COURSES

Goals

The course objectives are to (a) to give essential knowledge on stochastic optimization methods, (b) present the types of stochastic optimization algorithms, and their advantages and drawbacks, (c) present the methodology of evaluating the results of stochastic optimization algorithms and their adaptation for solving specific types of problems, (d) show their practical potential. The students who will successfully complete this course will master the basics of stochastic optimization and will be capable of applying stochastic algorithms in solving demanding optimization problems and following further development in this field.

Curriculum

Introduction: Optimization, optimization problems, duality of minimization and maximization. Types of optimization: exact and stochastic, analytical and empirical, continuous and discrete, static and dynamic, single-objective and multi-objective. Optimization based on numerical models. Examples of optimization problems and sources of their difficulty. Stochastic optimization: Stochasticity of data and optimization procedures, motivation for stochastic optimization, advantages and disadvantages of stochastic optimization methods. Simple stochastic methods: random search and local optimization. Stochastic optimization algorithms: Simulated annealing. Evolutionary algorithms: genetic algorithms, evolution strategies, evolutionary programming, genetic programming and differential evolution. Tabu search, particle swarm optimization, ant colony optimization. Characteristics of the algorithms and their comparison, examples of application. Evaluation of results: Statistical analysis of stochastic algorithm results, performance measures and presentation of results. Differences between design and routine problems, and between synthetic test problems and real-world problems. Applied aspects: Setting parameter values in stochastic optimization algorithms, hybridization of algorithms, multi-objective optimization and optimization with subjective evaluation of solutions. Typical domains of application and practical case studies from design and modeling, empirical data analysis, scheduling and resource management.