Optimization Methods Based On Mutivalued Random Variables

In stochastic decision systems, taking non-additive measure as research tool, this thesis first establishes a framework of multivalued random theory, including the definitions of multivalued random variables (vectors), Belief, Plausibility and Confidence measures of multivalued random event, and three kinds of expected value operators of multivalued random variables. Then a class of multivalued random chance-constrained programming model is presented, based on belief measure, and a class of multivalued random expected-value programming model is built by using expected value operator. Finally we desire a hybrid algorithm, which integrates stochastic simulation, neural network and genetic algorithm, to solve general multivalued stochastic programming, and numerical examples are provided to show the feasibility and effectivity of the algorithm.The contributions of the thesis: Establish a framework of multivalued random theory; Present two classes of multivalued stochastic programming models, i.e., multivalued random chance-constrained programming model and set-valued random expected-value programming model; Desire a hybrid algorithm to solve general multivalued stochastic programming.