Algorytmy stochastyczne w optymalizacji dyskretnej przy zaburzonych wartościach funkcji

The paper deals with stochastic methods for searching approximately global minimum of function defined on discrete set. A measure of quality of solution is defined to compare different algorithms. Simple Monte Carlo method is analysed as main algorithm for which formulas dealing with the measure of quality are derived(two cases: exact values and noisy values of function). This Monte Carlo method is used as a base in simulation experiments for comparing other stochastic algorithms. The second part of the paper analyses asymptotic properties of the generalised simulated annealing algorithms. Theory of Markov chains is used in modelling this class of algorithms. Theorems about convergence of the records of algorithms to set of optima with probability one are presented in the case of function having random noisy values. The paper also reviews known results in the field of simulated annealing type algorithms for function with randomly perturbated values.