Course objectives
Understand fundamental ideas of optimization methods. Mathematically formulate given optimization problems in engineering practice, recognize type and application of appropriate methods.
Expected course learning outcomes
Analyze described optimal control problems. Set appropriate mathematical formulation of the problem. Classify optimization problems. Solve optimization problems with the aid of software. Evaluate results of applied methods. Correctly explain fundamental ideas and properties of some optimization methods. Develop basic ideas for optimization enhancements such as upgrades or simplification of optimization problem or underlying model, enhancements of optimization method, sensitivity analysis, metamodel use, and improvement of optimization process computational effectiveness.
Course content
Transport problem, work schedule problem, and similar problems. Linear programming. Basics of the simplex method. Application of LP software. Examples of nonlinear optimal control problems. Mathematical analysis tools. Numerical methods. Golden section search method. Powel methods. Ameba. CGD method. Application of software. Traveling salesman problem and similar problems. Genetic algorithms. GA operators: selection, crossover, and mutation. Application of GA software. Stochastic, heuristic and metaheuristic methods. Swarm intelligence methods: particle swarm optimization, ant colony optimization and related methods. Parametrization, shape optimization and topology optimization. Solving and presenting the results of complex engineering and multidisciplinary project tasks.