After successful completion of the course, students are able to...
After successful completion of the course, students are able to name, understand, reproduce, and apply methods of optimization in IoT networks. This course will help students in the decision of optimization tasks in IoT networks and telecommunication networks. The theory of optimization and practical cases described in this course will help to choose the optimal variant from existing alternatives (technologies, devices, software and systems) based on criteria of estimation and selection. Students will be able to choose the optimal path for passing information packets in the IoT network (smart transport, smart factory, smart city, etc.), choose the best option for organizing such a network according to various evaluation criteria, calculate the optimal number of spare system elements, applying the tasks of optimal resource allocation to various components of the IoT system and to data centers with which information is exchanged, and when processing Big Data and Edge computing.
Topic 1. General characteristics of optimization methods.
Formulation of the optimization problem. Features of the optimization approach from the point of view of decision-making issues. An example for IoT networks illustrating the transition from a verbal formulation of the optimization problem to its formal formulation. Classification and general characteristics of optimization problems in IoT systems.
Topic 2. Non-linear optimization.
Classification and general characteristics of methods for solving nonlinear optimization problems. Formulation of the quadratic programming problem. Unconditional nonlinear optimization: the method of fastest descent. Conditional nonlinear optimization in IoT networks: the method of uncertain Lagrange multipliers and others.
Topic 3. Linear optimization.
Basic concepts in the field of linear programming: examples of linear programming problems (PLP). The main ZLP and the conditions for its admissible solution; ZLP with constraints-inequalities and the transition from it to the canonical form of ZLP. Geometric interpretation of ZLP.
Linear optimization. The simplex method for solving the problem of linear programming in IoT networks: the general idea of the simplex method and its connection with the geometrical interpretation of the FP, the standard form of representation of the general FP, the algorithm for solving the FP using the simplex method.
Linear optimization. The solution of the problem of linear programming based on the tabular algorithm of the simplex method: the generalized algorithm of the solution of the ZLP with the help of simplex tables, the algorithm of finding an admissible solution of the ZLP, the algorithm of finding the optimal solution of the ZLP. Optimizing Gradient Methods for IoT Applications.
Topic 4. Discrete optimization.
General formulation of the discrete optimization problem for IoT networks. Formulation of the most common discrete optimization problems. Assignment problem, knapsack problem, set coverage problem and features of methods and algorithms for solving them.
Topic 5. Multi-criteria optimization in IoT systems.
Methods of solving multi-criteria optimization problems in IoT networks using additive, multiplicative, maximin and minimax convolutions and the method of expert evaluations.
Topic 6. Dynamic programming in IoT systems.
The general idea and scope of the dynamic programming method. Statement of the problem of dynamic programming. Dynamic Modeling and Optimization for Intelligent IoT Networks. Solving combinatorial optimization problems using dynamic programming. Determination of critical paths of the IoT network by solving Steiner's problem, problems of finding the shortest path according to the Dijkstra, Bellman-Ford algorithm, problems of optimal allocation of resources in IoT network.
Dynamic programming. The task of a traveling salesman in IoT networks. Methods for solving this problem: the method of complete lexical search, greedy algorithms (the nearest neighbor method), the method of including the nearest city, the method of the cheapest inclusion, the method of the minimum tree skeleton.
Dynamic programming. Modifications of more effective methods: method of branches and boundaries, method of genetic algorithms, ant colony algorithm. The sequence of the solution of the integer linear programming problem using the Gomori cut-off method.
Topic 7. Solving optimization problems in IoT networks using genetic algorithms.
The general idea and areas of application of genetic algorithms (GA). Classic GA. An example of using a simple GA to solve optimization problems. Characterization of GA capabilities for solving optimization problems for IoT networks.
To choose the optimal technology (devices, software, etc.) for IoT network organization, using criterias of selection and methods of optimization
