High SE Precoding Matrices Wi for the Fixed H 6.2 Generating Matrices Wi,j Using Hi as Condition for CVAE 6.3 Computational Complexity 7 Conclusion References Spectrum Allocation in Optical Networks: DSatur Coloring and Upper Bounds 1 Introduction 2 Background 2.1 Spectrum Allocation 2.2 Mathematical Programming 3 Main Algorithm 3.1 DSatur Coloring 3.2 Bi-Loop 4 Upper Bounds 4.1 Clique-Based Upper-Bound 5 Experiments 5.1 Synthetic Instances 5.2 Lower Bounds 5.3 Upper Bounds 5.4 Optimality Gap 5.5 Real-world Telecommunication Networks 6 Conclusions References Comparison of Reinforcement Learning Based Control Algorithms for One Autonomous Driving Problem 1 Introduction 2 Reinforcement Learning Algorithms 3 Simulation Environment 4 State-Action-Reward Model 5 Simulation Results 6 Conclusion References Author Index