Short description
Stochastic Algorithms introduces computational methods that use randomness to solve complex optimization and simulation problems. The module covers stochastic methods for continuous optimization as well as Monte Carlo and Markov Chain Monte Carlo methods for simulation and statistical inference. Particular emphasis is placed on the principles underlying these algorithms, their convergence and practical implementation, and the connections between optimization and sampling. Students learn to select, implement, and critically evaluate stochastic algorithms for challenging computational problems.
Module content
Stochastic algorithms for continuous optimization
- Random and multi-start search
- Simulated annealing
- Genetic algorithms for continuous optimization
- Particle swarm optimization
- Stochastic gradient descent
- Exploration–exploitation trade-off, convergence behavior, parameter selection, and comparative evaluation of stochastic optimization methods
Stochastic algorithms for simulation
- Monte Carlo methods, including Monte Carlo integration
- Markov chains: stationary distributions, convergence, and mixing
- Markov Chain Monte Carlo (MCMC) methods
- Metropolis–Hastings algorithm
- Gibbs sampler
- Convergence diagnostics and evaluation of stochastic simulation methods
Connections between optimization and simulation
- Relationship between simulated annealing and Metropolis–Hastings
- Optimization versus sampling
- Applications to continuous parameter estimation, statistical inference, and high-dimensional problems